# Critical Relaxation in the Quantum Yang–Lee Edge Singularity

## TL;DR

This paper investigates the relaxation dynamics near critical points in a quantum Ising chain, revealing distinct scaling behaviors for different Hamiltonians.

## Contribution

The study introduces a scaling theory for the Yang–Lee edge singularity in quantum systems, validated through relaxation dynamics analysis.

## Key findings

- Magnetization oscillates periodically for the paramagnetic Hamiltonian.
- Magnetization decays to a saturated value for the ferromagnetic Hamiltonian.
- Magnetization increases linearly for the critical Hamiltonian.

## Abstract

We study the relaxation dynamics near the critical points of the Yang–Lee edge singularities (YLESs) in the quantum Ising chain in an imaginary longitudinal field with a polarized initial state. We find that scaling behaviors are manifested in the relaxation process after a non-universal transient time. We show that for the paramagnetic Hamiltonian, the magnetization oscillates periodically with the period being inversely proportional to the gap between the lowest energy level; for the ferromagnetic Hamiltonian, the magnetization decays to a saturated value; while for the critical Hamiltonian, the magnetization increases linearly. A scaling theory is developed to describe these scaling properties. In this theory, we show that for a small- and medium-sized system, the scaling behavior is described by the (0+1)-dimensional YLES.