skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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

Journal Article · · Physical Review. X
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »; « less

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.

Research Organization:
College of William and Mary, Williamsburg, VA (United States); Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Contributing Organization:
Simons Collaboration on the Many-Electron Problem
Grant/Contract Number:
SC0001303; DOE-SC0008624; ER 46932; ER16391; SC0008696; PHY-1314735; hp120174; hp140092; hp160126; hp170079; SC0010381
OSTI ID:
1395398
Alternate ID(s):
OSTI ID: 1426200; OSTI ID: 1843757
Journal Information:
Physical Review. X, Journal Name: Physical Review. X Vol. 7 Journal Issue: 3; ISSN 2160-3308
Publisher:
American Physical SocietyCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 165 works
Citation information provided by
Web of Science

References (89)

Size-consistent variational approaches to nonlocal pseudopotentials: Standard and lattice regularized diffusion Monte Carlo methods revisited journal April 2010
Quadratic configuration interaction. A general technique for determining electron correlation energies journal November 1987
Communication: A flexible multi-reference perturbation theory by minimizing the Hylleraas functional with matrix product states journal September 2014
Assessing weak hydrogen binding on Ca + centers: An accurate many-body study with large basis sets journal October 2011
Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group journal March 2002
The closed‐shell coupled cluster single and double excitation (CCSD) model for the description of electron correlation. A comparison with configuration interaction (CISD) results journal March 1987
Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: Potential energy curves of low-lying C2 singlet states journal March 2009
Auxiliary-field quantum Monte Carlo calculations with multiple-projector pseudopotentials journal April 2017
Quantum Monte Carlo Calculations in Solids with Downfolded Hamiltonians journal June 2015
Fully self-consistent GW calculations for atoms and molecules journal October 2006
Studying Two-Dimensional Systems with the Density Matrix Renormalization Group journal March 2012
Molpro: a general-purpose quantum chemistry program package: Molpro
  • Werner, Hans-Joachim; Knowles, Peter J.; Knizia, Gerald
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 2 https://doi.org/10.1002/wcms.82
journal July 2011
Determinant Diagrammatic Monte Carlo Algorithm in the Thermodynamic Limit journal July 2017
Quantum Mechanics of Many-Electron Systems journal April 1929
Self-consistent second-order Green’s function perturbation theory for periodic systems journal February 2016
Many – Body Methods in Chemistry and Physics book January 2009
A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples journal February 1982
Density Matrix Embedding: A Simple Alternative to Dynamical Mean-Field Theory journal November 2012
Fixed‐node quantum Monte Carlo for molecules a) b) journal December 1982
Explicitly correlated multireference configuration interaction with multiple reference functions: Avoided crossings and conical intersections journal May 2011
Local Hamiltonians for quantitative Green's function embedding methods journal November 2014
Large-Scale Semidefinite Programming for Many-Electron Quantum Mechanics journal February 2011
Strong electronic correlation in the hydrogen chain: A variational Monte Carlo study journal December 2011
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen journal January 1989
Molecular Properties by Quantum Monte Carlo: An Investigation on the Role of the Wave Function Ansatz and the Basis Set in the Water Molecule journal September 2013
Variational energy functionals tested on atoms journal May 2004
Ab initio quantum chemistry using the density matrix renormalization group journal March 1999
An efficient internally contracted multiconfiguration–reference configuration interaction method journal November 1988
Density matrix formulation for quantum renormalization groups journal November 1992
The density matrix renormalization group for ab initio quantum chemistry journal September 2014
Systematically improvable multiscale solver for correlated electron systems journal March 2015
Monte Carlo calculations of coupled boson-fermion systems. I journal October 1981
Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory journal January 2017
A direct atomic orbital driven implementation of the coupled cluster singles and doubles (CCSD) model journal September 1994
Efficient Temperature-Dependent Green’s Function Methods for Realistic Systems: Using Cubic Spline Interpolation to Approximate Matsubara Green’s Functions journal April 2016
Coupled-cluster theory in quantum chemistry journal February 2007
Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms journal December 2015
An efficient method for the evaluation of coupling coefficients in configuration interaction calculations journal April 1988
Self‐Consistent Orbitals for Radicals journal March 1954
