One dimensional bosons: From condensed matter systems to ultracold gases

The physics of one-dimensional interacting bosonic systems is reviewed. Beginning with results from exactly solvable models and computational approaches, the concept of bosonic Tomonaga-Luttinger liquids relevant for one-dimensional Bose fluids is introduced, and compared with Bose-Einstein condensates existing in dimensions higher than one. The effects of various perturbations on the Tomonaga-Luttinger liquid state are discussed as well as extensions to multicomponent and out of equilibrium situations. Finally, the experimental systems that can be described in terms of models of interacting bosons in one dimension are discussed.

[1]  E. Lieb.  Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum , 1963 .

[2]  A. Minguzzi,et al.  Exact Coherent States of a Harmonically Confined Tonks-Girardeau Gas , 2005, cond-mat/0504024.

[3]  M. Lukin,et al.  Controlling spin exchange interactions of ultracold atoms in optical lattices. , 2002, Physical review letters.

[4]  E. Lieb,et al.  Exact Solution of a Many-Fermion System and Its Associated Boson Field , 1965 .

[5]  H. Bethe.  On the theory of metals. 1. Eigenvalues and eigenfunctions for the linear atomic chain , 1931 .

[6]  M. Girardeau,et al.  Wave functions of the super-Tonks-Girardeau gas and the trapped one-dimensional hard-sphere Bose gas , 2009, 0912.1633.

[7]  Low-energy Effective Theory for One-dimensional Lattice Bosons near Integer Filling , 2007, cond-mat/0703015.

[8]  Fisher,et al.  Random antiferromagnetic quantum spin chains. , 1994, Physical review. B, Condensed matter.

[9]  Marcos Rigol,et al.  Breakdown of thermalization in finite one-dimensional systems. , 2009, Physical review letters.

[10]  Eytan Barouch,et al.  Statistical Mechanics of the X Y Model. II. Spin-Correlation Functions , 1971 .

[11]  D. Weiss,et al.  A quantum Newton's cradle , 2006, Nature.

[12]  J. Cardy.  Scaling and Renormalization in Statistical Physics , 1996 .

[13]  Kawashima,et al.  Loop algorithms for quantum simulations of fermion models on lattices. , 1994, Physical review. B, Condensed matter.

[14]  Universality of the one-dimensional Bose gas with delta interaction , 2004, cond-mat/0405155.

[15]  T. D. Lee,et al.  Many-Body Problem in Quantum Mechanics and Quantum Statistical Mechanics , 1957 .

[16]  A. Kamenev,et al.  Dynamics of excitations in a one-dimensional bose liquid. , 2007, Physical review letters.

[17]  L. Pollet,et al.  Ultracold atoms in one-dimensional optical lattices approaching the Tonks-Girardeau regime. , 2004, Physical review letters.

[18]  Edmond Orignac,et al.  Statics and Dynamics of Weakly Coupled Antiferromagnetic Spin-1/2 Ladders in a Magnetic Field , 2010, 1009.0840.

[19]  A. Polkovnikov.  Microscopic diagonal entropy and its connection to basic thermodynamic relations , 2008, 0806.2862.

[20]  M. Cazalilla.  Effect of suddenly turning on interactions in the Luttinger model. , 2006, Physical review letters.

[21]  A. Talapov,et al.  Ground State, Spectrum, and Phase Diagram of Two-Dimensional Incommensurate Crystals , 1979 .

[22]  S. Sondhi,et al.  Devil's staircases and supersolids in a one-dimensional dipolar Bose gas , 2009, 0901.4366.

[23]  Schulz.  Correlation exponents and the metal-insulator transition in the one-dimensional Hubbard model. , 1990, Physical review letters.

[24]  H. Stoof,et al.  Phase fluctuations in atomic Bose gases. , 2001, Physical review letters.

[25]  Y. Kato,et al.  Direct mapping of the finite temperature phase diagram of strongly correlated quantum models. , 2009, Physical review letters.

[26]  Edmond Orignac,et al.  Luttinger hydrodynamics of confined one-dimensional Bose gases with dipolar interactions , 2008 .

[27]  C. Wieman,et al.  Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor , 1995, Science.

[28]  C. Tracy,et al.  One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature , 1979 .

[29]  Electron transport in a disordered Luttinger liquid , 2006, cond-mat/0608590.

[30]  Batrouni,et al.  World-line quantum Monte Carlo algorithm for a one-dimensional Bose model. , 1992, Physical review. B, Condensed matter.

[31]  A. A. Ovchinnikov.  Fisher–Hartwig conjecture and the correlators in the inpenetrable Bose gas , 2009 .

[32]  Weakly disordered spin ladders , 1997, cond-mat/9709297.

[33]  Svetlana Ya. Jitomirskaya.  Metal-insulator transition for the almost Mathieu operator , 1999 .

[34]  Toshiya Kinoshita,et al.  Observation of a One-Dimensional Tonks-Girardeau Gas , 2004, Science.

[35]  Quantum phase transitions for bosons in one dimension , 1997, cond-mat/9705261.

[36]  E. Lieb,et al.  EXACT ANALYSIS OF AN INTERACTING BOSE GAS. I. THE GENERAL SOLUTION AND THE GROUND STATE , 1963 .

[37]  Chen Ning Yang,et al.  Concept of Off-Diagonal Long-Range Order and the Quantum Phases of Liquid He and of Superconductors , 1962 .

[38]  Fractional statistics in one dimension: view from an exactly solvable model , 1994, cond-mat/9410101.

[39]  J. Danzl,et al.  Realization of an Excited, Strongly Correlated Quantum Gas Phase , 2009, Science.

[40]  A. Kamenev,et al.  Replica Treatment of the Calogero-Sutherland Model , 2001, cond-mat/0102405.

[41]  Quantum Monte Carlo study of quasi-one-dimensional Bose gases , 2003, cond-mat/0310749.

[42]  A. Lenard.  One‐Dimensional Impenetrable Bosons in Thermal Equilibrium , 1966 .

[43]  U. Schollwock,et al.  Dephasing and the steady state in quantum many-particle systems. , 2007, Physical review letters.

[44]  Ultracold bosonic atoms in two-colour superlattices , 2002, cond-mat/0205412.

[45]  J. Brand,et al.  Dynamic and static density-density correlations in the one-dimensional Bose gas: Exact results and approximations , 2008, 0812.3264.

[46]  T. Nattermann,et al.  Weakly interacting Bose gas in a random environment , 2008, 0811.1269.

[47]  Roderich Tumulka,et al.  Canonical typicality. , 2006, Physical review letters.

[48]  Correlation amplitude for the XXZ spin chain in the disordered regime , 1998, cond-mat/9809254.

[49]  C. Yang,et al.  Thermodynamics of a One‐Dimensional System of Bosons with Repulsive Delta‐Function Interaction , 1969 .

[50]  V Dunjko,et al.  Bosons in cigar-shaped traps: Thomas-Fermi regime, Tonks-Girardeau regime, and in between. , 2001, Physical review letters.

[51]  I. Danshita,et al.  Heavily damped motion of one-dimensional Bose gases in an optical lattice. , 2008, Physical review letters.

[52]  G Ferrari,et al.  Quasipure Bose-Einstein condensate immersed in a Fermi sea. , 2001, Physical review letters.

[53]  I. McCulloch,et al.  Spin-charge separation in two-component Bose gases , 2007, 0706.0709.

