Anyons in an exactly solved model and beyond

[1]  M. Freedman,et al.  Non-Abelian topological phases in an extended Hubbard model , 2003, cond-mat/0309120.

[2]  Ben Reichardt,et al.  Fault-Tolerant Quantum Computation , 2016, Encyclopedia of Algorithms.

[3]  M. Flohr,et al.  Conformal Field Theory , 2006 .

[4]  V. Goldman,et al.  Direct observation of fractional statistics in two dimensions , 2005 .

[5]  Lev B. Ioffe,et al.  Discrete non-Abelian gauge theories in Josephson-junction arrays and quantum computation , 2004 .

[6]  M. Freedman,et al.  A class of P,T-invariant topological phases of interacting electrons , 2003, cond-mat/0307511.

[7]  C. Mochon Anyon computers with smaller groups , 2003, quant-ph/0306063.

[8]  M. Hastings Lieb-Schultz-Mattis in higher dimensions , 2003, cond-mat/0305505.

[9]  L. B. Ioffe,et al.  Discrete non-Abelian gauge theories in two-dimensional lattices and their realizations in Josephson-junction arrays , 2003, cond-mat/0302104.

[10]  L. Ioffe,et al.  Topological order in the insulating Josephson junction array. , 2002, Physical review letters.

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

[12]  X. Wen Quantum orders in an exact soluble model. , 2002, Physical review letters.

[13]  A. Kitaev,et al.  Fault tolerant quantum computation by anyons , 1997, quant-ph/9707021.

[14]  Kevin Walker,et al.  On Witten’s 3-manifold Invariants , 2003 .

[15]  J. Loday Realization of the Stasheff polytope , 2002, math/0212126.

[16]  L. Ioffe,et al.  Possible realization of an ideal quantum computer in Josephson junction array , 2002, cond-mat/0205186.

[17]  P. Lochak LECTURES ON TENSOR CATEGORIES AND MODULAR FUNCTORS (University Lecture Series 21) By BOJKO BAKALOV and ALEXANDER KIRILLOV, JR: 221 pp., US$29.00, ISBN 0-8218-2686-7 (American Mathematical Society, Providence, RI, 2001). , 2002 .

[18]  P. Etingof,et al.  On fusion categories , 2002, math/0203060.

[19]  J. Vidal,et al.  Pairing of Cooper pairs in a fully frustrated Josephson-junction chain. , 2002, Physical review letters.

[20]  A. Cappelli,et al.  Thermal Transport in Chiral Conformal Theories and Hierarchical Quantum Hall States , 2001, cond-mat/0111437.

[21]  X. Wen Quantum orders and symmetric spin liquids , 2001, cond-mat/0107071.

[22]  J. Kellendonk,et al.  EDGE CURRENT CHANNELS AND CHERN NUMBERS IN THE INTEGER QUANTUM HALL EFFECT , 2002 .

[23]  R. Liang,et al.  A limit on spin–charge separation in high-Tc superconductors from the absence of a vortex-memory effect , 2001, Nature.

[24]  M. Freedman,et al.  A Magnetic Model with a Possible Chern-Simons Phase , 2001, quant-ph/0110060.

[25]  R. Moessner,et al.  Resonating valence bond phase in the triangular lattice quantum dimer model. , 2000, Physical review letters.

[26]  D. Tennant,et al.  Experimental realization of a 2D fractional quantum spin liquid. , 2000, Physical review letters.

[27]  M. Fisher,et al.  Fractionalization in the cuprates: detecting the topological order. , 2000, Physical review letters.

[28]  D. Ivanov Non-Abelian statistics of half-quantum vortices in p-wave superconductors. , 2000, Physical review letters.

[29]  A. Kirillov,et al.  Lectures on tensor categories and modular functors , 2000 .

[30]  A. Kitaev Unpaired Majorana fermions in quantum wires , 2000, cond-mat/0010440.

[31]  E. Rains Correlation functions for symmetrized increasing subsequences , 2000, math/0006097.

[32]  Michael Larsen,et al.  A Modular Functor Which is Universal¶for Quantum Computation , 2000, quant-ph/0001108.

[33]  N. Read,et al.  Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect , 1999, cond-mat/9906453.

[34]  I. Gelfand,et al.  The Gelfand Mathematical Seminars, 1996–1999 , 2000 .

[35]  A. Rosenberg The Existence of Fiber Functors , 2000 .

[36]  J. Kellendonk,et al.  LETTER TO THE EDITOR: Simultaneous quantization of edge and bulk Hall conductivity , 1999, cond-mat/9912186.

[37]  N. Read,et al.  Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level , 1998, cond-mat/9809384.

[38]  永長 直人 Quantum field theory in condensed matter physics , 1999 .

[39]  John Preskill,et al.  Topological Quantum Computation , 1998, QCQC.

[40]  Andrew Pressley,et al.  QUANTUM GROUPS (Graduate Texts in Mathematics 155) , 1997 .

[41]  D. Mahalu,et al.  Direct observation of a fractional charge , 1997, Nature.

[42]  France.,et al.  Observation of the e/3 Fractionally Charged Laughlin Quasiparticle , 1997, cond-mat/9706307.

[43]  A. Davydov Twisting of monoidal structures , 1997 .

[44]  C. Kane,et al.  Quantized thermal transport in the fractional quantum Hall effect , 1996, cond-mat/9603118.

[45]  Andrew Lesniewski,et al.  Noncommutative Geometry , 1997 .

[46]  L. Crane,et al.  Deformations of (bi)tensor categories , 1996, q-alg/9612011.

