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

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.

18 pages, 8 figures

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• Advanced measurement techniques in quantum Monte Carlo: The permutation matrix representation approach
• A quantum Monte Carlo algorithm for arbitrary high-spin Hamiltonians