Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases

Reboredo, Fernando A.; Kim, Jeongnim

doi:10.1063/1.4861222

Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases

Journal Article · Thu Feb 20 23:00:00 EST 2014 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4861222· OSTI ID:1127367

Reboredo, Fernando A.; Kim, Jeongnim

The self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo J. Chem. Phys. {\bf 136}, 204101 (2012)] and some ideas of the correlation function Monte Carlo approach [D. M. Ceperley and B. Bernu, J. Chem. Phys. {\bf 89}, 6316 (1988)] are blended to obtain a method for the calculation of thermodynamic properties of many-body systems at low temperatures. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric trial wave functions. A statistical method is derived for the calculation of finite temperature properties of many-body systems near the ground state. In the process we also obtain a parallel algorithm that optimizes the many-body basis of a small subspace of the many-body Hilbert space. This small subspace is optimized to have maximum overlap with the one expanded by the lower energy eigenstates of a many-body Hamiltonian. We show in a model system that the Helmholtz free energy is minimized within this subspace as the iteration number increases. We show that the subspace expanded by the small basis systematically converges towards the subspace expanded by the lowest energy eigenstates. Possible applications of this method to calculate the thermodynamic properties of many-body systems near the ground state are discussed. The resulting basis can be also used to accelerate the calculation of the ground or excited states with Quantum Monte Carlo.

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE

DOE Contract Number:: AC05-00OR22725

OSTI ID:: 1127367

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 7 Vol. 140; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

References (58)

