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 in the case of a semi-infinite subsystem, both theories agree with each other and with the exact calculation. In the case of a finite subsystem, however, both theories qualitatively differ, with the quasiparticle picture predicting a non-monotonic growth of entanglement, in contrast to the membrane picture. We show that such non-monotonic behavior can arise even in random chaotic circuits, pointing to a hitherto unknown shortcoming of the membrane picture in describing such systems.