# Probing the Lee-Yang zeros of a spin bath by correlation functions and entanglement of two spins

## TL;DR

This paper investigates how the Lee-Yang zeros of a ferromagnetic Ising bath can be detected through the dynamics of two probe spins, linking zeros to correlation functions and entanglement, with applications to 1D spin models.

## Contribution

It establishes a method to relate Lee-Yang zeros to measurable correlation functions and entanglement of probe spins, extending previous work to a 1D Ising model.

## Key findings

- Relation between Lee-Yang zeros and probe spin correlation functions
- Connection between Lee-Yang zeros and entanglement of probe spins
- Application to 1D Ising model with trapped atoms

## Abstract

We study the Lee-Yang zeros of the ferromagnetic Ising bath via the interaction with the two probe spins. Similarly as in paper [Bo-Bo Wei, Ren-Bao Liu, Phys. Rev. Lett. 109, 185701 (2012)] the problem of detecting the zeros is reduced to the exploration of time evolution of probe spins. As a result, the relation between the Lee-Yang zeros of the bath and correlation functions of the probe system is obtained. Also we obtain relation between the Lee-Yang zeros and values of the entanglement of probe spins. We apply these results to the 1D Ising spin model with nearest-neighbor interaction which can be prepared on trapped atoms.