Many-body-localization transition in matchgate-dominated quantum circuits

Presenting Author: Adrian Chapman, University of New Mexico
Contributing Author(s): Akimasa Miyake

Many-body-localization is the phenomenon whereby locally-encoded quantum information remains confined forever under the dynamics of a disordered many-body quantum system. Its onset marks a dynamical phase transition from scrambling behavior, a phenomenon akin to quantum chaos. In this work, we demonstrate the application of new technical tools for characterizing this nuanced transition by the behavior of the so-called out-of-time-ordered (OTO) correlator, a four-point correlation function between two local observables, one of which is time-evolved. We are able to extend the number of qubits for which this quantity may be classically evaluated efficiently by decomposing universal quantum circuits into circuits which describe free-fermion evolution together with "interaction" gates. In the noninteracting case, there exists a simulation technique for the OTO correlator which scales efficiently in the number of qubits, and exponentially with the number of interaction gates when extended to computational universality. Nevertheless, we find that for sufficiently weak interactions, this quantity may be efficiently approximated using perturbation theory. This allows us to numerically characterize the many-body localization-to-scrambling transition in a regime which has so-far remained completely unexplored.

(Session 5 : Thursday from 5:00pm - 7:00 pm)


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