Entanglement in dual unitary quantum circuits with impurities

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 nonmonotonic growth in contrast to the membrane picture. We show that such nonmonotonic behavior can arise even in random chaotic circuits, shedding light on the range of validity of the membrane picture in such systems.