Test of variational approximation for $phi^4$ quantum chain by Monte Carlo simulation

TL;DR

This paper uses Monte Carlo simulations with advanced techniques to test the accuracy of a variational approximation in the $$ quantum chain, revealing its strengths and limitations across different parameters.

Contribution

It introduces a combined multigrid and refined discretization Monte Carlo method to accurately test a variational approximation in the $$ quantum chain.

Findings

Variational approximation matches well for many parameters.

Significant deviations occur at low temperatures and high couplings.

Enhanced simulation techniques improve accuracy of quantum chain analysis.

Abstract

We report results of a Monte Carlo simulation of the $\phi^4$ quantum chain. In order to enhance the efficiency of the simulation we combine multigrid simulation techniques with 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.