Statistical and computational intelligence approach to analytic continuation in Quantum Monte Carlo

TL;DR

This paper reviews a genetic algorithm-based method for performing analytic continuation in quantum Monte Carlo simulations, enabling accurate inference of real-time properties from imaginary-time data in strongly correlated quantum systems.

Contribution

It introduces and pedagogically explains the Genetic Inversion via Falsification of Theories method for analytic continuation, applicable across various scientific fields.

Findings

High-accuracy computation of dynamical properties in quantum many-body systems

General framework applicable to multiple areas of applied science

Effective extension of imaginary-time data to the complex plane

Abstract

The term analytic continuation emerges in many branches of Mathematics, Physics, and, more generally, applied Science. Generally speaking, in many situations, given some amount of information that could arise from experimental or numerical measurements, one is interested in extending the domain of such information, to infer the values of some variables which are central for the study of a given problem. For example, focusing on Condensed Matter Physics, state-of-the-art methodologies to study strongly correlated quantum physical systems are able to yield accurate estimations of dynamical correlations in imaginary time. Those functions have to be extended to the whole complex plane, via analytic continuation, in order to infer real-time properties of those physical systems. In this Review, we will present the Genetic Inversion via Falsification of Theories method, which allowed us to compute dynamical properties of strongly interacting quantum many--body systems with very high accuracy. Even though the method arose in the realm of Condensed Matter Physics, it provides a very general framework to face analytic continuation problems that could emerge in several areas of applied Science. Here we provide a pedagogical review that elucidates the approach we have developed.