Stochastic method for analytic continuation of quantum Monte Carlo data

Abstract

A method for analytic continuation of quantum Monte Carlo data is presented. The spectrum $A(\ensuremath{\omega})$ is parametrized as a sum of $\ensuremath{\delta}$ functions, the weights ${A}_{i}$ of which are sampled according to a distribution $p(A)\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}{\ensuremath{\chi}}^{2}/\ensuremath{\Theta})$. It is argued that the calculated entropy $S$ provides a criterion for determining the $\ensuremath{\Theta}$ corresponding to the ``best'' averaged spectrum. The appearance of spurious structure is signaled by a sharp drop in $〈S(\ensuremath{\Theta})〉$, 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.