[54]  T. V. Ramakrishnan,et al.  Disordered electronic systems , 1985 .

[55]  N. D. Mermin,et al.  Crystalline Order in Two Dimensions , 1968 .

[56]  Its,et al.  Temperature correlations of quantum spins. , 1992, Physical review letters.

[57]  Affleck,et al.  Magnetic impurities in half-integer-spin Heisenberg antiferromagnetic chains. , 1992, Physical review. B, Condensed matter.

[58]  T. Schultz.  Note on the One‐Dimensional Gas of Impenetrable Point‐Particle Bosons , 1963 .

[59]  T. Giamarchi,et al.  Variable-range hopping and quantum creep in one dimension. , 2003, Physical review letters.

[60]  R. Jastrow.  Many-Body Problem with Strong Forces , 1955 .

[61]  R. Graham,et al.  Ultracold bosons in lattices with binary disorder , 2008 .

[62]  Strongly correlated fermions after a quantum quench. , 2006, Physical review letters.

[63]  Trap-size scaling in confined-particle systems at quantum transitions , 2009, 0906.2640.

[64]  White,et al.  Real-space quantum renormalization groups. , 1992, Physical review letters.

[65]  E. Sezgin,et al.  Aspects of κ symmetry , 1993 .

[66]  M. Rigol,et al.  Fermionization in an Expanding 1D Gas of Hard-Core Bosons , 2004, cond-mat/0410683.

[67]  Maxim Olshanii.  Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons , 1998 .

[68]  L. Glazman,et al.  Dynamic response of one-dimensional bosons in a trap , 2009, 0907.0483.

[69]  R. Glauber.  The Quantum Theory of Optical Coherence , 1963 .

[70]  O. Penrose,et al.  Bose-Einstein Condensation and Liquid Helium , 1956 .

[71]  A. Gogolin.  Electron localization and hopping conductivity in one-dimensional disordered systems , 1982 .

[72]  Holger Frahm,et al.  Correlation functions of one-dimensional Bose-Fermi mixtures , 2005 .

[73]  Polarization of interacting bosons with spin. , 2002, Physical review letters.

[74]  X. Guan,et al.  Magnetic ordering and quantum statistical effects in strongly repulsive Fermi-Fermi and Bose-Fermi mixtures , 2008, 0806.2499.

[75]  Phase diagram of a bosonic ladder with two coupled chains , 2008, 0802.0396.

[76]  CORRELATION AMPLITUDE FOR THE S=1/2 XXZ SPIN CHAIN IN THE CRITICAL REGION:NUMERICAL RENORMALIZATION-GROUP STUDY OF AN OPEN CHAIN , 1998 .

[77]  A. Sandvik,et al.  Quantum Monte Carlo with directed loops. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[78]  M. Fisher.  The theory of equilibrium critical phenomena , 1967 .

[79]  T. D. Kuehner,et al.  Phases of the one-dimensional Bose-Hubbard model , 1997, cond-mat/9712307.

[80]  Srednicki.  Chaos and quantum thermalization. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[81]  F Minardi,et al.  Expansion of a coherent array of Bose-Einstein condensates. , 2001, Physical review letters.

[82]  Short-distance correlation properties of the Lieb-Liniger system and momentum distributions of trapped one-dimensional atomic gases. , 2002, Physical review letters.

[83]  R. Scalettar,et al.  Mott domains of bosons confined on optical lattices. , 2002, Physical review letters.

[84]  Jr.,et al.  Momentum distribution for a one-dimensional trapped gas of hard-core bosons , 2002, 1303.5637.

[85]  U. Schollwock,et al.  Spatial correlations of trapped one-dimensional bosons in an optical lattice , 2003, cond-mat/0310388.

[86]  Kerson Huang,et al.  Quantum-Mechanical Many-Body Problem with Hard-Sphere Interaction , 1957 .

[87]  Marcos Rigol,et al.  Relaxation in a completely integrable many-body quantum system: an ab initio study of the dynamics of the highly excited states of 1D lattice hard-core bosons. , 2007, Physical review letters.

[88]  L. Mandel,et al.  Coherence Properties of Optical Fields , 1965 .

[89]  Form factors of soliton-creating operators in the sine-Gordon model , 2001, hep-th/0102079.

[90]  M. Jimbo,et al.  Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent , 1980 .

[91]  Dynamics and thermodynamics of the Bose-Hubbard model , 1998, cond-mat/9807033.

[92]  T. Giamarchi,et al.  Dynamical properties of the one-dimensional spin-1/2 Bose-Hubbard model near a Mott-insulator to ferromagnetic-liquid transition. , 2008, Physical review letters.

[93]  BRAGG SPECTROSCOPY OF A BOSE-EINSTEIN CONDENSATE , 1999, cond-mat/9901109.

[94]  K. B. Davis,et al.  Bose-Einstein Condensation in a Gas of Sodium Atoms , 1995, EQEC'96. 1996 European Quantum Electronic Conference.

[95]  Marcos Rigol,et al.  Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[96]  Fye Rm.  New results on Trotter-like approximations. , 1986 .

[97]  P. Leboeuf,et al.  Localization by bichromatic potentials versus Anderson localization , 2009, 0905.2331.

[98]  G. Roux.  Finite size effects in global quantum quenches: examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard model , 2009, 0909.4620.

[99]  H. R. Krishnamurthy,et al.  Canonical trajectories and critical coupling of the Bose-Hubbard Hamiltonian in a harmonic trap , 2008, 0803.2900.

[100]  National Tsing Hua University,et al.  Scaling Analysis of Magnetic-Field-Tuned Phase Transitions in One-Dimensional Josephson Junction Arrays , 2001, cond-mat/0103245.

[101]  P. Reimann,et al.  Foundation of statistical mechanics under experimentally realistic conditions. , 2008, Physical review letters.

[102]  B. Halperin,et al.  Finite-size effects in tunneling between parallel quantum wires. , 2002, Physical review letters.

[104]  E. L. Ince.  Ordinary differential equations , 1927 .

[105]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[106]  A. Trombettoni,et al.  Expectation values in the Lieb-Liniger Bose gas. , 2009, Physical review letters.

[107]  Painlevé Transcendent Evaluations of Finite System Density Matrices for 1d Impenetrable Bosons , 2002, math-ph/0207005.

[108]  G. Santoro,et al.  Effective thermal dynamics following a quantum quench in a spin chain. , 2008, Physical review letters.

[109]  M. Troyer,et al.  Phase diagram of Bose-Fermi mixtures in one-dimensional optical lattices. , 2005, Physical Review Letters.

[110]  Full quantum distribution of contrast in interference experiments between interacting one-dimensional Bose liquids , 2006, cond-mat/0602475.

[111]  T. M. Rice,et al.  Surprises on the Way from One- to Two-Dimensional Quantum Magnets: The Ladder Materials , 1995, Science.

[112]  T. Esslinger,et al.  Transition from a strongly interacting 1d superfluid to a Mott insulator. , 2003, Physical review letters.

[113]  Expansion of a quantum gas released from an optical lattice. , 2008, Physical review letters.

[114]  P. Calabrese,et al.  Dynamical density-density correlations in the one-dimensional Bose gas , 2006, cond-mat/0603654.

[115]  A. Leggett,et al.  Bose-Einstein condensation in the alkali gases: Some fundamental concepts , 2001 .

