A Constrained Path Quantum Monte Carlo Method for Fermion Ground States

TL;DR

This paper introduces a new quantum Monte Carlo algorithm that effectively computes fermion ground states by constraining the sign problem, demonstrating its accuracy on large 2D Hubbard models with various parameters.

Contribution

The paper presents a constrained path quantum Monte Carlo method that mitigates the sign problem and is exact with an exact trial wavefunction, applied to large-scale fermionic systems.

Findings

Successfully computed ground states of 16x16 Hubbard model

Reduced sign problem via determinant constraints

Achieved accurate results across different fillings and interactions

Abstract

We propose a new quantum Monte Carlo algorithm to compute fermion ground-state properties. The ground state is projected from an initial wavefunction by a branching random walk in an over-complete basis space of Slater determinants. By constraining the determinants according to a trial wavefunction $|\Psi_T \rangle$, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if $|\Psi_T\rangle$ is exact. We report results on the two-dimensional Hubbard model up to size $16\times 16$, for various electron fillings and interaction strengths.