Many-body entanglement dynamics in the presence of a quantum impurity: Integrability vs chaos

Universal behaviors of nonequilibrium quantum many-body systems may be usefully captured by the dynamics of quantum information measures. Notably, the dynamics of bipartite entanglement entropy can distinguish integrable quantum systems from chaotic ones. The two most successful effective theories describing the evolution of entanglement from a low-entangled initial state are the quasiparticle picture and the membrane picture, which provide distinct predictions for integrable and chaotic systems, respectively.

I will present exact results [1] for entanglement dynamics in integrable and chaotic systems perturbed by a quantum impurity, showing that the impurity’s presence strongly alters the growth of entanglement. I will show that in the case of the integrable bulk, a modified version of the integrable quasiparticle picture still holds, despite the impurity generically breaking integrability. On the other hand, the analytical results indicate that for certain chaotic bulk systems, the membrane picture surprisingly fails, pointing to a hitherto unknown gap in its formulation. The exact calculations are facilitated by studying dual-unitary quantum circuits, a class of discrete-time nonequilibrium models that span various types of dynamics while retaining a large degree of analytical solvability. Finally, I will briefly discuss separate results regarding the interplay between entanglement and impurities in nonequilibrium steady states of free fermion systems [2-5].

[1] S. Fraenkel and C. Rylands, Entanglement in dual unitary quantum circuits with impurities, arXiv:2410.03442 (2024).

[2] S. Fraenkel and M. Goldstein, Entanglement measures in a nonequilibrium steady state: Exact results in one dimension, SciPost Phys. 11, 085 (2021).

[3] S. Fraenkel and M. Goldstein, Extensive long-range entanglement in a nonequilibrium steady state, SciPost Phys. 15, 134 (2023).

[4] S. Fraenkel and M. Goldstein, Exact asymptotics of long-range quantum correlations in a non-equilibrium steady state, J. Stat. Mech. 2024, 033107 (2024).

[5] S. Fraenkel and M. Goldstein, Extensive long-range entanglement at finite temperatures from a nonequilibrium bias, Phys. Rev. B 110, 035149 (2024).