Entanglement evolution across a conformal interface

Abstract

For two dimensional conformal field theories in the ground state, it is known that a conformal interface along the entanglement cut can suppress the entanglement entropy from $S_A\sim c\log L$ to $S_A\sim c_{\text{eff}}\log L$, where $L$ is the length of the subsystem $A$, and $c_{\text{eff}}\in [0,c]$ 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 $c_{\text{eff}}$, where $c_{\text{eff}}$ 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.

12 pages, 8 figures; v2&v3: refs added; v4: published version

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• Time evolution of entanglement negativity across a defect
• Entanglement asymmetry and symmetry defects in boundary conformal field theory
• Entanglement evolution after a global quench across a conformal defect
• Rényi entropy and negativity for massless complex boson at conformal interfaces and junctions
• Zero-mode entanglement across a conformal defect
• Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking
• Dissipation meets conformal interface in open quantum systems: How the relaxation rate is suppressed