Boundary Chaos: Exact Entanglement Dynamics

TL;DR

This paper provides exact analytical results on how entanglement evolves in a boundary-driven quantum circuit, revealing distinct behaviors depending on the impurity interactions, with implications for understanding ergodic and mixing quantum dynamics.

Contribution

It introduces an exactly solvable model of boundary chaos in quantum circuits and characterizes entanglement dynamics for different impurity interactions in the large system and time limit.

Findings

Impurity interactions cause different entanglement growth patterns.

Some impurities lead to persistent entanglement spikes and suppressed growth.

Other impurities result in linear entanglement growth at maximum speed.

Abstract

We compute the dynamics of entanglement in the minimal setup producing ergodic and mixing quantum many-body dynamics, which we previously dubbed {\em boundary chaos}. This consists of a free, non-interacting brickwork quantum circuit, in which chaos and ergodicity is induced by an impurity interaction, i.e., an entangling two-qudit gate, placed at the system's boundary. We compute both the conventional bipartite entanglement entropy with respect to a connected subsystem including the impurity interaction for initial product states as well as the so-called operator entanglement entropy of initial local operators. Thereby we provide exact results in a particular scaling limit of both time and system size going to infinity for either very small or very large subsystems. We show that different classes of impurity interactions lead to very distinct entanglement dynamics. For impurity gates preserving a local product state forming the bulk of the initial state, entanglement entropies of states show persistent spikes with period set by the system size and suppressed entanglement in between, contrary to the expected linear growth in ergodic systems. We observe similar dynamics of operator entanglement for generic impurities. In contrast, for T-dual impurities, which remain unitary under partial transposition, we find entanglement entropies of both states and operators to grow linearly in time with the maximum possible speed allowed by the geometry of the system. The intensive nature of interactions in all cases cause entanglement to grow on extensive time scales proportional to system size.