Ground-state properties via machine learning quantum constraints

TL;DR

This paper introduces a machine learning approach that uses quantum constraints on operator expectation values to efficiently determine ground-state properties of quantum many-body systems, bypassing the need for full state computation.

Contribution

It presents a novel method leveraging quantum constraints and machine learning to analyze ground states without directly computing the exponentially large Hilbert space.

Findings

Effective for strongly correlated systems

Applicable to thermodynamic-limit systems

Shows advantages over traditional methods

Abstract

Ground-state properties are central to our understanding of quantum many-body systems. At first glance, it seems natural and essential to obtain the ground state before analyzing its properties; however, its exponentially large Hilbert space has made such studies costly, if not prohibitive, on sufficiently large system sizes. Here, we propose an alternative strategy based upon the expectation values of an ensemble of operators and the elusive yet vital quantum constraints between them, where the search for ground-state properties simply equates to classical constrained minimization. These quantum constraints are generally obtainable via sampling and then machine learning on a large number of systematically consistent quantum many-body states. We showcase our perspective on 1D fermion chains and spin chains for applicability, effectiveness, caveats, and unique advantages, especially for strongly correlated systems, thermodynamic-limit systems, property designs, etc.