[47]  S. D. Chatterji Proceedings of the International Congress of Mathematicians , 1995 .

[48]  B. Simon,et al.  Charge deficiency, charge transport and comparison of dimensions , 1998, physics/9803014.

[49]  V. Turaev Quantum invariants of knots and three manifolds , 1994 .

[50]  N. Reshetikhin,et al.  Quantum Groups , 1993, hep-th/9311069.

[51]  E. Lieb,et al.  Flux phase of the half-filled band. , 1994, Physical review letters.

[52]  V. Turaev Quantum Invariants of Knots and 3-Manifolds , 1994, hep-th/9409028.

[53]  B. Simon,et al.  The Index of a Pair of Projections , 1994 .

[54]  Y. Hatsugai,et al.  Chern number and edge states in the integer quantum Hall effect. , 1993, Physical review letters.

[55]  Jon P. May Simplicial objects in algebraic topology , 1993 .

[56]  F. Bais,et al.  Anyons in discrete gauge theories with Chern-Simons terms , 1992, hep-th/9203047.

[57]  Nicolai Reshetikhin,et al.  Quantum Groups , 1993 .

[58]  K. Fredenhagen,et al.  Superselection sectors with braid group statistics and exchange algebras. 2. Geometric aspects and conformal covariance , 1992 .

[59]  F. Bais,et al.  Quantum symmetries in discrete gauge theories , 1992, hep-th/9203046.

[60]  G. Volovik Quantum hall and chiral edge states in thin 3He-A film , 1992 .

[61]  G. Moore,et al.  Fractional Quantum Hall Effect and Nonabelian Statistics , 1992, hep-th/9202001.

[62]  R. Haag,et al.  Local quantum physics , 1992 .

[63]  Vladimir Turaev,et al.  Invariants of 3-manifolds via link polynomials and quantum groups , 1991 .

[64]  Gregory W. Moore,et al.  Nonabelions in the fractional quantum Hall effect , 1991 .

[65]  Seiler,et al.  Quantum Hall effect and the relative index for projections. , 1990, Physical review letters.

[66]  F. Gabbiani,et al.  Braid statistics in local quantum theory , 1990 .

[67]  Maximilian Kreuzer,et al.  The gravitational anomalies , 1990 .

[68]  John E. Roberts,et al.  Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics , 1990 .

[69]  Einarsson,et al.  Fractional statistics on a torus. , 1990, Physical review letters.

[70]  E. Witten,et al.  Topological gauge theories and group cohomology , 1990 .

[71]  V. Pasquier,et al.  Quasihopf Algebras, Group Cohomology and Orbifold Models , 1990 .

[72]  Read,et al.  Statistics of the excitations of the resonating-valence-bond state. , 1989, Physical review. B, Condensed matter.

[73]  Edward Witten,et al.  Quantum field theory and the Jones polynomial , 1989 .

[74]  V. Yakovenko,et al.  Fractional charge, spin and statistics of solitons in superfluid 3He film , 1989 .

[75]  G. Moore,et al.  Classical and quantum conformal field theory , 1989 .

[76]  Bert Schroer,et al.  Superselection sectors with braid group statistics and exchange algebras , 1989 .

[77]  John E. Roberts,et al.  A new duality theory for compact groups , 1989 .

[78]  D. Rokhsar,et al.  Superconductivity and the quantum hard-core dimer gas. , 1988, Physical review letters.

[79]  C. Vafa Toward classification of conformal theories , 1988 .

[80]  E. Verlinde,et al.  Fusion Rules and Modular Transformations in 2D Conformal Field Theory , 1988 .

[81]  R. Laughlin,et al.  Equivalence of the resonating-valence-bond and fractional quantum Hall states. , 1987, Physical review letters.

[82]  Vincent Pasquier,et al.  Operator Content of the Ade Lattice Models , 1987 .

[83]  P. Anderson The Resonating Valence Bond State in La2CuO4 and Superconductivity , 1987, Science.

[84]  Y. Imry,et al.  Multichannel Landauer formula for thermoelectric transport with application to thermopower near the mobility edge. , 1986, Physical review. B, Condensed matter.

[85]  Frank Wilczek,et al.  Fractional Statistics and the Quantum Hall Effect , 1984 .

[86]  B. Halperin Statistics of quasiparticles and the hierarchy of fractional quantized Hall states , 1984 .

[87]  D. Thouless,et al.  Quantized Hall conductance in a two-dimensional periodic potential , 1992 .

[88]  B. Simon,et al.  Homotopy and Quantization in Condensed Matter Physics , 1983 .

[89]  R. Laughlin Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations , 1983 .

[90]  F. Wilczek Remarks on Dyons , 1982 .

[91]  Frank Wilczek,et al.  Magnetic flux, angular momentum, and statistics , 1982 .

[92]  B. Halperin Quantized Hall conductance, current carrying edge states, and the existence of extended states in a two-dimensional disordered potential , 1982 .

[93]  Robert B. Laughlin,et al.  Quantized Hall conductivity in two-dimensions , 1981 .

[94]  K. Goeke,et al.  Application of the adiabatic, time-dependent Hartree-Bogolyubov approximation to a solvable model , 1974 .

[95]  Philip W. Anderson,et al.  Resonating valence bonds: A new kind of insulator? , 1973 .

[96]  D. W. Robinson,et al.  The finite group velocity of quantum spin systems , 1972 .

[97]  Jim Stasheff,et al.  Homotopy associativity of $H$-spaces. II , 1963 .

[98]  K. Rehren Braid Group Statistics and their Superselection Rules , 2022 .

[99]  R. Ho Algebraic Topology , 2022 .