Machine learning effective models for quantum systems

TL;DR

This paper introduces a machine learning approach to optimize effective models for complex quantum systems, successfully applying it to impurity models and exploring observable-based learning versus partition function learning.

Contribution

It presents a novel machine learning method for constructing effective models of quantum systems, focusing on partition function estimation and observable learning.

Findings

Successfully applied to Anderson and quantum dot models

Non-perturbative results for Kondo model mapping

Discussed limitations of observable learning in capturing emergent scales

Abstract

The construction of good effective models is an essential part of understanding and simulating complex systems in many areas of science. It is a particular challenge for correlated many body quantum systems displaying emergent physics. We propose a machine learning approach that optimizes an effective model based on an estimation of its partition function. The success of the method is demonstrated by application to the single impurity Anderson model and double quantum dots, where non-perturbative results are obtained for the old problem of mapping to effective Kondo models. For quantum impurity parent Hamiltonians, we derive an alternative approach based on learning from observables. When mapping to minimal effective models, emergent scales may not be captured by observable learning, while partition function learning may not reproduce all observables.