A Constrained Path Monte Carlo Method for Fermion Ground States

TL;DR

This paper introduces a constrained path Monte Carlo algorithm for accurately computing the ground states of interacting fermion systems, effectively mitigating the sign problem through a trial wave function constraint.

Contribution

The paper presents a new quantum Monte Carlo method that constrains the path to eliminate the sign problem, enabling precise ground-state calculations for large fermionic systems.

Findings

Accurate ground-state energies for 2D Hubbard model up to 16x16 lattice.

Reliable estimates of ground-state observables like pairing correlations.

Method effectively reduces the sign problem in fermionic quantum Monte Carlo simulations.

Abstract

We describe and discuss a recently proposed quantum Monte Carlo algorithm to compute the ground-state properties of various systems of interacting fermions. In this method, the ground state is projected from an initial wave function by a branching random walk in an over-complete basis of Slater determinants. By constraining the determinants according to a trial wave function $|\psi_T\rangle$, 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 illustrate the method by describing in detail its implementation for the two-dimensional one-band Hubbard model. We show results for lattice sizes up to $16\times 16$ and for various electron fillings and interaction strengths. Besides highly accurate estimates of the ground-state energy, we find that the method also yields reliable estimates of other ground-state observables, such as superconducting pairing correlation functions. We conclude by discussing possible extensions of the algorithm.