Boundary Chaos

F. Fritzsch,1 T. Prosen1

1Faculty of Mathematics and Physics, University of Ljubljana , Jadranska ulica 19, SI-1000 Ljubljana, Slovenia

Spatiotemporal correlation functions provide the key diagnostic tool for studying spatially extended complex quantum many-body systems. In ergodic systems scrambling causes initially local observables to spread uniformly over the whole available Hilbert space and causes exponential suppression of correlation functions with the spatial size of the system. In this talk, we present a perturbed free quantum circuit model, in which ergodicity is induced by a unitary impurity placed on the system‘s boundary and that allows for demonstrating the underlying mechanism governing the asymptotic scaling of correlations with system size.

This is achieved by mapping dynamical correlation functions of local operators in a system of linear size L at time t to a partition function with complex weights defined on a two-dimensional lattice of smaller size t/L × L with a helix topology. We evaluate this partition function in terms of suitable transfer matrices. As this drastically reduces the complexity of the computation of correlation functions, we are able to treat system sizes far beyond what is accessible by exact diagonalization. By studying the spectra of transfer matrices numerically and combining our findings with analytical arguments we determine the asymptotic scaling of correlation functions with system size.

For impurities that remain unitary under partial transpose, we demonstrate that correlation functions at times proportional to system size L are generically exponentially suppressed with L. In contrast, for generic unitary impurities correlations show persistent revivals with a period given by the system size.

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