Ergodicity breaking Transition in East Circuits | Qiskit Quantum Seminar with Tomaž Prosen

Ergodicity breaking transition in East circuits: From dynamical localizaiton to quantum Ruelle resonances
Episode 171

I will discuss a family of clean quantum circuits with constrained chiral dynamics, the so-called East circuits. For small enough coupling parameter of the model and incommensurate Trotter time-step, analytical-perturbative as well as tensor-network-based-numerical arguments suggest existence of dynamical localization, i.e. asymptotic exponential localization of time dependent initially localized excitation.

For sufficiently large coupling parameter, the dynamics appears ergodic and quantum chaotic with uniform asymptotic exponential relaxation of all local observables. The latter is captured by the concept of quantum Ruelle-Pollicott resonances formulated in terms of the leading nontrivial eigenvalue of an open quantum circuit with absorbing boundary condition (implemented in terms of a reset channel). The corresponding eigenvector exhibits a clean self-similar fractal structure with characteristic power law scaling.

Tomaž Prosen has been a full professor of theoretical physics at University of Ljubljana since 2008, where he leads a group on nonequilibrium quantum and statistical physics. He obtained his Ph.D. in 1995 at the same university. His main current research interest is in fundamental problems in dynamical systems, quantum many-body dynamics, quantum chaos, nonequilibrium statistical mechanics, and transport theory.