Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods

We present numerical results for the equation of state of an infinite chain of hydrogen atoms. A variety of modern many-body methods are employed, with exhaustive cross-checks and validation. Approaches for reaching the continuous space limit and the thermodynamic limit are investigated, proposed, and tested. The detailed comparisons provide a benchmark for assessing the current state of the art in many-body computation, and for the development of new methods. The ground-state energy per atom in the linear chain is accurately determined versus bond length, with a confidence bound given on all uncertainties.

[1]  S. Sorella,et al.  Auxiliary Field Quantum Monte Carlo , 2017 .

[2]  B. Svistunov,et al.  Polynomial complexity despite the fermionic sign , 2017, 1703.10141.

[3]  Dominika Zgid,et al.  Generalized Self-Energy Embedding Theory. , 2017, The journal of physical chemistry letters.

[4]  Steven R White,et al.  Sliced Basis Density Matrix Renormalization Group for Electronic Structure. , 2017, Physical review letters.

[5]  Garnet Kin-Lic Chan,et al.  Stripe order in the underdoped region of the two-dimensional Hubbard model , 2016, Science.

[6]  Shiwei Zhang,et al.  Auxiliary-field quantum Monte Carlo calculations with multiple-projector pseudopotentials , 2016, 1610.06267.

[7]  X. Chen,et al.  Updated core libraries of the ALPS project , 2016, Comput. Phys. Commun..

[8]  Ali Alavi,et al.  Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory. , 2016, Journal of chemical theory and computation.

[9]  G. Chan,et al.  Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver , 2016, 1608.03316.

[10]  I. Tupitsyn,et al.  Stability of Dirac Liquids with Strong Coulomb Interaction. , 2016, Physical review letters.

[11]  Emanuel Gull,et al.  Finite temperature quantum embedding theories for correlated systems , 2016, 1611.00395.

[12]  Shiwei Zhang,et al.  Coupling quantum Monte Carlo and independent-particle calculations: Self-consistent constraint for the sign problem based on the density or the density matrix , 2016, 1608.07154.

[13]  Alexei A Kananenka,et al.  Rigorous Ab Initio Quantum Embedding for Quantum Chemistry Using Green's Function Theory: Screened Interaction, Nonlocal Self-Energy Relaxation, Orbital Basis, and Chemical Accuracy. , 2016, Journal of chemical theory and computation.

[14]  Alicia R. Welden,et al.  Exploring connections between statistical mechanics and Green's functions for realistic systems: Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green's function. , 2016, The Journal of chemical physics.

[15]  Garnet Kin-Lic Chan,et al.  Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms. , 2016, The Journal of chemical physics.

[16]  Qiming Sun,et al.  A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry. , 2016, Journal of chemical theory and computation.

[17]  N. Nagaosa,et al.  Coulomb and electron-phonon interactions in metals , 2016, 1603.06409.

[18]  Alicia R. Welden,et al.  Efficient Temperature-Dependent Green's Function Methods for Realistic Systems: Using Cubic Spline Interpolation to Approximate Matsubara Green's Functions. , 2016, Journal of chemical theory and computation.

[19]  Qiming Sun,et al.  N-Electron Valence State Perturbation Theory Based on a Density Matrix Renormalization Group Reference Function, with Applications to the Chromium Dimer and a Trimer Model of Poly(p-Phenylenevinylene). , 2015, Journal of chemical theory and computation.

[20]  Alexander A Rusakov,et al.  Self-consistent second-order Green's function perturbation theory for periodic systems. , 2015, The Journal of chemical physics.

[21]  Alexei A Kananenka,et al.  Efficient Temperature-Dependent Green's Functions Methods for Realistic Systems: Compact Grids for Orthogonal Polynomial Transforms. , 2015, Journal of chemical theory and computation.

[22]  Alexei A Kananenka,et al.  Communication: Towards ab initio self-energy embedding theory in quantum chemistry. , 2015, The Journal of chemical physics.

[23]  Andrey E. Antipov,et al.  Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms , 2015, 1505.02290.

[24]  D. Zgid,et al.  Fractional charge and spin errors in self-consistent Green's function theory. , 2015, The Journal of chemical physics.

[25]  Garnet Kin-Lic Chan,et al.  The ab-initio density matrix renormalization group in practice. , 2015, The Journal of chemical physics.

[26]  Shiwei Zhang,et al.  Quantum Monte Carlo Calculations in Solids with Downfolded Hamiltonians. , 2014, Physical review letters.

[27]  Emanuel Gull,et al.  Systematically improvable multiscale solver for correlated electron systems , 2014, 1410.5118.

[28]  R. Orlando,et al.  CRYSTAL14: A program for the ab initio investigation of crystalline solids , 2014 .