Coupling quantum Monte Carlo and independent-particle calculations: Self-consistent constraint for the sign problem based on the density or the density matrix journal December 2016
Resonating valence bond wave function with molecular orbitals: Application to first-row molecules journal October 2009
Stability, Energetics, and Magnetic States of Cobalt Adatoms on Graphene journal October 2014
Bond breaking with auxiliary-field quantum Monte Carlo journal October 2007
Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis journal June 2006
Fractional charge and spin errors in self-consistent Green’s function theory journal May 2015
Diagrammatic Monte Carlo journal January 2010
Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory journal February 2013
The ab-initio density matrix renormalization group in practice journal January 2015
Application of systematic sequences of wave functions to the water dimer journal April 1992
Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms journal July 2016
Quantum-information analysis of electronic states of different molecular structures journal January 2011
Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Concepts journal October 2013
Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants journal April 2003
Pressure-induced diamond to β -tin transition in bulk silicon: A quantum Monte Carlo study journal December 2009
Finite temperature quantum embedding theories for correlated systems journal February 2017
Calculation of Partition Functions journal July 1959
Constrained path Monte Carlo method for fermion ground states journal March 1997
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) journal March 2016
New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem journal August 1965
Multireference explicitly correlated F12 theories journal March 2013
Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver journal January 2017
The choice of a zeroth‐order Hamiltonian for second‐order perturbation theory with a complete active space self‐consistent‐field reference function journal March 1995
Levels of self-consistency in the GW approximation journal March 2009
Strong correlation in hydrogen chains and lattices using the variational two-electron reduced density matrix method journal July 2010
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 journal November 2016
Communication: The description of strong correlation within self-consistent Green's function second-order perturbation theory journal June 2014
Polynomial complexity despite the fermionic sign journal April 2017
Communication: Towards ab initio self-energy embedding theory in quantum chemistry journal December 2015
Dynamical Mean-Field Theory for Quantum Chemistry journal March 2011
Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group journal October 2006
r 12-Dependent terms in the wave function as closed sums of partial wave amplitudes for large l journal December 1985
Stability of Dirac Liquids with Strong Coulomb Interaction journal January 2017
C RYSTAL14 : A program for the ab initio investigation of crystalline solids journal March 2014
Self-Consistent Approximations in Many-Body Systems journal August 1962
Efficient Temperature-Dependent Green’s Functions Methods for Realistic Systems: Compact Grids for Orthogonal Polynomial Transforms journal January 2016
Self-consistent G W : All-electron implementation with localized basis functions journal August 2013
Coulomb and electron-phonon interactions in metals journal October 2016
Variational second-order Møller–Plesset theory based on the Luttinger–Ward functional journal April 2004
Basis-set convergence of correlated calculations on water journal June 1997
Explicitly correlated multireference configuration interaction: MRCI-F12 journal January 2011
Ground-State Energy of a Many-Fermion System. II journal June 1960
New perspectives in multireference perturbation theory: the n-electron valence state approach journal December 2006
Variational Total Energies from Φ- and Ψ- Derivable Theories journal March 1999
Bold Diagrammatic Monte Carlo Technique: When the Sign Problem Is Welcome journal December 2007
Bold Diagrammatic Monte Carlo Method Applied to Fermionized Frustrated Spins journal February 2013
Rigorous Ab Initio Quantum Embedding for Quantum Chemistry Using Green’s Function Theory: Screened Interaction, Nonlocal Self-Energy Relaxation, Orbital Basis, and Chemical Accuracy journal September 2016
Strong correlations via constrained-pairing mean-field theory journal September 2009
A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry journal May 2016
Perturbative correction for the basis set incompleteness error of complete-active-space self-consistent field journal November 2010

Similar Records

Ground-State Properties of the Hydrogen Chain: Dimerization, Insulator-to-Metal Transition, and Magnetic Phases
Journal Article · Mon Sep 14 00:00:00 EDT 2020 · Physical Review. X · OSTI ID:1395398
+14 more
Preparing quantum many-body scar states on quantum computers
Journal Article · Tue Nov 07 00:00:00 EST 2023 · Quantum · OSTI ID:1395398
+6 more
Avalanches and many-body resonances in many-body localized systems
Journal Article · Thu May 12 00:00:00 EDT 2022 · Physical Review. B · OSTI ID:1395398
+2 more

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS