Flat histogram quantum Monte Carlo for analytic continuation to real time

The Quantum Monte Carlo (QMC) method can yield the imaginary-time dependence of a correlation function $C(τ)$ 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 $A(ω)$ corresponding to $\hat O$. Such a technique is very sensitive to the statistical errors in $C(τ)$ especially for large values of $τ$, 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} $C(τ)$ 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.

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