[29]  D. Zgid,et al.  Local Hamiltonians for quantitative Green's function embedding methods. , 2014, The Journal of chemical physics.

[30]  Garnet Kin-Lic Chan,et al.  Communication: A flexible multi-reference perturbation theory by minimizing the Hylleraas functional with matrix product states. , 2014, The Journal of chemical physics.

[31]  Dimitri Van Neck,et al.  The density matrix renormalization group for ab initio quantum chemistry , 2014, The European Physical Journal D.

[32]  Stability, energetics, and magnetic states of cobalt adatoms on graphene. , 2014, Physical review letters.

[33]  Dominika Zgid,et al.  Communication: the description of strong correlation within self-consistent Green's function second-order perturbation theory. , 2014, The Journal of chemical physics.

[34]  Ye Luo,et al.  Molecular Properties by Quantum Monte Carlo: An Investigation on the Role of the Wave Function Ansatz and the Basis Set in the Water Molecule. , 2013, Journal of chemical theory and computation.

[35]  Gerald Knizia,et al.  Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Concepts. , 2013, Journal of chemical theory and computation.

[36]  Angel Rubio,et al.  Self-consistent GW: an all-electron implementation with localized basis functions , 2013, 1304.4039.

[37]  Toru Shiozaki,et al.  Multireference explicitly correlated F12 theories , 2013 .

[38]  Garnet Kin-Lic Chan,et al.  Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory. , 2012, Journal of chemical theory and computation.

[39]  B. Svistunov,et al.  Bold diagrammatic Monte Carlo method applied to fermionized frustrated spins. , 2012, Physical review letters.

[40]  Shiwei Zhang,et al.  Auxiliary-field quantum Monte Carlo for correlated electron systems , 2013 .

[41]  Garnet Kin-Lic Chan,et al.  Density matrix embedding: a simple alternative to dynamical mean-field theory. , 2012, Physical review letters.

[42]  Martin Schütz,et al.  Molpro: a general‐purpose quantum chemistry program package , 2012 .

[43]  Steven R. White,et al.  Studying Two Dimensional Systems With the Density Matrix Renormalization Group , 2011, 1105.1374.

[44]  L. Stella,et al.  Strong electronic correlation in the hydrogen chain: A variational Monte Carlo study , 2011, 1110.1746.

[45]  Henry Krakauer,et al.  Assessing weak hydrogen binding on Ca+ centers: an accurate many-body study with large basis sets. , 2011, The Journal of chemical physics.

[46]  Toru Shiozaki,et al.  Explicitly correlated multireference configuration interaction with multiple reference functions: avoided crossings and conical intersections. , 2011, The Journal of chemical physics.

[47]  D. Mazziotti.  Large-scale semidefinite programming for many-electron quantum mechanics. , 2011, Physical review letters.

[48]  Toru Shiozaki,et al.  Explicitly correlated multireference configuration interaction: MRCI-F12. , 2011, The Journal of chemical physics.

[49]  Nan Lin,et al.  Dynamical mean-field theory for quantum chemistry. , 2010, Physical review letters.

[50]  M. Reiher,et al.  Quantum-information analysis of electronic states of different molecular structures , 2010, 1008.4607.

[51]  Edward F. Valeev,et al.  Perturbative correction for the basis set incompleteness error of complete-active-space self-consistent field. , 2010, The Journal of chemical physics.

[52]  Anton V. Sinitskiy,et al.  Strong correlation in hydrogen chains and lattices using the variational two-electron reduced density matrix method. , 2010, The Journal of chemical physics.

[53]  M. Casula,et al.  Size-consistent variational approaches to nonlocal pseudopotentials: Standard and lattice regularized diffusion Monte Carlo methods revisited. , 2010, The Journal of chemical physics.

[54]  Henry Krakauer,et al.  Pressure-induced diamond to β-tin transition in bulk silicon: A quantum Monte Carlo study , 2009, 0908.4477.

[55]  M. Casula,et al.  Resonating valence bond wave function with molecular orbitals: application to first-row molecules. , 2009, The Journal of chemical physics.

[56]  G. Scuseria,et al.  Strong correlations via constrained-pairing mean-field theory. , 2009, The Journal of chemical physics.

[57]  Robert van Leeuwen,et al.  Levels of self-consistency in the GW approximation. , 2009, The Journal of chemical physics.

[58]  Henry Krakauer,et al.  Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: Potential energy curves of low-lying C(2) singlet states. , 2008, The Journal of chemical physics.

[59]  Isaiah Shavitt,et al.  Many – Body Methods in Chemistry and Physics: Preface , 2009 .

[60]  Kris Van Houcke,et al.  Diagrammatic Monte Carlo , 2008, 0802.2923.

[61]  R. Cimiraglia,et al.  New perspectives in multireference perturbation theory: the n-electron valence state approach , 2007 .

