Lee–Yang zeros in the Rydberg atoms

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.

Graphical abstract

Keywords

Lee–Yang zeros / Rydberg atom / statistical mechanics

References

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Acknowledgements

We thank Hui Zhai for helpful discussions. Both authors are supported by the International Postdoctoral Exchange Fellowship Program and the Shuimu Tsinghua Scholar Program.

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