Reptation quantum Monte Carlo for lattice Hamiltonians with a directed-update scheme

TL;DR

This paper extends the reptation quantum Monte Carlo algorithm to lattice systems, introduces a systematic improvement for the sign problem, and demonstrates its effectiveness on models like the Heisenberg and Hubbard models.

Contribution

It develops a lattice-adapted reptation QMC method with a new approach to mitigate the sign problem and measures off-diagonal observables efficiently.

Findings

Accurate ground-state energy estimates for the 2D fermionic Hubbard model.

Effective systematic improvement over fixed-node approximation.

Successful application to quantum dynamics of the 1D Heisenberg model.

Abstract

We provide an extension to lattice systems of the reptation quantum Monte Carlo algorithm, originally devised for continuous Hamiltonians. For systems affected by the sign problem, a method to systematically improve upon the so-called fixed-node approximation is also proposed. The generality of the method, which also takes advantage of a canonical worm algorithm scheme to measure off-diagonal observables, makes it applicable to a vast variety of quantum systems and eases the study of their ground-state and excited-states properties. As a case study, we investigate the quantum dynamics of the one-dimensional Heisenberg model and we provide accurate estimates of the ground-state energy of the two-dimensional fermionic Hubbard model.