[116]  Fragmentation of Bose-Einstein Condensates , 2006, cond-mat/0605711.

[117]  I. McCulloch,et al.  Excitations in two-component Bose gases , 2007, 0712.1448.

[118]  M. Greiner,et al.  Probing the Superfluid–to–Mott Insulator Transition at the Single-Atom Level , 2010, Science.

[119]  A. Efros,et al.  Electron-Electron Interactions in Disordered Systems , 1986, March 1.

[120]  Giuseppe Mussardo,et al.  Quantum quenches in integrable field theories , 2009, 0911.3345.

[121]  A. Bijl,et al.  The lowest wave function of the symmetrical many particles system , 1940 .

[122]  Quantum coherence of Hard-Core-Bosons and Fermions : Extended, Glassy and Mott Phases , 2006, cond-mat/0601307.

[123]  C. Zimmermann,et al.  Perspectives of ultracold atoms trapped in magnetic micro potentials , 2004, cond-mat/0501528.

[124]  K. West,et al.  Tunneling Spectroscopy of the Elementary Excitations in a One-Dimensional Wire , 2002, Science.

[125]  Evidence for the super Tonks–Girardeau gas , 2005, cond-mat/0508009.

[126]  Y. Castin,et al.  Matter-wave localization in disordered cold atom lattices. , 2004, Physical review letters.

[127]  T. Giamarchi,et al.  Bose–Einstein condensation in magnetic insulators , 2007, 0712.2250.

[128]  M. Gaudin.  Un systeme a une dimension de fermions en interaction , 1967 .

[129]  The 1D interacting Bose gas in a hard wall box , 2005, cond-mat/0505550.

[130]  P. Drummond,et al.  Nonlocal pair correlations in the one-dimensional Bose gas at finite temperature , 2008, 0812.4447.

[131]  D. Thouless,et al.  Ordering, metastability and phase transitions in two-dimensional systems , 1973 .

[132]  S. Will,et al.  Time-resolved observation of coherent multi-body interactions in quantum phase revivals , 2010, Nature.

[133]  Chen Ning Yang,et al.  One-Dimensional Chain of Anisotropic Spin-Spin Interactions. II. Properties of the Ground-State Energy Per Lattice Site for an Infinite System , 1966 .

[134]  D. Huse,et al.  Many-body localization phase transition , 2010, 1010.1992.

[135]  T. Giamarchi,et al.  Spin dynamics in a one-dimensional ferromagnetic bose gas. , 2007, Physical review letters.

[136]  T. Niemeijer.  Some exact calculations on a chain of spins {1}/{2} II , 1967 .

[137]  Shastry,et al.  Persistent currents in a one-dimensional ring for a disordered Hubbard model. , 1995, Physical review. B, Condensed matter.

[138]  Giamarchi,et al.  Variational theory of elastic manifolds with correlated disorder and localization of interacting quantum particles. , 1996, Physical review. B, Condensed matter.

[139]  V. Korepin,et al.  Quantum Inverse Scattering Method and Correlation Functions , 1993, cond-mat/9301031.

[140]  A. Tsvelik,et al.  On the spin-liquid phase of one-dimensional spin-1 bosons , 2008, 0811.0844.

[141]  Nevill Mott,et al.  The theory of impurity conduction , 1961 .

[142]  B. McCoy,et al.  Spin Correlation Functions of theX−YModel , 1968 .

[143]  M. Olshanii,et al.  The Memory of Initial Conditions in Isolated Quantum Systems , 2009 .

[144]  J. B. McGuire,et al.  Study of Exactly Soluble One-Dimensional N-Body Problems , 1964 .

[145]  H. Tasaki.  From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example , 1997, cond-mat/9707253.

[146]  F. Haldane,et al.  Effective Harmonic-Fluid Approach to Low-Energy Properties of One-Dimensional Quantum Fluids , 1981 .

[147]  Muttalib Ka,et al.  Soluble two-band model of fermions. , 1986 .

[148]  A. Sandvik.  A generalization of Handscomb's quantum Monte Carlo scheme-application to the 1D Hubbard model , 1992 .

[149]  Competition between Vortex Unbinding and Tunneling in an Optical Lattice , 2007, cond-mat/0701761.

[150]  D. Haviland,et al.  Superconducting and Insulating Behavior in One-Dimensional Josephson Junction Arrays , 2000, cond-mat/0001143.

[151]  G. Refael,et al.  Superfluid-insulator transition of disordered bosons in one dimension , 2009, 0909.4096.

[152]  T. Garel,et al.  Many-body localization transition in a lattice model of interacting fermions: Statistics of renormalized hoppings in configuration space , 2010, 1001.2984.

[153]  V. Popov.  Functional integrals and collective excitations , 1987 .

[154]  P D Drummond,et al.  Canonical Bose gas simulations with stochastic gauges. , 2004, Physical review letters.

[155]  D. Rokhsar,et al.  Gutzwiller projection for bosons. , 1991, Physical review. B, Condensed matter.

[156]  Density Matrix Renormalization Group Study of the S= 1/2 Antiferromagnetic Heisenberg Chains with Quasiperiodic Exchange Modulation , 1999, cond-mat/9911424.

[157]  P. Hohenberg.  Existence of Long-Range Order in One and Two Dimensions , 1967 .

[158]  One-dimensional gas of bosons with Feshbach-resonant interactions (20 pages) , 2005, cond-mat/0511411.

[159]  Interacting Bose gases in quasi-one-dimensional optical lattices , 2006, cond-mat/0605419.

[160]  Yoseph Imry,et al.  Random-Field Instability of the Ordered State of Continuous Symmetry , 1975 .

[161]  H. Mutka,et al.  Bose–Einstein condensation of the triplet states in the magnetic insulator TlCuCl3 , 2003, Nature.

[162]  T. Giamarchi,et al.  Thermodynamics of the spin Luttinger liquid in a model ladder material. , 2008, Physical review letters.

[163]  T. Wu,et al.  Theory of Toeplitz Determinants and the Spin Correlations of the Two-Dimensional Ising Model. III , 1967 .

[164]  F. Lesage,et al.  Solving 1D plasmas and 2D boundary problems using Jack polynomials and functional relations , 1994, hep-th/9409176.

[165]  M. Cazalilla,et al.  Quantum quench dynamics of the sine-Gordon model in some solvable limits , 2010, 1003.5167.

[166]  M. Lewenstein,et al.  Observation of phase fluctuations in elongated Bose-Einstein condensates. , 2001, Physical review letters.

[167]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[168]  J. Boronat,et al.  Ground-state properties of a one-dimensional system of hard rods. , 2007, Physical review letters.

[169]  S. White,et al.  The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction , 1999, cond-mat/9906019.

[170]  M. Rigol.  Quantum quenches and thermalization in one-dimensional fermionic systems , 2009, 0908.3188.

[171]  A. Vishwanath,et al.  Noise Correlations in low-dimensional systems of ultracold atoms , 2008, 0810.1555.

[172]  Quantum phase transitions and vortex dynamics in superconducting networks , 2000, cond-mat/0011152.

[173]  B. Svistunov,et al.  Mott-insulator-superfluid-liquid transition in a one-dimensional bosonic Hubbard model: Quantum Monte Carlo method , 1996 .

