Combining Bayesian reconstruction entropy with maximum entropy method for analytic continuations of matrix-valued Green's functions

TL;DR

This paper introduces an extension of Bayesian reconstruction entropy for spectral function reconstruction in quantum many-body physics, demonstrating improved noise resilience and applicability to matrix-valued Green's functions.

Contribution

It extends Bayesian reconstruction entropy to matrix-valued Green's functions and integrates it with the positive-negative entropy algorithm for analytic continuation.

Findings

Comparable performance to Shannon-Jaynes entropy with preblur trick

Greater resilience to moderate noise levels in input data

Effective for both diagonal and off-diagonal matrix components

Abstract

The Bayesian reconstruction entropy is considered an alternative to the Shannon-Jaynes entropy, as it does not exhibit the asymptotic flatness characteristic of the Shannon-Jaynes entropy and obeys the scale invariance. It is commonly utilized in conjunction with the maximum entropy method to derive spectral functions from Euclidean time correlators produced by lattice QCD simulations. This study expands the application of the Bayesian reconstruction entropy to the reconstruction of spectral functions for Matsubara or imaginary-time Green's functions in quantum many-body physics. Furthermore, it extends the Bayesian reconstruction entropy to implement the positive-negative entropy algorithm, enabling the analytic continuations of matrix-valued Green's functions on an element-wise manner. Both the diagonal and off-diagonal components of the matrix-valued Green's functions are treated equally. Benchmark results for the analytic continuations of synthetic Green's functions indicate that the Bayesian reconstruction entropy, when combined with the preblur trick, demonstrates comparable performance to the Shannon-Jaynes entropy. Notably, it exhibits greater resilience to noises in the input data, particularly when the noise level is moderate.