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

Abstract

We report results of a Monte Carlo simulation of the $ϕ^4$ 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.