[174]  A. Abrikosov,et al.  Conductivity of quasi-one-dimensional metal systems , 1978 .

[175]  Eytan Barouch,et al.  Statistical Mechanics of the XY Model. III , 1970 .

[176]  M. Kollar,et al.  Relaxation of a one-dimensional Mott insulator after an interaction quench , 2008, 0804.2254.

[177]  Junpeng Cao,et al.  Paired state in an integrable spin-1 boson model , 2006, cond-mat/0610435.

[178]  Scott,et al.  Crystal-structure, magnetic-susceptibility, and EPR studies of bis(piperidinium)tetrabromocuprate(II): A novel monomer system showing spin diffusion. , 1990, Physical review. B, Condensed matter.

[179]  W. Ketterle,et al.  Bose-Einstein condensation of a finite number of particles trapped in one or three dimensions. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[180]  A. Arkhipov,et al.  Ground-state properties of a one-dimensional system of dipoles , 2005 .

[181]  Phase diagram of bosonic atoms in two-color superlattices , 2003, cond-mat/0304063.

[182]  Walter Kohn,et al.  THEORY OF THE INSULATING STATE , 1964 .

[183]  Shu Chen,et al.  Ground-state properties of hard-core anyons in one-dimensional optical lattices , 2009, 0901.1224.

[184]  J. Dalibard,et al.  Many-Body Physics with Ultracold Gases , 2007, 0704.3011.

[185]  Thierry Giamarchi,et al.  Quantum physics in one dimension , 2004 .

[186]  Ultracold Bose Gases in 1D Disorder: From Lifshits Glass to Bose-Einstein Condensate , 2006, cond-mat/0610389.

[187]  S. Inagaki,et al.  Helium-4 Bose fluids formed in one-dimensional 18 A diameter pores. , 2001, Physical review letters.

[188]  M. Fisher,et al.  Helicity Modulus, Superfluidity, and Scaling in Isotropic Systems , 1973 .

[189]  Stefan Wessel,et al.  Generalized directed loop method for quantum Monte Carlo simulations. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[190]  Low energy effective Hamiltonian for the XXZ spin chain , 1997, cond-mat/9712314.

[191]  G. Shlyapnikov,et al.  Spin waves in a one-dimensional spinor bose gas. , 2005, Physical review letters.

[192]  A. Polkovnikov.  Microscopic expression for heat in the adiabatic basis. , 2008, Physical review letters.

[193]  Markus Greiner,et al.  A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice , 2009, Nature.

[194]  White,et al.  Sign problem in the numerical simulation of many-electron systems. , 1990, Physical review. B, Condensed matter.

[195]  Chuang Liu,et al.  Scaling and Renormalization , 2002 .

[196]  V. Natarajan,et al.  Observation of persistent flow of a Bose-Einstein condensate in a toroidal trap. , 2007, Physical review letters.

[197]  Robert Jördens,et al.  Observation of elastic doublon decay in the Fermi-Hubbard model. , 2009, Physical review letters.

[198]  A. Trombettoni,et al.  Local Correlations in the Super Tonks-Girardeau Gas , 2010, 1008.4383.

[199]  M. Kohmoto,et al.  ELECTRONIC SPECTRAL AND WAVEFUNCTION PROPERTIES OF ONE-DIMENSIONAL QUASIPERIODIC SYSTEMS: A SCALING APPROACH , 1992 .

[200]  N. Prokof'ev,et al.  Monte Carlo study of the two-dimensional Bose-Hubbard model , 2007, 0710.2703.

[201]  S. Giorgini,et al.  Beyond the Tonks-Girardeau gas: strongly correlated regime in quasi-one-dimensional Bose gases. , 2004, Physical review letters.

[202]  F. Haldane.  “Solidification” in a soluble model of bosons on a one-dimensional lattice: The “Boson-Hubbard chain” , 1980 .

[203]  V. J. Emery,et al.  Backward Scattering in the One-Dimensional Electron Gas , 1974 .

[204]  David M. Ceperley,et al.  Fixed-node quantum Monte Carlo for molecules , 1982 .

[205]  Takemi Yamada,et al.  Spin Ordering in a Spin-Pair System , 1970 .

[206]  Guillaume Roux,et al.  Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined , 2008, 0810.3720.

[207]  T. Esslinger,et al.  Exciting collective oscillations in a trapped 1D gas. , 2003, Physical review letters.

[208]  H. Bethe,et al.  Zur Theorie der Metalle , 1931 .

[209]  Edmond Orignac,et al.  Field{Controlled Magnetic Order in the Quantum Spin{Ladder System (Hpip)2CuBr4 , 2008, 0809.0440.

[210]  Salvatore R. Manmana,et al.  Diagonalization‐ and Numerical Renormalization‐Group‐Based Methods for Interacting Quantum Systems , 2005 .

[211]  U. Schollwoeck.  The density-matrix renormalization group , 2004, cond-mat/0409292.

[212]  Kashurnikov,et al.  Exact diagonalization plus renormalization-group theory: Accurate method for a one-dimensional superfluid-insulator-transition study. , 1996, Physical review. B, Condensed matter.

[213]  Y. Tserkovnyak,et al.  Spin-charge separation in a strongly correlated spin-polarized chain , 2007, 0708.4012.

[214]  M. Inguscio,et al.  Exploring correlated 1D bose gases from the superfluid to the mott-insulator state by inelastic light scattering. , 2008, Physical review letters.

[215]  Deutsch,et al.  Quantum statistical mechanics in a closed system. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[216]  F. Dalfovo,et al.  Theory of Bose-Einstein condensation in trapped gases , 1998, cond-mat/9806038.

[217]  A. M. Finkel'stein.  Weak localization and coulomb interaction in disordered systems , 1984 .

[218]  Eugene Demler,et al.  Exactly solvable case of a one-dimensional Bose–Fermi mixture , 2005, cond-mat/0505632.

[219]  E. Burovski,et al.  Multiparticle composites in density-imbalanced quantum fluids. , 2009, Physical review letters.

[220]  H. Primakoff,et al.  Field dependence of the intrinsic domain magnetization of a ferromagnet , 1940 .

[221]  Low-dimensional trapped gases , 2004, cond-mat/0409230.

[222]  Sachdev.  Quantum criticality: competing ground states in low dimensions , 2000, Science.

[223]  Matthew J. Davis,et al.  Spatial nonlocal pair correlations in a repulsive 1D Bose gas. , 2007, Physical review letters.

[224]  G. Shlyapnikov,et al.  Off-diagonal correlations of lattice impenetrable bosons in one dimension , 2006, cond-mat/0606319.

[225]  G. Blatter,et al.  Dynamical properties of ultracold bosons in an optical lattice , 2006, cond-mat/0610773.

[226]  H. Buljan,et al.  Fermi-bose transformation for the time-dependent Lieb-Liniger gas. , 2007, Physical review letters.

[227]  Massimo Inguscio,et al.  Anderson localization of a non-interacting Bose–Einstein condensate , 2008, Nature.

[228]  Pollock,et al.  Path-integral computation of superfluid densities. , 1987, Physical review. B, Condensed matter.

[229]  J. Brink,et al.  Polarization Suppression and Nonmonotonic Local Two-Body Correlations in the Two-Component Bose Gas in One Dimension , 2009, 0906.0955.

[230]  S. Katsura,et al.  Statistical Mechanics of the Anisotropic Linear Heisenberg Model , 1962 .

