Lee-Yang zeros in the Rydberg atoms

TL;DR

This paper analytically studies Lee-Yang zeros in 1D classical Rydberg blockade models, showing all zeros are real and negative, indicating no phase transitions, and discusses potential experimental observations.

Contribution

It provides an analytical characterization of Lee-Yang zeros in 1D Rydberg blockade models, revealing their real and negative nature for arbitrary blockade radii.

Findings

All Lee-Yang zeros are real and negative in 1D Rydberg blockade models.

No phase transitions occur in these 1D classical Rydberg chains.

Zeros redistribute as blockade radii vary, with potential for experimental measurement.

Abstract

Lee-Yang (LY) zeros play a fundamental role in the formulation of statistical physics in terms of (grand) partition functions, and assume theoretical significance for the phenomenon of phase transitions. In this paper, motivated by recent progress in cold Rydberg atom experiments, we explore the LY zeros in classical Rydberg blockade models. We find that the distribution of zeros of partition functions for these models in one dimension (1d) can be obtained analytically. We prove that all the LY zeros are real and negative for such models with arbitrary blockade radii. Therefore, no phase transitions happen in 1d classical Rydberg chains. We investigate how the zeros redistribute as one interpolates between different blockade radii. We also discuss possible experimental measurements of these zeros.