Coupling quantum Monte Carlo and independent-particle calculations: self-consistent constraint for the sign problem based on density or density matrix

Abstract

Quantum Monte Carlo (QMC) methods are one of the most important tools for studying interacting quantum many-body systems. The vast majority of QMC calculations in interacting fermion systems require a constraint to control the sign problem. The constraint involves an input trial wave function which restricts the random walks. We introduce a systematically improvable constraint which relies on the fundamental role of the density or one-body density matrix. An independent-particle calculation is coupled to an auxiliary-field QMC calculation. The independent-particle solution is used as the constraint in QMC, which then produces the input density or density matrix for the next iteration. The constraint is optimized by the self-consistency between the many-body and independent-particle calculations. The approach is demonstrated in the two-dimensional Hubbard model by accurately determining the ground state when collective modes separated by tiny energy scales are present in the magnetic and charge correlations. Our approach also provides an ab initio way to predict effective interaction parameters for independent-particle calculations.

Published version, 6 pages, 4 figures

References in corpus (6)

• Continuous-time Monte Carlo methods for quantum impurity models
• Applications of quantum Monte Carlo methods in condensed systems
• Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis
• Spatially inhomogeneous phase in the two-dimensional repulsive Hubbard model
• Quantum Monte Carlo calculations in solids with downfolded Hamiltonians
• Electronic Origin of the Volume Collapse in Cerium

Cited by in corpus (8)

• Plaquette versus ordinary $d$-wave pairing in the $t^{\prime }$-Hubbard model on a width 4 cylinder
• Stripes and spin-density waves in the doped two-dimensional Hubbard model: ground state phase diagram
• Computation of ground-state properties in molecular systems: back-propagation with auxiliary-field quantum Monte Carlo
• Hamiltonian symmetries in auxiliary-field quantum Monte Carlo calculations for electronic structure
• Constrained-Path Auxiliary-Field Quantum Monte Carlo for Coupled Electrons and Phonons
• Benchmark study of an auxiliary-field quantum Monte Carlo technique for the Hubbard model with shifted-discrete Hubbard-Stratonovich transformations
• Numerical results on the short-range spin correlation functions in the ground state of the two-dimensional Hubbard model
• Combination of Tensor Network States and Green's function Monte Carlo