Flat histogram quantum Monte Carlo for analytic continuation to real time

Abstract

The Quantum Monte Carlo (QMC) method can yield the imaginary-time dependence of a correlation function $C(\tau )$ of an operator $\hat{O}$. The analytic continuation to real-time proceeds by means of a "numerical inversion" of these data to find the response function or spectral density $A(\omega )$ corresponding to $\hat{O}$. Such a technique is very sensitive to the statistical errors in $C(\tau )$ especially for large values of $\tau$, when we are interested in the low-energy excitations. In this paper, we find that if we use the flat histogram technique in the QMC method, in such a way to make the {\it histogram of} $C(\tau )$ flat, the results of the analytic continuation for low-energy excitations improve using the same amount of computational time. To demonstrate the idea we select an exactly soluble version of the single-hole motion in the $t-J$ model and the diagrammatic Monte Carlo technique.

10 latex two column pages, 4 figures with subfigures