[231]  Batrouni,et al.  Quantum critical phenomena in one-dimensional Bose systems. , 1990, Physical review letters.

[232]  Lana,et al.  Cluster algorithm for vertex models. , 1993, Physical review letters.

[233]  T. Giamarchi,et al.  Umklapp process and resistivity in one-dimensional fermion systems. , 1991, Physical review. B, Condensed matter.

[234]  P. Calabrese,et al.  One-particle dynamical correlations in the one-dimensional Bose gas , 2006, cond-mat/0611321.

[235]  B. McCoy,et al.  Time-dependent correlation functions of the transverse Ising chain at the critical magnetic field , 1983 .

[236]  H. Evertz,et al.  The loop algorithm , 2003 .

[237]  Hanbury Brown–Twiss interferometry for fractional and integer Mott phases , 2006, cond-mat/0604154.

[238]  L. Glazman,et al.  Universal Theory of Nonlinear Luttinger Liquids , 2008, Science.

[239]  B. Svistunov,et al.  Phase diagram and thermodynamics of the three-dimensional Bose-Hubbard model , 2007, cond-mat/0701178.

[240]  Matthias Troyer,et al.  Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations , 2004, Physical review letters.

[241]  J. Schmiedmayer,et al.  Probing quantum and thermal noise in an interacting many-body system , 2007, 0710.1575.

[242]  Nikos L. Doltsinis,et al.  Quantum Simulations of complex many-body systems:from theory to algorithms , 2002 .

[243]  Martin Eckstein,et al.  Thermalization after an interaction quench in the Hubbard model. , 2009, Physical review letters.

[244]  J. Kosterlitz,et al.  The critical properties of the two-dimensional xy model , 1974 .

[245]  Ladders in a magnetic field: a strong coupling approach , 1998, cond-mat/9805029.

[246]  P. Drummond,et al.  Finite-temperature correlations and density profiles of an inhomogeneous interacting one-dimensional Bose gas (17 pages) , 2005, cond-mat/0502438.

[247]  Yoshikazu Suzumura,et al.  Localization-Delocalization Transition by Interactions in One-Dimensional Fermion Systems (アンダ-ソン局在の総合的研究(昭和57年度文部省科学研究費研究会報告)) , 1983 .

[248]  D. Basko,et al.  Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states , 2005, cond-mat/0506617.

[249]  A. Sandvik.  Stochastic series expansion method with operator-loop update , 1999, cond-mat/9902226.

[250]  M. Lukin,et al.  Probing many-body states of ultracold atoms via noise correlations (4 pages) , 2003, cond-mat/0306226.

[251]  Michael E. Fisher,et al.  Toeplitz Determinants: Some Applications, Theorems, and Conjectures , 2007 .

[252]  H. Trotter.  On the product of semi-groups of operators , 1959 .

[253]  J. Schmiedmayer,et al.  Thermalization in a quasi-one-dimensional ultracold bosonic gas , 2009, 0912.4493.

[254]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[255]  C. Castellani,et al.  Kosterlitz-Thouless behavior in layered superconductors: the role of the vortex core energy. , 2006, Physical review letters.

[256]  B. Sutherland.  Further Results for the Many-Body Problem in One Dimension , 1968 .

[257]  J. Schmiedmayer,et al.  Breakdown of integrability in a quasi-1D ultracold bosonic gas. , 2008, Physical review letters.

[258]  Cheng Chin,et al.  In situ observation of incompressible Mott-insulating domains in ultracold atomic gases , 2009, Nature.

[259]  J. Cardy,et al.  Quantum quenches in extended systems , 2007, 0704.1880.

[260]  A. Minguzzi,et al.  Soluble models of strongly interacting ultracold gas mixtures in tight waveguides. , 2007, Physical review letters.

[261]  Kerson Huang,et al.  Eigenvalues and Eigenfunctions of a Bose System of Hard Spheres and Its Low-Temperature Properties , 1957 .

[262]  E. Demler,et al.  Quantum critical states and phase transitions in the presence of non-equilibrium noise , 2009, 0908.0868.

[263]  L. F. Santos,et al.  Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[264]  Maier,et al.  Controlling cold atoms using nanofabricated surfaces: atom chips , 1999, Physical review letters.

[265]  N. J. van Druten,et al.  Yang-Yang thermodynamics on an atom chip. , 2007, Physical review letters.

[266]  Phase transition in a chain of quantum vortices , 1998, cond-mat/9809118.

[267]  D. Weiss,et al.  Local pair correlations in one-dimensional Bose gases. , 2005, Physical review letters.

[268]  E. Gross,et al.  Hydrodynamics of a Superfluid Condensate , 1963 .

[270]  S. Stringari,et al.  Collective oscillations of a one-dimensional trapped Bose-Einstein gas , 2002 .

[271]  E. Chow,et al.  Length-Scale Dependence of the Superconductor-to-Insulator Quantum Phase Transition in One Dimension , 1998 .

[272]  B. McCoy,et al.  Off-Diagonal Time-Dependent Spin Correlation Functions of theX−YModel , 1971 .

[273]  Ground-state properties of a one-dimensional system of hard-core bosons in a harmonic trap , 2000, cond-mat/0008480.

[274]  E. Vicari,et al.  Quantum critical behavior and trap-size scaling of trapped bosons in a one-dimensional optical lattice , 2010, 1003.3334.

[275]  P. Hānggi,et al.  Levy distribution in many-particle quantum systems , 2009, 0907.4328.

[276]  C. Westbrook,et al.  Experimental evidence for the breakdown of a Hartree-Fock approach in a weakly interacting Bose gas. , 2006, Physical review letters.

[277]  D. O. Krimer,et al.  Universal spreading of wave packets in disordered nonlinear systems. , 2008, Physical review letters.

[278]  Bosonizing one-dimensional cold atomic gases , 2003, cond-mat/0307033.

[279]  Quasi 1 and 2d Dilute Bose Gas in Magnetic Traps: Existence of Off-Diagonal Order and Anomalous Quantum Fluctuations , 1997, cond-mat/9703034.

[280]  T. Giamarchi,et al.  Anderson localization and interactions in one-dimensional metals. , 1988, Physical review. B, Condensed matter.

[281]  Millis,et al.  Conductivity of a Luttinger liquid. , 1992, Physical review. B, Condensed matter.

[282]  Interacting electrons in disordered wires: Anderson localization and low-T transport. , 2005, Physical review letters.

[283]  Phase-locking transition of coupled low-dimensional superfluids , 2006, cond-mat/0612174.

[284]  W. Ketterle,et al.  Bose-Einstein condensation , 1997 .

[285]  Edmond Orignac,et al.  Controlling Luttinger liquid physics in spin ladders under a magnetic field. , 2008, Physical review letters.

[286]  Jacek Dziarmaga,et al.  Dynamics of a quantum phase transition and relaxation to a steady state , 2009, 0912.4034.

[287]  Richard Blankenbecler,et al.  Monte Carlo Simulations of One-dimensional Fermion Systems , 1982 .

[288]  G. Wentzel.  The Interaction of Lattice Vibrations with Electrons in a Metal , 1951 .

[289]  E. Demler,et al.  Exact methods in the analysis of the non-equilibrium dynamics of integrable models: application to the study of correlation functions for non-equilibrium 1D Bose gas , 2009, 0904.3221.

