Detecting the Lee-Yang zeros of a high-spin system by the evolution of probe spin

TL;DR

This paper extends the method of detecting Lee-Yang zeros via probe spin coherence from spin-1/2 baths to high-spin systems, providing a theoretical framework and potential experimental implementations.

Contribution

It generalizes the detection of Lee-Yang zeros to arbitrary high-spin baths and establishes the connection between observable probe spin properties and Lee-Yang zeros.

Findings

Derived the relationship between probe spin observables and Lee-Yang zeros for high-spin systems.

Applied the theoretical framework to specific models like the triangle spin cluster and Ising models.

Proposed feasible physical implementations of the models for experimental observation.

Abstract

Recently in paper [Peng et al., Phys. Rev. Lett. 114, 010601 (2015)] the experimental observation of the Lee-Yang zeros of an Ising-type spin-1/2 bath, by measuring the coherence of a probe spin, was reported. We generalize this problem to the case of an arbitrary high-spin bath. Namely, we consider the evolution of a probe arbitrary spin which interacts with bath composed by N arbitrary spins. As a result, the connection between the observed values of the probe spin, such as magnetization and susceptibility, and the Lee-Yang zeros is found. We apply these results to some models, namely, a triangle spin cluster, the Ising model with a long-range interaction and the 1D Ising model with nearest-neighbor interaction. Also we propose the implementation of these models on real physical systems.