A quantum Monte Carlo algorithm for arbitrary spin-1/2 Hamiltonians

TL;DR

This paper introduces a universal, parameter-free quantum Monte Carlo algorithm capable of simulating any spin-1/2 Hamiltonian with guaranteed ergodicity and detailed balance, demonstrated on various models.

Contribution

The authors develop a new, automated QMC algorithm that is universally applicable to spin-1/2 systems, ensuring convergence and ergodicity without parameter tuning.

Findings

Successfully simulates XY model on a triangular lattice

Able to simulate the toric code and random k-local Hamiltonians

Code is publicly available on GitHub

Abstract

We present a universal parameter-free quantum Monte Carlo (QMC) algorithm designed to simulate arbitrary spin-$1/2$ Hamiltonians. To ensure the convergence of the Markov chain to equilibrium for every conceivable case, we devise a clear and simple automated protocol that produces QMC updates that are provably ergodic and satisfy detailed balance. We demonstrate the applicability and versatility of our method by considering several illustrative examples, including the simulation of the XY model on a triangular lattice, the toric code, and random $k$-local Hamiltonians. We have made our program code freely accessible on GitHub.