# Bayesian parametric analytic continuation of Green's functions

## TL;DR

This paper introduces Bayesian parametric analytic continuation (BPAC), a method for inferring spectral functions from noisy Green's function data, providing a more reliable alternative to the maximum entropy method, especially for complex spectral structures.

## Contribution

The paper presents BPAC, a novel Bayesian approach using model comparison and nested sampling for analytic continuation of Green's functions, improving reliability over traditional methods.

## Key findings

- BPAC accurately reconstructs spectral functions from noisy data.
- BPAC can assess the support for specific spectral structures.
- Application to AIM demonstrates effectiveness in complex scenarios.

## Abstract

Bayesian parametric analytic continuation (BPAC) is proposed for the analytic continuation of noisy imaginary-time Green's function data as, e.g., obtained by continuous-time quantum Monte Carlo simulations (CTQMC). Within BPAC, the spectral function is inferred from a suitable set of parametrized basis functions. Bayesian model comparison then allows to assess the reliability of different parametrizations. The required evidence integrals of such a model comparison are determined by nested sampling. Compared to the maximum entropy method (MEM), routinely used for the analytic continuation of CTQMC data, the presented approach allows to infer whether the data support specific structures of the spectral function. We demonstrate the capability of BPAC in terms of CTQMC data for an Anderson impurity model (AIM) that shows a generalized Kondo scenario and compare the BPAC reconstruction to the MEM as well as to the spectral function obtained from the real-time fork tensor product state impurity solver where no analytic continuation is required. Furthermore, we present a combination of MEM and BPAC and its application to an AIM arising from the ab initio treatment of SrVO$_3$.