Exact Results on Quantum Many-Body Chaos

ITS Seminar with Tomaz Prosen (University of Ljubljana)

I will discuss two recent analytical results on dynamics of chaotic many-body lattice systems which can be formulated as local quantum circuits and have a remarkable duality property, namely that the dynamics is unitary not only in time but also in space direction: (1) For a particularly clean example of such models, specifically, for a self-dual kicked Ising spin 1/2 chain, we can prove rigorously that the spectral form factor in thermodynamic limit matches the one of random matrix theory at all time scales. (2) Spatiotemporal correlation function of any pair of local observables in dual-unitary lattice models is given exactly in terms of a single-site trace-preserving quantum channel and can be used to classify ergodic properties which can range from non-ergodic to ergodic and dynamically mixing.