Simulating `Complex' Problems with Quantum Monte Carlo

TL;DR

This paper introduces a quantum Monte Carlo algorithm designed for complex problems, demonstrating how gauge choices and phase cancellations can significantly reduce statistical noise in simulations involving magnetic fields and anyons.

Contribution

The paper presents a novel quantum Monte Carlo method that effectively handles complex systems by leveraging gauge choices and phase cancellation techniques.

Findings

Gauge choice impacts statistical noise reduction.

Phase cancellations between fluxes improve simulation accuracy.

Method applicable to systems with external magnetic fields and anyons.

Abstract

We present a new quantum Monte Carlo algorithm suitable for generically complex problems, such as systems coupled to external magnetic fields or anyons in two spatial dimensions. We find that the choice of gauge plays a nontrivial role, and can be used to reduce statistical noise in the simulation. Furthermore, it is found that noise can be greatly reduced by approximate cancellations between the phases of the (gauge dependent) statistical flux and the external magnetic flux.