Entanglement in dual unitary quantum circuits with impurities

TL;DR

This paper studies entanglement dynamics in a dual unitary quantum circuit with an impurity, comparing the quasiparticle and membrane theories, and reveals their differing predictions for finite subsystems.

Contribution

It introduces a model with an impurity in a dual unitary circuit and compares the effective theories' predictions with exact entanglement calculations.

Findings

Both theories agree with exact results for semi-infinite subsystems.

For finite subsystems, the theories qualitatively differ in entanglement growth predictions.

Non-monotonic entanglement growth can occur even in chaotic circuits, challenging the membrane picture.

Abstract

Bipartite entanglement entropy is one of the most useful characterizations of universal properties in a many-body quantum system. Far from equilibrium, there exist two highly effective theories describing its dynamics -- the quasiparticle and membrane pictures. In this work we investigate entanglement dynamics, and these two complementary approaches, in a quantum circuit model perturbed by an impurity. In particular, we consider a dual unitary quantum circuit containing a spatially fixed, non-dual-unitary impurity gate, allowing for differing local Hilbert space dimensions to either side. We compute the entanglement entropy for both a semi-infinite and a finite subsystem within a finite distance of the impurity, comparing exact results to predictions of the effective theories. We find that for a semi-infinite subsystem, both theories agree with each other and the exact calculation. For a finite subsystem, however, both theories qualitatively differ, with the quasiparticle picture predicting a non-monotonic growth in contrast to the membrane picture. We show that such non-monotonic behavior can arise even in random chaotic circuits, shedding light on the range of validity of the membrane picture in such systems.