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

TL;DR

This paper introduces a self-consistent method coupling quantum Monte Carlo with independent-particle calculations, using density matrices to control the sign problem and accurately determine ground states in complex quantum systems.

Contribution

A novel, systematically improvable constraint based on density matrices that self-consistently couples QMC with independent-particle calculations to address the sign problem.

Findings

Accurately determines ground states in the 2D Hubbard model.

Provides an ab initio method to predict effective interaction parameters.

Demonstrates improved control of the sign problem in fermionic systems.

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.