Tunneling problems by quantum Monte Carlo

TL;DR

This paper introduces a novel quantum Monte Carlo method capable of accurately computing extremely small tunneling amplitudes in both single-particle and many-body quantum systems, overcoming previous numerical limitations.

Contribution

The authors develop a new numerical scheme that precisely solves tunneling problems and directly computes instanton shapes and amplitudes with arbitrary accuracy.

Findings

Accurately computes exponentially small tunneling amplitudes

Works for both single-particle and many-body systems

Provides direct access to instanton configurations

Abstract

We develop a new numerical scheme which allows precise solution of coherent tunneling problems, i.e., problems with exponentially small transition amplitudes between quasidegenerate states. We explain how this method works for the single-particle (tunneling in the double-well potential) and many-body systems (e.g., vacuum-to-vacuum transitions), and gives directly the instanton shape and tunneling amplitude. Most importantly, transition amplitudes may be calculated to arbitrary accuracy (being limited solely by statistical errors) no matter how small are their absolute values.