Boundary Chaos

TL;DR

This paper introduces a boundary impurity model in a quantum circuit to study scrambling and ergodicity, revealing how boundary interactions influence correlation decay or revival in many-body quantum systems.

Contribution

It presents a novel boundary impurity circuit model and maps boundary correlation functions to a complex-weighted lattice partition function, enabling analysis of scrambling mechanisms.

Findings

Correlations decay exponentially with system size for certain boundary impurities.

Generic impurities or operator locations lead to persistent correlation revivals.

Transfer matrix spectral properties determine the asymptotic correlation behavior.

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.