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arXiv:1712.02709 · Physica A Statistical Mechanics and its Applications

Lee–Yang zeros and two-time spin correlation function

Kh. P. Gnatenko, Alina Kargol, V. M. Tkachuk

Published Jun 25, 2018• 25 citations
arXivHTMLPDF
DOI
10.1016/j.physa.2018.06.103

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Abstract We study the Lee–Yang zeros of the quantum ferromagnetic Ising bath via the interaction with the two probe spins. Similarly, as in an earlier paper (Wei and Liu 2012 Phys. Rev. Lett. 109 , 185701), the problem of detecting the zeros is reduced to the exploration of the time evolution of the probe spins. As a result, the relation between the Lee–Yang zeros of the bath and correlation functions of the probe system is obtained. Also, we obtain the relation between the Lee–Yang zeros and values of the entanglement of the probe spins. We apply these results to the 1D Ising spin model with nearest-neighbor interaction, which can be prepared on trapped atoms.
Phase transitions are not usually seen in the time domain. Here, we report on the finding of critical times at which a physical observable, in the thermodynamic limit, becomes nonanalytic as a function of time. We find that the coherence of a probe spin coupled to a many-body system vanishes at times in one-to-one correspondence to the Lee-Yang zeros of the partition function of the many-body system. In the thermodynamic limit, the Lee-Yang zeros form a continuum cut in the complex plane of fugacity and the probe spin coherence presents sudden death and birth at the critical times corresponding to the Yang-Lee singularities. These results provide new experimental possibilities in many-body physics.