[62]  Henry Krakauer,et al.  Bond breaking with auxiliary-field quantum Monte Carlo. , 2007, The Journal of chemical physics.

[63]  Boris Svistunov,et al.  Bold diagrammatic Monte Carlo technique: when the sign problem is welcome. , 2007, Physical review letters.

[64]  R. Bartlett,et al.  Coupled-cluster theory in quantum chemistry , 2007 .

[65]  Robert van Leeuwen,et al.  Fully self-consistent GW calculations for atoms and molecules , 2006, cond-mat/0610330.

[66]  G. Chan,et al.  Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group. , 2006, The Journal of chemical physics.

[67]  R. Martin,et al.  Finite-size error in many-body simulations with long-range interactions. , 2006, Physical review letters.

[68]  Shiwei Zhang,et al.  Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis. , 2006, The Journal of chemical physics.

[69]  M. Casula,et al.  Diffusion Monte Carlo method with lattice regularization. , 2005, Physical review letters.

[70]  U. V. Barth,et al.  Variational energy functionals tested on atoms , 2004 .

[71]  N. Dahlen,et al.  Variational second-order Møller-Plesset theory based on the Luttinger-Ward functional. , 2004, The Journal of chemical physics.

[72]  Shiwei Zhang,et al.  Quantum Monte Carlo method using phase-free random walks with slater determinants. , 2002, Physical review letters.

[73]  M. Head‐Gordon,et al.  Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group , 2002 .

[74]  Josef Paldus,et al.  A Critical Assessment of Coupled Cluster Method in Quantum Chemistry , 2007 .

[75]  S. White,et al.  Ab initio quantum chemistry using the density matrix renormalization group , 1998, cond-mat/9808118.

[76]  Trygve Helgaker,et al.  Basis-set convergence of correlated calculations on water , 1997 .

[77]  J. Carlson,et al.  Constrained path Monte Carlo method for fermion ground states , 1996, cond-mat/9607062.

[78]  Kenneth G. Dyall,et al.  The choice of a zeroth-order Hamiltonian for second-order perturbation theory with a complete active space self-consistent-field reference function , 1995 .

[79]  Trygve Helgaker,et al.  A direct atomic orbital driven implementation of the coupled cluster singles and doubles (CCSD) model , 1994 .

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

[81]  David Feller,et al.  Application of systematic sequences of wave functions to the water dimer , 1992 .

[82]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[83]  P. Knowles,et al.  An efficient internally contracted multiconfiguration–reference configuration interaction method , 1988 .

[84]  P. Knowles,et al.  An efficient method for the evaluation of coupling coefficients in configuration interaction calculations , 1988 .

[85]  Martin Head-Gordon,et al.  Quadratic configuration interaction. A general technique for determining electron correlation energies , 1987 .

[86]  Julia E. Rice,et al.  The closed‐shell coupled cluster single and double excitation (CCSD) model for the description of electron correlation. A comparison with configuration interaction (CISD) results , 1987 .

[87]  Werner Kutzelnigg,et al.  r12-Dependent terms in the wave function as closed sums of partial wave amplitudes for large l , 1985 .

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

[89]  R. Bartlett,et al.  A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples , 1982 .

[90]  R. Sugar,et al.  Monte Carlo calculations of coupled boson-fermion systems. I , 1981 .

[91]  D. Ceperley,et al.  Monte Carlo simulation of a many-fermion study , 1977 .

[92]  G. A. Baker,et al.  R-Matrix Expansion for the Ground-State Energy of a Many-Fermion System , 1970 .

[93]  L. Trainor,et al.  SELF-CONSISTENT APPROXIMATIONS IN MANY-BODY SYSTEMS , 1969 .

[94]  L. Hedin.  NEW METHOD FOR CALCULATING THE ONE-PARTICLE GREEN'S FUNCTION WITH APPLICATION TO THE ELECTRON-GAS PROBLEM , 1965 .

[95]  F. Y. Wu,et al.  The Ground State of Liquid He4 , 1962 .

[96]  G. Baym,et al.  Self-Consistent Approximations in Many-Body Systems , 1962 .

[97]  J. C. Ward,et al.  Ground-State Energy of a Many-Fermion System. II , 1960 .

[98]  C. C. J. Roothaan,et al.  Self-Consistent Field Theory for Open Shells of Electronic Systems , 1960 .

[99]  J. Hubbard.  Calculation of Partition Functions , 1959 .

[100]  R. L. Stratonovich.  On a Method of Calculating Quantum Distribution Functions , 1957 .

[101]  R. K. Nesbet,et al.  Self‐Consistent Orbitals for Radicals , 1954 .

[102]  P. Dirac.  Quantum Mechanics of Many-Electron Systems , 1929 .