[290]  Noise correlations of hard-core bosons: quantum coherence and symmetry breaking , 2005, cond-mat/0511700.

[291]  A. Muramatsu,et al.  Time evolution of one-dimensional Quantum Many Body Systems , 2005, cond-mat/0502396.

[292]  C. Clark,et al.  Extended fermionization of 1D bosons in optical lattices , 2005, cond-mat/0505325.

[293]  Schulz Hj.  Dynamics of Coupled Quantum Spin Chains. , 1996 .

[294]  S. Korshunov.  Phase diagram of a chain of dissipative Josephson junctions (Erratum) , 1989 .

[295]  S. Doniach,et al.  Quantum fluctuations in chains of Josephson junctions , 1984 .

[296]  P. Anderson.  Absence of Diffusion in Certain Random Lattices , 1958 .

[297]  Perturbation Theory for Singular Potentials in Quantum Mechanics , 1998, cond-mat/9803271.

[298]  E. Schmidt.  Zur Theorie der linearen und nichtlinearen Integralgleichungen , 1907 .

[299]  E. Caianiello,et al.  On the algorithm of Dirac spurs , 1952 .

[300]  J. Grotendorst,et al.  Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms , 2001 .

[301]  S. Giorgini,et al.  Correlation functions of a Lieb–Liniger Bose gas , 2005, cond-mat/0510463.

[302]  T. C. Choy,et al.  Failure of Bethe-Ansatz solutions of generalisations of the Hubbard chain to arbitrary permutation symmetry , 1982 .

[303]  T. Giamarchi,et al.  Localization and interaction in one-dimensional quantum fluids , 1987 .

[304]  A. Griesmaier,et al.  Bose-Einstein condensation of chromium. , 2005, Physical review letters.

[305]  Thierry Giamarchi,et al.  Rise and fall of hidden string order of lattice bosons , 2008, 0803.2851.

[306]  S. Rolston,et al.  Observation of reduced three-body recombination in a correlated 1D degenerate Bose gas. , 2004, Physical review letters.

[307]  A. Aspect,et al.  One-Dimensional Anderson Localization in Certain Correlated Random Potentials , 2009, 0902.0107.

[308]  G. Blatter,et al.  Amplitude mode in the quantum phase model. , 2007, Physical review letters.

[309]  R. Scalettar,et al.  Localization in interacting, disordered, Bose systems. , 1991, Physical review letters.

[310]  Wang,et al.  Nonuniversal critical dynamics in Monte Carlo simulations. , 1987, Physical review letters.

[311]  B. Sutherland.  EXACT COHERENT STATES OF A ONE-DIMENSIONAL QUANTUM FLUID IN A TIME-DEPENDENT TRAPPING POTENTIAL , 1998 .

[312]  C. Yang.  Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction , 1967 .

[313]  M. Suzuki,et al.  Generalized Trotter's formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems , 1976 .

[314]  X. Guan,et al.  Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems , 2010, 1010.4842.

[315]  Applications of exact solution for strongly interacting one-dimensional Bose-Fermi mixture : Low-temperature correlation functions, density profiles, and collective modes , 2005, cond-mat/0510801.

[316]  E. Lieb,et al.  Two Soluble Models of an Antiferromagnetic Chain , 1961 .

[317]  M. Troyer,et al.  Accessing the dynamics of large many-particle systems using the stochastic series expansion. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[318]  S. Stringari,et al.  Uncertainty principle, quantum fluctuations, and broken symmetries , 1991 .

[319]  Alessandro Silva,et al.  Colloquium: Nonequilibrium dynamics of closed interacting quantum systems , 2010, 1007.5331.

[320]  Immanuel Bloch,et al.  Collapse and revival of the matter wave field of a Bose–Einstein condensate , 2002, Nature.

[321]  A. A. Ovchinnikov.  Formfactors and the functional form of correlators in the XX-spin chain , 2004 .

[322]  Schulz,et al.  Correlation functions of one-dimensional quantum systems. , 1989, Physical review. B, Condensed matter.

[323]  B. Sutherland.  Exact results for a quantum many body problem in one-dimension , 1971 .

[324]  V. Popov.  On the theory of the superfluidity of two- and one-dimensional bose systems , 1972 .

[325]  Exact Analysis of δ-Function Attractive Fermions and Repulsive Bosons in One-Dimension , 2005, cond-mat/0503033.

[326]  H. Mori,et al.  Mixing-Demixing Transition in 1D Boson-Fermion Mixture at Low Fermion Densities , 2005, cond-mat/0509393.

[327]  Bradley,et al.  Evidence of Bose-Einstein Condensation in an Atomic Gas with Attractive Interactions. , 1995, Physical review letters.

[328]  J. Schmiedmayer,et al.  Microscopic atom optics: from wires to an atom chip , 2008, 0805.2613.

[329]  L. Glazman,et al.  Exact exponents of edge singularities in dynamic correlation functions of 1D bose gas. , 2007, Physical review letters.

[330]  N. Trivedi,et al.  Spectral weight redistribution in strongly correlated bosons in optical lattices , 2008, 0801.4672.

[331]  L. Walker.  Antiferromagnetic Linear Chain , 1959 .

[332]  G. De Chiara,et al.  Density Matrix Renormalization Group for Dummies , 2006 .

[333]  Universal correlations of trapped one-dimensional impenetrable bosons , 2004, cond-mat/0404104.

[334]  M. Rigol,et al.  Thermalization and its mechanism for generic isolated quantum systems , 2007, Nature.

[335]  M. Rigol,et al.  Focus on Dynamics and Thermalization in Isolated Quantum Many-Body Systems , 2010 .

[336]  P. Simon,et al.  Disordered one-dimensional bose-fermi mixtures: the Bose-Fermi glass. , 2010, Physical review letters.

[337]  Mooij,et al.  One-Dimensional Mott Insulator Formed by Quantum Vortices in Josephson Junction Arrays. , 1996, Physical review letters.

[338]  A. Klein,et al.  Localization in the ground-state of the one dimensionalX−Y model with a random transverse field , 1990 .

[339]  Immanuel Bloch,et al.  Tonks–Girardeau gas of ultracold atoms in an optical lattice , 2004, Nature.

[340]  Michael Moeckel,et al.  Interaction quench in the Hubbard model. , 2008, Physical review letters.

[341]  Sachdev,et al.  Finite-temperature properties of quantum antiferromagnets in a uniform magnetic field in one and two dimensions. , 1994, Physical review. B, Condensed matter.

[342]  Shastry,et al.  Twisted boundary conditions and effective mass in Heisenberg-Ising and Hubbard rings. , 1990, Physical review letters.

[343]  Fisher,et al.  Boson localization and the superfluid-insulator transition. , 1989, Physical review. B, Condensed matter.

[344]  A. Tsvelik,et al.  Bosonization and Strongly Correlated Systems , 1999 .

[345]  J. Caux,et al.  Computation of dynamical correlation functions of Heisenberg chains: the gapless anisotropic regime , 2005, cond-mat/0506698.

[346]  J. Taniguchi,et al.  Superfluidity of liquid 4He confined to one-dimensional straight nanochannel structures , 2010 .

[347]  S. Rolston,et al.  Strongly inhibited transport of a degenerate 1D Bose gas in a lattice. , 2004, Physical review letters.

