Random Matrix Spectral Fluctuations in Quantum Lattice Systems

Abstract: I will discuss the problem of unreasonable effectiveness of random matrix theory for description of spectral fluctuations in extended quantum lattice systems. A class of interacting spin systems has been recently identified - specifically, the so-called dual unitary circuits - where the spectral form factor is proven to match with circular ensembles of random matrix theory. The key ideas of novel methodology needed in the proofs will be discussed which are very different than the standard periodic-orbit based methods in quantum chaos of few body semiclassical systems.

mathematical physics

Audience: researchers in the discipline

( video )

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