Probing Lee-Yang zeros and coherence sudden death

TL;DR

This paper demonstrates that the coherence zeros of a probe spin can be used to experimentally observe Lee-Yang zeros of a many-body system, linking time and temperature in fundamental physics.

Contribution

It introduces a method to measure Lee-Yang zeros via probe spin coherence, enabling experimental access to complex zeros of partition functions.

Findings

Probe spin coherence zeros map to Lee-Yang zeros.

Sudden death of coherence at Lee-Yang edge singularities.

Reconstruction of the partition function from coherence measurements.

Abstract

As a foundation of statistical physics, Lee and Yang in 1952 proved that the partition functions of thermal systems can be zero at certain points (called Lee-Yang zeros) on the complex plane of temperature. In the thermodynamic limit, the Lee-Yang zeros approach to real numbers at the critical temperature. However, the imaginary Lee-Yang zeros have not been regarded as experimentally observable since they occur at imaginary field or temperature, which are unphysical. Here we show that the coherence of a probe spin weakly coupled to a many-body system presents zeros as a function of time that are one-to-one mapped to the Lee-Yang zeros of the many-body system. In the thermodynamic limit, of which the Lee-Yang zeros form a continuum, the probe spin coherence presents a sudden death at the edge singularities of the Lee-Yang zeros. By measuring the probe spin coherence, one can directly reconstruct the partition function of a many-body system. These discoveries establish a profound relation between two most fundamental quantities in the physical world, time and temperature, and also provide a universal approach to studying interacting many-body systems through measuring coherence of only one probe spin (or one qubit in quantum computing).