[348]  H. Evertz,et al.  Excitation spectra of strongly correlated lattice bosons and polaritons , 2009, 0904.1350.

[349]  R. Konik,et al.  Short distance expansions of correlation functions in the Sine-Gordon theory , 1995, hep-th/9503112.

[350]  J Eisert,et al.  Exact relaxation in a class of nonequilibrium quantum lattice systems. , 2008, Physical review letters.

[351]  A. Bijl.  Properties of the condensed phases of helium and hydrogen , 1937 .

[352]  E. Berg,et al.  Hidden order in 1D bose insulators. , 2006, Physical review letters.

[353]  E. Demler,et al.  Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench. , 2008, Physical review letters.

[354]  M. Cazalilla.  Differences between the Tonks regimes in the continuum and on the lattice , 2004 .

[355]  Local-density approximation for confined bosons in an optical lattice (7 pages) , 2004, cond-mat/0404395.

[356]  F. Dalfovo,et al.  Parametric excitation of a Bose-Einstein condensate in a one-dimensional optical lattice , 2004, cond-mat/0410122.

[357]  A. Lenard.  Momentum Distribution in the Ground State of the One-Dimensional System of Impenetrable Bosons , 1964 .

[358]  C. A. Murray,et al.  Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions , 1979 .

[359]  T. Roscilde.  Bosons in one-dimensional incommensurate superlattices , 2007, 0712.2741.

[360]  M. Segev,et al.  Anderson localization of a Tonks-Girardeau gas in potentials with controlled disorder , 2010, 1005.4726.

[361]  I Bloch,et al.  Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. , 2001, Physical review letters.

[362]  E. Demler,et al.  Scaling approach to quantum non-equilibrium dynamics of many-body systems , 2009, 0912.2744.

[363]  Spectroscopy of ultracold atoms by periodic lattice modulations. , 2006, Physical review letters.

[364]  K. Krämer,et al.  Direct observation of magnon fractionalization in the quantum spin ladder. , 2008, Physical review letters.

[365]  B. McCoy,et al.  Statistical Mechanics of the XY Model. 4. Time-Dependent Spin-Correlation Functions , 1971 .

[366]  N. Mermin,et al.  Absence of Ferromagnetism or Antiferromagnetism in One- or Two-Dimensional Isotropic Heisenberg Models , 1966 .

[367]  Finite one-dimensional impenetrable Bose systems: Occupation numbers , 2002, cond-mat/0211126.

[368]  Exact dynamical correlation functions of Calogero-Sutherland model and one-dimensional fractional statistics. , 1994, Physical review letters.

[369]  E. Bettelheim,et al.  Nonlinear quantum shock waves in fractional quantum Hall edge states. , 2006, Physical review letters.

[370]  Bose-Einstein condensation of dilute magnons in TlCuCl3. , 1999, Physical review letters.

[371]  C. Clark,et al.  Creating a supersolid in one-dimensional Bose mixtures , 2008, 0806.0461.

[372]  M. Troyer,et al.  Bosons in Optical Lattices – from the Mott Transition to the Tonks–Girardeau Gas , 2004, cond-mat/0411473.

[373]  R. Bistritzer,et al.  Intrinsic dephasing in one-dimensional ultracold atom interferometers , 2006, Proceedings of the National Academy of Sciences.

[374]  FREE EXPANSION OF IMPENETRABLE BOSONS ON ONE-DIMENSIONAL OPTICAL LATTICES , 2005, cond-mat/0507351.

[375]  Elliott H. Lieb,et al.  Residual Entropy of Square Ice , 1967 .

[376]  B. McCoy,et al.  Correlation functions of the transverse Ising chain at the critical field for large temporal and spatial separations , 1983 .

[377]  H. Fukuyama,et al.  Dynamics of the charge-density wave. I. Impurity pinning in a single chain , 1978 .

[378]  E. Demler,et al.  Interference between independent fluctuating condensates. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[379]  P. Zoller,et al.  Repulsively bound atom pairs in an optical lattice , 2006, Nature.

[380]  Petrov,et al.  Regimes of quantum degeneracy in trapped 1D gases , 2000, Physical review letters.

[381]  Elliott H. Lieb,et al.  Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension , 1968 .

[382]  M. Lukin,et al.  Decoherence dynamics in low-dimensional cold atom interferometers. , 2007, Physical review letters.

[383]  T. Hänsch,et al.  Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms , 2002, Nature.

[384]  Krishnamurthy,et al.  One-dimensional disordered bosonic Hubbard model: A density-matrix renormalization group study. , 1996, Physical review letters.

[385]  J. Bardeen.  Electron-Vibration Interactions and Superconductivity , 1951 .

[386]  Mattias Gustavsson,et al.  Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons , 2010, Nature.

[387]  H P Büchler,et al.  Commensurate-incommensurate transition of cold atoms in an optical lattice. , 2003, Physical review letters.

[388]  Krauth.  Bethe ansatz for the one-dimensional boson Hubbard model. , 1991, Physical review. B, Condensed matter.

[389]  B. B. Beard,et al.  Simulations of Discrete Quantum Systems in Continuous Euclidean Time. , 1996 .

[390]  Chen Ning Yang,et al.  One-Dimensional Chain of Anisotropic Spin-Spin Interactions. I. Proof of Bethe's Hypothesis for Ground State in a Finite System , 1966 .

[391]  Dynamics of a Tonks-Girardeau gas released from a hard-wall trap , 2005, cond-mat/0511747.

[392]  Dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain. , 2006, Physical review letters.

[393]  C. P. Yang,et al.  One-Dimensional Chain of Anisotropic Spin-Spin Interactions. III. Applications , 1966 .

[394]  C. Clark,et al.  Generalized thermalization in an integrable lattice system. , 2010, Physical review letters.

[395]  G. Batrouni,et al.  Supersolids in one dimensional Bose Fermi mixtures , 2008, 0808.3321.

[396]  A. Madouri,et al.  EXPERIMENTAL PHASE DIAGRAM OF CU2(C5H12N2)2CL4 : A QUASI-ONE-DIMENSIONAL ANTIFERROMAGNETIC SPIN-1/2 HEISENBERG LADDER , 1997 .

[397]  T. Gustavson,et al.  Realization of Bose-Einstein condensates in lower dimensions. , 2001, Physical review letters.

[398]  K. Wilson.  The renormalization group: Critical phenomena and the Kondo problem , 1975 .

[399]  Elliott H. Lieb,et al.  Bosons in a trap: A rigorous derivation of the Gross-Pitaevskii energy functional , 1999, math-ph/9908027.

[400]  Marcos Rigol,et al.  Entropy of isolated quantum systems after a quench. , 2011, Physical review letters.

[401]  L. Pollet,et al.  Criticality in trapped atomic systems. , 2010, Physical review letters.

[402]  Ehud Altman,et al.  Quench dynamics and nonequilibrium phase diagram of the bose-hubbard model. , 2007, Physical review letters.

[403]  Off-diagonal correlations of the Calogero-Sutherland model. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[404]  R. Orbach.  Linear antiferromagnetic chain with anisotropic coupling , 1958 .

[405]  R. Shankar.  SOLVABLE MODEL OF A METAL-INSULATOR TRANSITION , 1990 .

[406]  Bose-Einstein condensation in trapped bosons: A variational Monte Carlo analysis , 2000, cond-mat/0008368.

