TY - JOUR

T1 - Entanglement evolution across a conformal interface

AU - Wen, Xueda

AU - Wang, Yuxuan

AU - Ryu, Shinsei

N1 - Funding Information:
We thank Andreas W W Ludwig, Tokiro Numasawa, and Tomonori Ugajin for helpful discussions and collaborations on related works. In particular, XW thanks John Cardy for his helpful interpretation on the work [35]. We are grateful to the KITP Program Quantum Physics of Information (18 Sep–15 Dec, 2017). XW is supported by the postdoc fellowship from the Gordon and Betty Moore Foundation EPiQS Initiative through Grant No. GBMF4303 at MIT. YW is supported by the Gordon and Betty Moore Foundation EPiQS Initiative through Grant No. GBMF4305 at the University of Illinois. This work was supported by the NSF under Grant No. NSF PHY-1125915 (SR).
Publisher Copyright:
© 2018 IOP Publishing Ltd.

PY - 2018/4/17

Y1 - 2018/4/17

N2 - 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 SA ∼ c log L to SA∼ ceff log L, where L is the length of the subsystem A, and ceff ∈ [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 ceff, where ceff 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.

AB - 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 SA ∼ c log L to SA∼ ceff log L, where L is the length of the subsystem A, and ceff ∈ [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 ceff, where ceff 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.

KW - conformal field theory

KW - quantum entanglement

KW - quantum quench

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U2 - 10.1088/1751-8121/aab561

DO - 10.1088/1751-8121/aab561

M3 - Article

AN - SCOPUS:85045558142

SN - 1751-8113

VL - 51

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 19

M1 - 195004

ER -