Theory Seminar: Membrane picture for entanglement growth in  monitored random circuits

Caterina Zerba
TUM
Quantum Many-Body Seminar, at the Theory Seminar Room
Thursday, March 05, 11:30 CET

In this talk, we investigate entanglement growth in monitored random circuits. We revisit the membrane picture of entanglement dynamics in unitary random circuits and extend it to monitored dynamics using a Hamiltonian formulation. We show that the membrane description accurately predicts both the growth rate and the saturation value of the averaged Rényi entropy in the volume-law phase, where the dominant domain-wall configurations correspond to excitations of the effective Hamiltonian. We further relate the entanglement phase transition to the behavior of the membrane tension. Finally, we analyze the fluctuations of the purity and Rényi entropy in the volume law phase.