[407]  E. Demler,et al.  Mapping of Coulomb Gases and Sine-Gordon Models to Statistics of Random Surfaces , 2006, cond-mat/0612011.

[408]  F. Haldane,et al.  Luttinger liquid theory of one-dimensional quantum fluids. I. Properties of the Luttinger model and their extension to the general 1D interacting spinless Fermi gas , 1981 .

[409]  Kennedy,et al.  The XY model has long-range order for all spins and all dimensions greater than one. , 1988, Physical review letters.

[410]  A. Tsvelik,et al.  Optical conductivity of one-dimensional Mott insulators. , 2000, Physical review letters.

[411]  M. Cazalilla,et al.  Instabilities in binary mixtures of one-dimensional quantum degenerate gases. , 2003, Physical review letters.

[412]  White,et al.  Density-matrix algorithms for quantum renormalization groups. , 1993, Physical review. B, Condensed matter.

[413]  Phase transition in a system of one-dimensional bosons with strong disorder. , 2004, Physical review letters.

[414]  Young,et al.  Numerical study of the random transverse-field Ising spin chain. , 1996, Physical review. B, Condensed matter.

[415]  T. Roscilde.  Exploring the grand-canonical phase diagram of interacting bosons in optical lattices by trap squeezing , 2010, 1003.4005.

[416]  Energy absorption of a Bose gas in a periodically modulated optical lattice , 2005, cond-mat/0508054.

[417]  A. Campo.  Fermionization and bosonization of expanding one-dimensional anyonic fluids , 2008, 0805.3786.

[418]  M. Bortz,et al.  Exact results for the one-dimensional mixed boson-fermion interacting gas , 2005 .

[419]  A. Trombettoni,et al.  One-dimensional Lieb-Liniger Bose gas as nonrelativistic limit of the sinh-Gordon model , 2009, 0912.3502.

[420]  Nevill Mott,et al.  Metal-insulator transitions , 1974 .

[421]  E. Wigner,et al.  Über das Paulische Äquivalenzverbot , 1928 .

[422]  R. Scalettar,et al.  Universal state diagrams for harmonically trapped bosons in optical lattices , 2008, 0811.2219.

[423]  K. Efetov.  Supersymmetry and theory of disordered metals , 1983 .

[424]  A. J. Short,et al.  Entanglement and the foundations of statistical mechanics , 2005 .

[425]  M. Modugno,et al.  Effects of interaction on the diffusion of atomic matter waves in one-dimensional quasiperiodic potentials , 2009, 0909.1714.

[426]  D. Pritchard,et al.  Trapping and focusing ground state atoms with static fields , 1992 .

[427]  H. Schulz.  Critical behavior of commensurate-incommensurate phase transitions in two dimensions , 1980 .

[428]  M. Troyer,et al.  Absence of a direct superfluid to mott insulator transition in disordered bose systems. , 2009, Physical review letters.

[429]  I. S. Tupitsyn,et al.  Exact quantum Monte Carlo process for the statistics of discrete systems , 1996, cond-mat/9612091.

[430]  Phase diagram for ultracold bosons in optical lattices and superlattices , 2004, cond-mat/0405254.

[431]  Transport in an inhomogeneous interacting one-dimensional system. , 1995, Physical review. B, Condensed matter.

[432]  Stefan Wessel,et al.  Quantum monte carlo simulations of confined bosonic atoms in optical lattices , 2004 .

[433]  Xiaolong Deng R. Citro A. Minguzzi E. Orignac.  Phase diagram and momentum distribution of an interacting Bose gas in a bichromatic lattice , 2008, 0803.3128.

[434]  D. Hofstadter.  Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields , 1976 .

[435]  L. Pollet,et al.  Phase diagram of the disordered Bose-Hubbard model , 2009, 0909.4593.

[436]  Ground-state wave functionals for (1 + 1)-dimensional fermion field theories☆ , 1992, hep-th/9207003.

[437]  Giamarchi.  Resistivity of a one-dimensional interacting quantum fluid. , 1992, Physical review. B, Condensed matter.

[438]  F. Calogero.  Solution of a three-body problem in one-dimension , 1969 .

[439]  L. Ryder,et al.  Quantum Field Theory , 2001, Foundations of Modern Physics.

[440]  White,et al.  Density matrix formulation for quantum renormalization groups. , 1992, Physical review letters.

[441]  P. G. Harper,et al.  Single Band Motion of Conduction Electrons in a Uniform Magnetic Field , 1955 .

[442]  A. A. Ovchinnikov.  Asymptotics and functional form of correlators in the XX-spin chain of finite length , 2002 .

[443]  A. Kamenev,et al.  Dynamics of a one-dimensional spinor Bose liquid: A phenomenological approach , 2008, 0808.0479.

[444]  C. Gardiner,et al.  Cold Bosonic Atoms in Optical Lattices , 1998, cond-mat/9805329.

[445]  B. Altshuler,et al.  A finite-temperature phase transition for disordered weakly interacting bosons in one dimension , 2009, 0910.4534.

[446]  P. Drummond,et al.  Pair correlations in a finite-temperature 1D Bose gas. , 2002, Physical review letters.

[447]  Density matrix renormalization group for disordered bosons in one dimension , 1999, cond-mat/9901080.

[448]  M. Lukin,et al.  Luttinger liquid of polarons in one-dimensional boson-fermion mixtures. , 2004, Physical review letters.

[449]  J. Schmiedmayer,et al.  Non-equilibrium coherence dynamics in one-dimensional Bose gases. , 2007, Nature.

[450]  Quantum phase transition and Coulomb blockade with one-dimensional SQUID arrays , 2002 .

[451]  A. Sur,et al.  Spin dynamics for the one-dimensional XY model at infinite temperature , 1975 .

[452]  E. Wigner,et al.  About the Pauli exclusion principle , 1928 .

[453]  S. M. Girvin,et al.  Numerical study of the random dimerized XX spin-1/2 chain , 1998 .

[454]  S. Sachdev.  Quantum magnetism and criticality , 2007, 0711.3015.

[455]  A. Aspect,et al.  Direct observation of Anderson localization of matter waves in a controlled disorder , 2008, Nature.

[456]  Free expansion of a Lieb-Liniger gas: Asymptotic form of the wave functions , 2008, 0804.2580.

[457]  Y. Kato,et al.  Sharp peaks in the momentum distribution of bosons in optical lattices in the normal state , 2008 .

[458]  Robert Seiringer,et al.  Proof of Bose-Einstein condensation for dilute trapped gases. , 2002, Physical review letters.

[459]  I. McCulloch,et al.  Quasiperiodic Bose-Hubbard model and localization in one-dimensional cold atomic gases , 2008, 0802.3774.

[460]  X. Guan,et al.  Magnetism of one-dimensional strongly repulsive spin-1 bosons with antiferromagnetic spin exchange interaction , 2009, 0909.2097.

[461]  B. Sutherland.  Quantum many body problem in one-dimension: Ground state , 1971 .

[462]  C. Tracy,et al.  CROSSOVER SCALING FUNCTION FOR THE ONE-DIMENSIONAL XY MODEL AT ZERO TEMPERATURE , 1978 .

[463]  D. Huse,et al.  Localization of interacting fermions at high temperature , 2006, cond-mat/0610854.

[464]  M. Girardeau,et al.  Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension , 1960 .