Lee-Yang zeros in the Rydberg atoms

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.

Automated summary

In this paper, the authors explore the Lee-Yang (LY) zeros in classical Rydberg blockade models, motivated by recent progress in cold Rydberg atom experiments. They find that the distribution of partition function zeros for these models in one dimension (1d) can be analytically obtained, and prove that all LY zeros are real and negative for models with arbitrary blockade radii. Therefore, no phase transitions occur in 1d classical Rydberg chains. The authors also investigate how these zeros redistribute as different blockade radii are interpolated, and discuss possible experimental measurements for these zeros.