Non-perturbative False Vacuum Decay Using Lattice Monte Carlo in Imaginary Time

TL;DR

This paper introduces a non-perturbative lattice Monte Carlo method in imaginary time to accurately compute false vacuum decay rates, applicable to quantum field theories and complex systems.

Contribution

It develops a novel lattice Monte Carlo approach with a new decay rate formula and sampling technique for non-perturbative false vacuum decay analysis.

Findings

Successfully reproduces tunneling rates in 1D quantum systems

Provides a new formula similar to Fermi's Golden Rule for decay rates

Introduces a sampling method to handle vacuum suppression in Euclidean path integrals

Abstract

We present a new method for calculating quantum tunneling rates using lattice Monte Carlo simulations in imaginary time. This method is designed with the goal of studying false vacuum decay non-perturbatively on the lattice. We derive a new formula, which is similar in form to Fermi's Golden Rule, which gives the decay rate in terms of an implicit decay amplitude. We then show how to calculate this implicit decay amplitude on the lattice. To deal with the suppression of the false vacuum state in the Euclidean path integral, we develop a new sampling method which combines results from multiple Monte Carlo simulations. For a simple family of one-dimensional quantum systems, we reproduce the tunneling rates calculated from the Schrodinger equation.