Entanglement evolution across a conformal interface

For two-dimensional conformal field theories (CFTs) in the ground state, it is known that a conformal interface along the entanglement cut can suppress the entanglement entropy from S_A ∼ c log L to S_A∼ c_eff log L, where L is the length of the subsystem A, and c_eff ∈ [0, c] is the effective central charge which depends on the transmission property of the conformal interface. In this work, by making use of conformal mappings, we show that a conformal interface has the same effect on entanglement evolution in non-equilibrium cases, including global, local and certain inhomogeneous quantum quenches. I.e. a conformal interface suppresses the time evolution of entanglement entropy by effectively replacing the central charge c with c_eff, where c_eff is exactly the same as that in the ground state case. We confirm this conclusion by a numerical study on a critical fermion chain. Furthermore, based on the quasi-particle picture, we conjecture that this conclusion holds for an arbitrary quantum quench in CFTs, as long as the initial state can be described by a regularized conformal boundary state.