CMTC Seminar

Wed, Feb 24, 2021 11:00 am - 12:00 pm


Speaker: Yunxiang Liao
Title: Emergence of many-body quantum chaos via spontaneous breaking of unitarity
Abstract: Despite numerous efforts, there lacks a microscopic understanding of the emergence of irreversible statistics mechanics behavior in isolated many-body quantum systems evolving under the reversible unitary dynamics. The fundamental question of thermalization is intertwined with many-body quantum chaos, and in particular its connection with random matrix theory. It has been found that many-body level statistics of noninteracting fermions populating single-particle levels of a Gaussian unitary ensemble exhibits rich structure, which stems from single-particle quantum chaos and is reflected by the exponential ramp in the spectral form factor (SFF). We generalize this study to interacting theory and evaluate the SFF for both cases of zero and positive infinitesimal inverse temperature \beta using the field integral formulation. The SFF for \beta=0 in the regime of interest is dominated by contribution from the fluctuations around the “standard” saddle point. The associated soft modes responsible for the exponential ramp of the noninteracting theory acquire a mass in the presence of interactions, resulting in the suppression of the exponential ramp -- a necessary prerequisite for the emergence of random matrix structure in many-body spectrum. By contrast, the SFF for positive infinitesimal \beta is instead governed by fluctuations around a series of “nonstandard” saddle points in addition to the “standard” one. Furthermore, for a particular “nonstandard” saddle point, the presence of interactions does not lead to a mass suppressing the exponential ramp. This work suggests that the emergence of many-body quantum chaos might appear as spontaneous symmetry breaking of unitarity and consequently time-reversal invariance.

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