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Title:
Unitary designs and approximate invariance in many-body quantum chaos
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Abstract:
In this talk we will describe some quantum information theoretic diagnostics of many-body quantum chaos. The first is the notion of a unitary k-design, ensembles which capture the randomness of the unitary group and approximate Haar moments. We focus on random quantum circuits, a solvable model of strongly-interacting dynamics, and by employing an exact statistical mechanical mapping, we show that local random circuits rapidly converge to unitary designs. We then argue this notion of ergodicity needs to be refined for time-independent systems, using evolution by random matrix Hamiltonians as an example, and introduce k-invariance as a measure of random matrix behavior in physical systems.
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