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 respon
se 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.
The diagrammatic Monte Carlo (Diag-MC) method is a numerical technique which samples the entire diagrammatic series of the Greens function in quantum many-body systems. In this work, we incorporate the flat histogram principle in the diagrammatic Mon
te method and we term the improved version Flat Histogram Diagrammatic Monte Carlo method. We demonstrate the superiority of the method over the standard Diag-MC in extracting the long-imaginary-time behavior of the Greens function, without incorporating any a priori knowledge about this function, by applying the technique to the polaron problem
