Stochastic method for analytic continuation of quantum Monte Carlo data

A method for analytic continuation of quantum Monte Carlo data is presented. The spectrum $A\left(\omega \right)$ is parametrized as a sum of $\delta$ functions, the weights $A_i$ of which are sampled according to a distribution $p\left(A\right)\mathrm{}\sim \exp (-{\chi }^2/\Theta )$. It is argued that the calculated entropy $S$ provides a criterion for determining the $\Theta$ corresponding to the “best” averaged spectrum. The appearance of spurious structure is signaled by a sharp drop in $〈S\left(\Theta \right)〉$, which in test cases is preceded by a local maximum. Results for the dynamic spin structure factor of a $16$-site Heisenberg chain obtained at this maximum are in better agreement with exact results than “classic” maximum-entropy results.