Yang-Lee Zeros in Quantum Phase Transition: An Entanglement Perspective

TL;DR

This paper explores the distribution of Yang-Lee zeros in quantum phase transitions using entanglement entropy, revealing how zeros approach transition points and induce entanglement transitions in specific models.

Contribution

It introduces a novel entanglement-based approach to analyze Yang-Lee zeros and their edge singularities in quantum phase transitions, applicable to various Hamiltonians.

Findings

Yang-Lee zeros approach quantum critical points in complex parameter space.

Yang-Lee edge singularity induces ground-state entanglement transition.

Results extend to non-interacting parity-time-symmetric Hamiltonians.

Abstract

We study the Yang-Lee theory in quantum phase transitions from the perspective of quantum entanglement in one-dimensional many-body systems. We primarily focus on the distribution of Yang-Lee zeros and its associated Yang-Lee edge singularity of two prototypical models: the Su-Schrieffer-Heeger model and the \emph{XXZ} spin chain. By taking the zero-temperature limit, we show how the Yang-Lee zeros approach the quantum phase transition points on the complex plane of parameters. To characterize the edge singularity induced by Yang-Lee zeros in quantum phase transition, we introduce the entanglement entropy of the ground state to show that the edges of Yang-Lee zeros lead to the ground-state entanglement transition. We further show that our results are also applicable to the general non-interacting parity-time-symmetric Hamiltonians.