Test of variational approximation for +4 quantum chain by Monte Carlo simulation

We report results of a Monte Carlo simulation of the @4 quantum chain. In order to enhance the efficiency of the simulation we combine muItig~d 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 va~ational ansatz. While the variational approximation is well reproduced for a large range of parameters we find significant deviations for low temperatures and iarge couplings.