Monte Carlo simulation of $1+1$-dimensional $\phi^4$ quantum field theory

TL;DR

This paper presents a Monte Carlo simulation of 1+1 dimensional phi^4 quantum field theory using advanced techniques, providing precise data that tests and reveals limitations of an analytical variational approximation.

Contribution

It introduces a refined simulation approach and provides high-accuracy data to evaluate the validity of a variational approximation in phi^4 theory.

Findings

Variational approximation matches data for many parameters

Deviations observed at low temperatures and high couplings

Simulation techniques improve accuracy of quantum field theory analysis

Abstract

We report results of a Monte Carlo simulation of the $\phi^4$ quantum field theory using multigrid simulation techniques and a refined discretization scheme. The resulting accuracy of our data allows for a significant test of an analytical approximation based on a variational ansatz. While the variational approximation is well reproduced for a large range of parameters we find significant deviations for low temperatures and large couplings.