TY - JOUR

T1 - Entanglement Hamiltonian evolution during thermalization in conformal field theory

AU - Wen, Xueda

AU - Ryu, Shinsei

AU - Ludwig, Andreas W.W.

N1 - Funding Information:
Foundation’s EPiQS initiative through Grant No. GBMF4303 at MIT (XW), the NSF under Grants No. NSF PHY-1125915 (SR), and the NSF under Grant No. DMR-1309667 (AWWL).
Funding Information:
We are grateful to the KITP Program Quantum Physics of Information (September 18–December 15, 2017). This work was supported by the Gordon and Betty Moore
Funding Information:
This work was supported by the Gordon and Betty Moore Foundation's EPiQS initiative through Grant No. GBMF4303 at MIT (XW), the NSF under Grants No. NSF PHY-1125915 (SR), and the NSF under Grant No. DMR-1309667 (AWWL).
Publisher Copyright:
© 2018 IOP Publishing Ltd and SISSA Medialab srl.

PY - 2018/11/19

Y1 - 2018/11/19

N2 - In this work, we study the time evolution of the entanglement Hamiltonian during the process of thermalization in a (1+1)-dimensional conformal field theory (CFT) after a quantum quench from a special class of initial states. In particular, we focus on a subsystem which is a finite interval at the end of a semi-infinite line. Based on conformal mappings, the exact forms of both entanglement Hamiltonian and entanglement spectrum of the subsystem can be obtained. Aside from various interesting features, it is found that in the infinite time limit the entanglement Hamiltonian and entanglement spectrum are exactly the same as those in the thermal ensemble. The entanglement spectrum approaches the steady state spectrum exponentially in time. We also study the modular flows generated by the entanglement Hamiltonian in Minkowski spacetime, which provides us with an intuitive picture of how the entanglement propagates and how the subsystem is thermalized. Furthermore, the effect of a generic initial state is also discussed.

AB - In this work, we study the time evolution of the entanglement Hamiltonian during the process of thermalization in a (1+1)-dimensional conformal field theory (CFT) after a quantum quench from a special class of initial states. In particular, we focus on a subsystem which is a finite interval at the end of a semi-infinite line. Based on conformal mappings, the exact forms of both entanglement Hamiltonian and entanglement spectrum of the subsystem can be obtained. Aside from various interesting features, it is found that in the infinite time limit the entanglement Hamiltonian and entanglement spectrum are exactly the same as those in the thermal ensemble. The entanglement spectrum approaches the steady state spectrum exponentially in time. We also study the modular flows generated by the entanglement Hamiltonian in Minkowski spacetime, which provides us with an intuitive picture of how the entanglement propagates and how the subsystem is thermalized. Furthermore, the effect of a generic initial state is also discussed.

KW - entanglement entropies

KW - entanglement in extended quantum systems

KW - thermalization

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U2 - 10.1088/1742-5468/aae84e

DO - 10.1088/1742-5468/aae84e

M3 - Article

AN - SCOPUS:85057585122

VL - 2018

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 11

M1 - 113103

ER -