Flat histogram quantum Monte Carlo for analytic continuation to real time

TL;DR

This paper introduces a flat histogram quantum Monte Carlo approach that enhances the accuracy of analytic continuation to real-time by reducing statistical errors in low-energy excitation data.

Contribution

The paper proposes using a flat histogram technique in QMC to improve the analytic continuation process for low-energy excitations.

Findings

Flat histogram QMC improves low-energy spectral density results.

Enhanced analytic continuation accuracy with same computational effort.

Validated on exactly solvable t-J model and diagrammatic Monte Carlo.

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.