# Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo data

## TL;DR

This paper introduces a sparse modeling regularization method for stable analytical continuation of noisy imaginary-time quantum Monte Carlo data, improving spectral resolution and data accuracy requirements.

## Contribution

It presents a novel sparse modeling approach that effectively regularizes the ill-conditioned inverse problem in analytical continuation, enhancing stability and spectral detail resolution.

## Key findings

- Stable spectral reconstructions with noisy data
- Reduced data accuracy needed for spectral detail resolution
- Effective elimination of noise-carrying degrees of freedom

## Abstract

A new approach of solving the ill-conditioned inverse problem for analytical continuation is proposed. The root of the problem lies in the fact that even tiny noise of imaginary-time input data has a serious impact on the inferred real-frequency spectra. By means of a modern regularization technique, we eliminate redundant degrees of freedom that essentially carry the noise, leaving only relevant information unaffected by the noise. The resultant spectrum is represented with minimal bases and thus a stable analytical continuation is achieved. This framework further provides a tool for analyzing to what extent the Monte Carlo data need to be accurate to resolve details of an expected spectral function.