Entanglement evolution across a conformal interface

TL;DR

This paper demonstrates that conformal interfaces in 2D conformal field theories suppress entanglement growth during non-equilibrium dynamics, with effects analogous to those in ground states, confirmed numerically and conjectured generally.

Contribution

It extends the understanding of entanglement suppression by conformal interfaces from ground states to non-equilibrium quantum quenches using conformal mappings and numerical validation.

Findings

Conformal interfaces reduce entanglement growth in quenched CFTs.

The effective central charge $c_{eff}$ governs entanglement suppression.

Numerical results support the universality of this effect across various quenches.

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.