Isomerization Through Conical Intersections Levine, Benjamin G.; Martínez, Todd J. Annual Review of Physical Chemistry, Vol. 58, Issue 1 https://doi.org/10.1146/annurev.physchem.57.032905.104612	journal	May 2007
Quantum Monte Carlo and Related Approaches Austin, Brian M.; Zubarev, Dmitry Yu.; Lester, William A. Chemical Reviews, Vol. 112, Issue 1 https://doi.org/10.1021/cr2001564	journal	December 2011
The calculation of excited states with quantum Monte Carlo. II. Vibrational excited states Bernu, B.; Ceperley, D. M.; Lester, W. A. The Journal of Chemical Physics, Vol. 93, Issue 1 https://doi.org/10.1063/1.459555	journal	July 1990
Core Structure of a Vortex in Superfluid He 4 Ortiz, Gerardo; Ceperley, David M. Physical Review Letters, Vol. 75, Issue 25 https://doi.org/10.1103/PhysRevLett.75.4642	journal	December 1995
Electronic structure of metallic ferromagnets above the Curie temperature Staunton, J.; Gyorffy, B. L.; Pindor, A. J. Journal of Physics F: Metal Physics, Vol. 15, Issue 6 https://doi.org/10.1088/0305-4608/15/6/019	journal	June 1985
Density-density functionals and effective potentials in many-body electronic structure calculations Reboredo, F. A.; Kent, P. R. C. Physical Review B, Vol. 77, Issue 24 https://doi.org/10.1103/PhysRevB.77.245110	journal	June 2008
Absorption Spectrum of the Green Fluorescent Protein Chromophore: A Difficult Case for ab Initio Methods? Filippi, Claudia; Zaccheddu, Maurizio; Buda, Francesco Journal of Chemical Theory and Computation, Vol. 5, Issue 8 https://doi.org/10.1021/ct900227j	journal	July 2009
Alleviation of the Fermion-Sign Problem by Optimization of Many-Body Wave Functions Umrigar, C. J.; Toulouse, Julien; Filippi, Claudia Physical Review Letters, Vol. 98, Issue 11 https://doi.org/10.1103/PhysRevLett.98.110201	journal	March 2007
Self-healing diffusion quantum Monte Carlo algorithms: Direct reduction of the fermion sign error in electronic structure calculations Reboredo, F. A.; Hood, R. Q.; Kent, P. R. C. Physical Review B, Vol. 79, Issue 19 https://doi.org/10.1103/PhysRevB.79.195117	journal	May 2009
Path integrals in the theory of condensed helium Ceperley, D. M. Reviews of Modern Physics, Vol. 67, Issue 2 https://doi.org/10.1103/RevModPhys.67.279	journal	April 1995
Density-Functional Theory for Time-Dependent Systems Runge, Erich; Gross, E. K. U. Physical Review Letters, Vol. 52, Issue 12 https://doi.org/10.1103/PhysRevLett.52.997	journal	March 1984
Order- N Multiple Scattering Approach to Electronic Structure Calculations Wang, Yang; Stocks, G. M.; Shelton, W. A. Physical Review Letters, Vol. 75, Issue 15 https://doi.org/10.1103/PhysRevLett.75.2867	journal	October 1995
Towards an exact description of electronic wavefunctions in real solids Booth, George H.; Grüneis, Andreas; Kresse, Georg Nature, Vol. 493, Issue 7432 https://doi.org/10.1038/nature11770	journal	December 2012
A fast and efficient algorithm for Slater determinant updates in quantum Monte Carlo simulations Nukala, Phani K. V. V.; Kent, P. R. C. The Journal of Chemical Physics, Vol. 130, Issue 20 https://doi.org/10.1063/1.3142703	journal	May 2009
Quantum chemistry by random walk: H4 square Anderson, James B. International Journal of Quantum Chemistry, Vol. 15, Issue 1 https://doi.org/10.1002/qua.560150111	journal	January 1979
The “disordered local moment” picture of itinerant magnetism at finite temperatures Staunton, J.; Gyorffy, B. L.; Pindor, A. J. Journal of Magnetism and Magnetic Materials, Vol. 45, Issue 1 https://doi.org/10.1016/0304-8853(84)90367-6	journal	November 1984
Fractional occupations and density-functional energies and forces Weinert, M.; Davenport, J. W. Physical Review B, Vol. 45, Issue 23 https://doi.org/10.1103/PhysRevB.45.13709	journal	June 1992
Released-phase quantum Monte Carlo method Jones, Matthew D.; Ortiz, Gerardo; Ceperley, David M. Physical Review E, Vol. 55, Issue 5 https://doi.org/10.1103/PhysRevE.55.6202	journal	May 1997
High Accuracy Molecular Heats of Formation and Reaction Barriers: Essential Role of Electron Correlation Grossman, Jeffrey C.; Mitas, Lubos Physical Review Letters, Vol. 79, Issue 22 https://doi.org/10.1103/PhysRevLett.79.4353	journal	December 1997
Self-Consistent Equations Including Exchange and Correlation Effects Kohn, W.; Sham, L. J. Physical Review, Vol. 140, Issue 4A, p. A1133-A1138 https://doi.org/10.1103/PhysRev.140.A1133	journal	November 1965
Implications of the two nodal domains conjecture for ground state fermionic wave functions Bressanini, Dario Physical Review B, Vol. 86, Issue 11 https://doi.org/10.1103/PhysRevB.86.115120	journal	September 2012
