Exact Quantum Monte Carlo Process for the Statistics of Discrete Systems

TL;DR

This paper presents an exact Monte Carlo method for analyzing discrete quantum systems, avoiding traditional approximations and utilizing local procedures based on exact solutions for two-level systems.

Contribution

It introduces a novel Monte Carlo approach that directly computes statistics of discrete quantum systems without fragmentation or small parameters.

Findings

Method accurately reproduces kink statistics in quantum systems.

Eliminates the need for imaginary time fragmentation.

Provides a local procedure based on exact two-level system solutions.

Abstract

We introduce an exact Monte Carlo approach to the statistics of discrete quantum systems which does not rely on the standard fragmentation of the imaginary time, or any small parameter. The method deals with discrete objects, kinks, representing virtual transitions at different moments of time. The global statistics of kinks is reproduced by explicit local procedures, the key one being based on the exact solution for the biased two-level system.