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

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.