Gaussian-Basis Monte Carlo Method for Numerical Study on Ground States of Itinerant and Strongly Correlated Electron Systems

Abstract

We examine Gaussian-basis Monte Carlo method (GBMC) introduced by Corney and Drummond. This method is based on an expansion of the density-matrix operator rho by means of the coherent Gaussian-type operator basis Lambda and does not suffer from the minus sign problem. The original method, however, often fails in reproducing the true ground state and causes systematic errors of calculated physical quantities because the samples are often trapped in some metastable or symmetry broken states. To overcome this difficulty, we combine the quantum-number projection scheme proposed by Assaad, Werner, Corboz, Gull and Troyer in conjunction with the importance sampling of the original GBMC method. This improvement allows us to carry out the importance sampling in the quantum-number-projected phase-space. Some comparisons with the previous quantum-number projection scheme indicate that, in our method, the convergence with the ground state is accelerated, which makes it possible to extend the applicability and widen the range of tractable parameters in the GBMC method. The present scheme offers an efficient practical way of computation for strongly correlated electron systems beyond the range of system sizes, interaction strengths and lattice structures tractable by other computational methods such as the quantum Monte Carlo method.

24 pages, 25 figures

References in corpus (11)

• Nonmagnetic Insulating States near the Mott Transitions on Lattices with Geometrical Frustration and Implications for $\kappa$-(ET)${}_2$Cu${}_2(CN{)}_3$
• Path-Integral Renormalization Group Method for Numerical Study on Ground States of Strongly Correlated Electronic Systems
• Magnetic and Metal-Insulator Transitions through Bandwidth Control in Two-Dimensional Hubbard Models with Nearest and Next-Nearest Neighbor Transfers
• Path-Integral Renormalization Group Method for Numerical Study of Strongly Correlated Electron Systems
• Quantum-number projection in the path-integral renormalization group method
• Gaussian phase-space representations for fermions
• Gaussian quantum operator representation for bosons
• Gaussian operator bases for correlated fermions
• Precise Determination of Phase Diagram for Two-Dimensional Hubbard Model with Filling- and Bandwidth-Control Mott Transitions: Grand-Canonical Path-Integral Renormalization Group Approach
• Symmetry projection schemes for Gaussian Monte Carlo methods
• Monte Carlo techniques for real-time quantum dynamics

Cited by in corpus (23)

• Variational Monte Carlo Method Combined with Quantum-Number Projection and Multi-Variable Optimization
• Electronic Structure Calculation by First Principles for Strongly Correlated Electron Systems
• Quantum Spin Liquid in Spin 1/2 J1-J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
• Does Simple Two-Dimensional Hubbard Model Account for High-Tc Superconductivity in Copper Oxides?
• Non-local pair correlations in the 1D Bose gas at finite temperature
• Cofermion Theory for Pseudogap Phenomena and Superconducting Mechanism of Underdoped Cuprate Superconductors
• Projective studies of spin nematics in a quantum frustrated ferromagnet
• Projector quantum Monte Carlo with matrix product states
• Probabilistic Q-function distributions in fermionic phase-space
• Simulation of the Dynamics of Many-Body Quantum Spin Systems Using Phase-Space Techniques
• Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method
• Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants
• Linear entropy in quantum phase space
• Phase space methods for Majorana fermions
• Gaussian phase-space representation of Fermion dynamics; Beyond the time-dependent-Hartree-Fock approximation
• Intertwined orders from symmetry projected wavefunctions of repulsively interacting Fermi gases in optical lattices
• Multi-time correlations in the positive-P, Q, and doubled phase-space representations
• Improved Multi-Variable Variational Monte Carlo Method Examined by High-Precision Calculations of One-Dimensional Hubbard Model
• Resolution of unity for fermionic Gaussian operators
• Parallel optimized sampling for stochastic equations
• Real-space renormalized dynamical mean field theory
• Simulations of quantum dynamics with fermionic phase-space representations using numerical matrix factorizations as stochastic gauges
• Coherent functional expansions in quantum field theory