Lee-Yang theory of criticality in interacting quantum many-body systems

TL;DR

This paper introduces a Lee-Yang theoretical framework for analyzing quantum phase transitions in many-body systems, enabling the prediction of critical points through tensor network methods and high cumulant measurements.

Contribution

It develops a novel Lee-Yang approach for quantum criticality that can be implemented with tensor networks and experimental measurements, advancing the study of quantum phase transitions.

Findings

Successfully applied to quantum Ising chain and Heisenberg model

Predicted critical behavior via high cumulants of operators

Facilitates analysis of quantum criticality in 2D systems

Abstract

Quantum phase transitions are a ubiquitous many-body phenomenon that occurs in a wide range of physical systems, including superconductors, quantum spin liquids, and topological materials. However, investigations of quantum critical systems also represent one of the most challenging problems in physics, since highly correlated many-body systems rarely allow for an analytic and tractable description. Here we present a Lee-Yang theory of quantum phase transitions including a method to determine quantum critical points which readily can be implemented within the tensor network formalism and even in realistic experimental setups. We apply our method to a quantum Ising chain and the anisotropic quantum Heisenberg model and show how the critical behavior can be predicted by calculating or measuring the high cumulants of properly defined operators. Our approach provides a powerful formalism to analyze quantum phase transitions using tensor networks, and it paves the way for systematic investigations of quantum criticality in two-dimensional systems.