Minimum energy pathways via quantum Monte Carlo Saccani, S.; Filippi, C.; Moroni, S. The Journal of Chemical Physics, Vol. 138, Issue 8 https://doi.org/10.1063/1.4792717	journal	February 2013
Fixed‐node quantum Monte Carlo for molecules ^a) b) Reynolds, Peter J.; Ceperley, David M.; Alder, Berni J. The Journal of Chemical Physics, Vol. 77, Issue 11 https://doi.org/10.1063/1.443766	journal	December 1982
A diffusion Monte Carlo algorithm with very small time‐step errors Umrigar, C. J.; Nightingale, M. P.; Runge, K. J. The Journal of Chemical Physics, Vol. 99, Issue 4 https://doi.org/10.1063/1.465195	journal	August 1993
Fermion nodes Ceperley, D. M. Journal of Statistical Physics, Vol. 63, Issue 5-6 https://doi.org/10.1007/BF01030009	journal	June 1991
Many-body calculations of low-energy eigenstates in magnetic and periodic systems with self-healing diffusion Monte Carlo: Steps beyond the fixed phase Reboredo, Fernando Agustín The Journal of Chemical Physics, Vol. 136, Issue 20 https://doi.org/10.1063/1.4711023	journal	May 2012
Inhomogeneous backflow transformations in quantum Monte Carlo calculations López Ríos, P.; Ma, A.; Drummond, N. D. Physical Review E, Vol. 74, Issue 6 https://doi.org/10.1103/PhysRevE.74.066701	journal	December 2006
Systematic reduction of sign errors in many-body problems: Generalization of self-healing diffusion Monte Carlo to excited states Reboredo, Fernando Agustín Physical Review B, Vol. 80, Issue 12 https://doi.org/10.1103/PhysRevB.80.125110	journal	September 2009
Diffusion Monte Carlo: Exponential scaling of computational cost for large systems Nemec, Norbert Physical Review B, Vol. 81, Issue 3 https://doi.org/10.1103/PhysRevB.81.035119	journal	January 2010
Finite-temperature electronic simulations without the Born-Oppenheimer constraint Mazzola, Guglielmo; Zen, Andrea; Sorella, Sandro The Journal of Chemical Physics, Vol. 137, Issue 13 https://doi.org/10.1063/1.4755992	journal	October 2012
All-Electron Path Integral Monte Carlo Simulations of Warm Dense Matter: Application to Water and Carbon Plasmas Driver, K. P.; Militzer, B. Physical Review Letters, Vol. 108, Issue 11 https://doi.org/10.1103/PhysRevLett.108.115502	journal	March 2012
Impact of electron density on the fixed-node errors in Quantum Monte Carlo of atomic systems Rasch, K. M.; Mitas, L. Chemical Physics Letters, Vol. 528 https://doi.org/10.1016/j.cplett.2012.01.016	journal	March 2012
Ground State of the Electron Gas by a Stochastic Method Ceperley, D. M.; Alder, B. J. Physical Review Letters, Vol. 45, Issue 7, p. 566-569 https://doi.org/10.1103/PhysRevLett.45.566	journal	August 1980
Delayed rejection variational Monte Carlo Bressanini, Dario; Morosi, Gabriele; Tarasco, Silvia The Journal of Chemical Physics, Vol. 121, Issue 8 https://doi.org/10.1063/1.1775789	journal	August 2004
A first-principles theory of ferromagnetic phase transitions in metals Gyorffy, B. L.; Pindor, A. J.; Staunton, J. Journal of Physics F: Metal Physics, Vol. 15, Issue 6 https://doi.org/10.1088/0305-4608/15/6/018	journal	June 1985
Effect of lattice vibrations on magnetic phase transition in bcc iron Yin, Junqi; Eisenbach, Markus; Nicholson, Don M. Physical Review B, Vol. 86, Issue 21 https://doi.org/10.1103/PhysRevB.86.214423	journal	December 2012
Electronic excitations: density-functional versus many-body Green’s-function approaches Onida, Giovanni; Reining, Lucia; Rubio, Angel Reviews of Modern Physics, Vol. 74, Issue 2 https://doi.org/10.1103/RevModPhys.74.601	journal	June 2002
Fixed-phase correlation-function quantum Monte Carlo calculations for ground and excited states of helium in neutron-star magnetic fields Meyer, Dirk; Boblest, Sebastian; Wunner, Günter Physical Review A, Vol. 87, Issue 3 https://doi.org/10.1103/PhysRevA.87.032515	journal	March 2013
Thermal Properties of the Inhomogeneous Electron Gas Mermin, N. David Physical Review, Vol. 137, Issue 5A https://doi.org/10.1103/PhysRev.137.A1441	journal	March 1965
New Transcorrelated Method Improving the Feasibility of Explicitly Correlated Calculations Ten-no, Seiichiro; Hino, Osamu International Journal of Molecular Sciences, Vol. 3, Issue 5 https://doi.org/10.3390/i3050459	journal	May 2002
Pfaffian pairing and backflow wavefunctions for electronic structure quantum Monte Carlo methods Bajdich, M.; Mitas, L.; Wagner, L. K. Physical Review B, Vol. 77, Issue 11 https://doi.org/10.1103/PhysRevB.77.115112	journal	March 2008
Path Integral Monte Carlo Calculation of the Deuterium Hugoniot Militzer, B.; Ceperley, D. M. Physical Review Letters, Vol. 85, Issue 9 https://doi.org/10.1103/PhysRevLett.85.1890	journal	August 2000
Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: Potential energy curves of low-lying C2 singlet states Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry The Journal of Chemical Physics, Vol. 130, Issue 9 https://doi.org/10.1063/1.3077920	journal	March 2009
Nonlocal pseudopotentials and diffusion Monte Carlo Mitáš, Luboš; Shirley, Eric L.; Ceperley, David M. The Journal of Chemical Physics, Vol. 95, Issue 5 https://doi.org/10.1063/1.460849	journal	September 1991
Composite-fermion antiparticle description of the hole excitation in a maximum-density droplet with a small number of electrons Jeon, Gun Sang; Güçlü, A. D.; Umrigar, C. J. Physical Review B, Vol. 72, Issue 24 https://doi.org/10.1103/PhysRevB.72.245312	journal	December 2005
Quantum Monte Carlo Calculations of Electronic Excitation Energies: The Case of the Singlet n→π∗ (CO) Transition in Acrolein Toulouse, Julien; Caffarel, Michel; Reinhardt, Peter Advances in the Theory of Quantum Systems in Chemistry and Physics https://doi.org/10.1007/978-94-007-2076-3_19	book	September 2011
New stochastic method for systems with broken time-reversal symmetry: 2D fermions in a magnetic field Ortiz, G.; Ceperley, D. M.; Martin, R. M. Physical Review Letters, Vol. 71, Issue 17 https://doi.org/10.1103/PhysRevLett.71.2777	journal	October 1993
Molecular Dissociation in Hot, Dense Hydrogen Magro, W. R.; Ceperley, D. M.; Pierleoni, C. Physical Review Letters, Vol. 76, Issue 8 https://doi.org/10.1103/PhysRevLett.76.1240	journal	February 1996
Systematic Reduction of Sign Errors in Many-Body Calculations of Atoms and Molecules Bajdich, Michal; Tiago, Murilo L.; Hood, Randolph Q. Physical Review Letters, Vol. 104, Issue 19 https://doi.org/10.1103/PhysRevLett.104.193001	journal	May 2010
Approaching chemical accuracy with quantum Monte Carlo Petruzielo, F. R.; Toulouse, Julien; Umrigar, C. J. The Journal of Chemical Physics, Vol. 136, Issue 12 https://doi.org/10.1063/1.3697846	journal	March 2012
Full optimization of Jastrow–Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules Toulouse, Julien; Umrigar, C. J. The Journal of Chemical Physics, Vol. 128, Issue 17 https://doi.org/10.1063/1.2908237	journal	May 2008
Inhomogeneous Electron Gas Hohenberg, P.; Kohn, W. Physical Review, Vol. 136, Issue 3B, p. B864-B871 https://doi.org/10.1103/PhysRev.136.B864	journal	November 1964
A new approach to Monte Carlo simulations in statistical physics: Wang-Landau sampling Landau, D. P.; Tsai, Shan-Ho; Exler, M. American Journal of Physics, Vol. 72, Issue 10 https://doi.org/10.1119/1.1707017	journal	October 2004
Monte Carlo Methods in Ab Initio Quantum Chemistry Hammond, B. L.; Lester, Jr., W. A.; Reynolds, P. J. World Scientific Lecture and Course Notes in Chemistry , Vol. 1 https://doi.org/10.1142/9789814317245	book	March 1994
Computing the energy of a water molecule using multideterminants: A simple, efficient algorithm Clark, Bryan K.; Morales, Miguel A.; McMinis, Jeremy The Journal of Chemical Physics, Vol. 135, Issue 24 https://doi.org/10.1063/1.3665391	journal	December 2011
On the eigenfunctions of many-particle systems in quantum mechanics Kato, Tosio Communications on Pure and Applied Mathematics, Vol. 10, Issue 2 https://doi.org/10.1002/cpa.3160100201	journal	January 1957
Equation of state of metallic hydrogen from coupled electron-ion Monte Carlo simulations Morales, Miguel A.; Pierleoni, Carlo; Ceperley, D. M. Physical Review E, Vol. 81, Issue 2 https://doi.org/10.1103/PhysRevE.81.021202	journal	February 2010
Quantum Monte Carlo simulations of solids Foulkes, W. M. C.; Mitas, L.; Needs, R. J. Reviews of Modern Physics, Vol. 73, Issue 1 https://doi.org/10.1103/RevModPhys.73.33	journal	January 2001

Similar Records

Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases

Journal Article · Thu Feb 20 23:00:00 EST 2014 · Journal of Chemical Physics · OSTI ID:22255091

Many-body calculations of low energy eigenstates in magnetic and periodic systems with self healing diffusion Monte Carlo: steps beyond the fixed-phase

Journal Article · Tue May 01 00:00:00 EDT 2012 · The Journal of Chemical Physics · OSTI ID:1041067

Excited states from quantum Monte Carlo in the basis of Slater determinants

Journal Article · Thu Nov 20 23:00:00 EST 2014 · Journal of Chemical Physics · OSTI ID:22415365

Related Subjects

Monte Carlo methods finite temperature

Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases

Citation Formats

References (58)

Similar Records

Related Subjects