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Abstract |
I will present a minimal model for quantum chaos in a spatially extended many-body
system. It consists of a chain of sites with nearest-neighbour coupling under Floquet time
evolution. Quantum states at each site span a q-dimensional Hilbert space and the time
evolution is specified as a random circuit, which is random in space but periodic in time
(Floquet). Each site is coupled via a random matrix to its neighbour on one side during the
first half of the evolution period, and to its neighbour on the other side during the second
half of the period. I will introduce a diagrammatic formalism useful to average the many-
body dynamics over realisations of the random matrices. This approach leads to exact
expressions in the large-q limit and sheds light on the universality of random matrices in
many-body quantum systems and the ubiquitous entanglement growth in out-of-equilibrium
dynamics. I will also discuss universal behaviour which goes beyond random matrix theory
and the role played by space dimensionality which emerges through a mapping into the
classical Potts model, exact at large q. |
