Boundary Chaos

Abstract: Scrambling in many-body quantum systems causes initially local observables to spread uniformly over the whole available Hilbert space under unitary dynamics, which in lattice systems causes exponential suppression of dynamical correlation functions with system size. Here, we present a perturbed free quantum circuit model, in which ergodicity is induced by an impurity interaction placed on the system's boundary, that allows for demonstrating the underlying mechanism. This is achieved by mapping dynamical correlation functions of local operators acting at the boundary to a partition function with complex weights defined on a two dimensional lattice with a helical topology. We evaluate this partition function in terms of transfer matrices, which allow for numerically treating system sizes far beyond what is accessible by exact diagonalization and whose spectral properties determine the asymptotic scaling of correlations. Combining analytical arguments with numerical results we show that for impurities which remain unitary under partial transpose correlations are exponentially suppressed with system size in a particular scaling limit. In contrast for generic impurities or generic locations of the local operators correlations show persistent revivals with a period given by the system size.