The role of winding numbers in quantum Monte Carlo simulations

TL;DR

This paper investigates how fixing winding numbers in quantum Monte Carlo simulations affects results, showing that exact ground state properties can be obtained without winding number fluctuations, especially in larger systems.

Contribution

It provides a geometric argument and numerical evidence that fixing winding numbers yields exact ground state results in periodic boundary conditions, with implications for simulation accuracy.

Findings

Exact ground state results achievable without winding number fluctuations

Deviation scales as temperature to the power gamma, depending on model and observable

Larger systems show reduced deviation, improving accuracy

Abstract

We discuss the effects of fixing the winding number in quantum Monte Carlo simulations. We present a simple geometrical argument as well as strong numerical evidence that one can obtain exact ground state results for periodic boundary conditions without changing the winding number. However, for very small systems the temperature has to be considerably lower than in simulations with fluctuating winding numbers. The relative deviation of a calculated observable from the exact ground state result typically scales as $T^{\gamma}$, where the exponent $\gamma$ is model and observable dependent and the prefactor decreases with increasing system size. Analytic results for a quantum rotor model further support our claim.