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

We extend the Yang-Lee theory to quantum phase transitions to show how singularity enters the phase transition points 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 (SSH) model and the 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 the edges of Yang-Lee zeros lead to the entanglement transition. We further show our results are also applicable to the general non-interacting parity-time-symmetric Hamiltonians.