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arXiv · 1708.07268

Entanglement Properties of Boundary State and Thermalization

Wu-zhong Guo
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Abstract

We discuss the regularized boundary state $e^{-τ_0 H}|B\rangle_a$ on two aspects in both 2D CFT and higher dimensional free field theory. One is its entanglement and correlation properties, which exhibit exponential decay in 2D CFT, the parameter $1/τ_0$ works as a mass scale. The other concerns with its time evolution, i.e., $e^{-i tH}e^{-τ_0 H}|B\rangle_a$. We investigate the Kubo-Martin-Schwinger (KMS) condition on correlation function of \emph{local} operators to detect the thermal properties. Interestingly we find the correlation functions in the initial state $e^{-τ_0 H}|B\rangle_a$ also partially satisfy the KMS condition. In the limit $t\to \infty$, the correlators will exactly satisfy the KMS condition. We generally analyse quantum quench by a pure state and obtain some constraints on the possible form of 2-point correlation function in the initial state if assuming they satisfies KMS condition in the final state . As a byproduct we find in an large $τ_0$ limit the thermal property of 2-point function in $e^{-τ_0 H}|B\rangle_a$ also appears.

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Wu-zhong Guo. 2018-06-20. Entanglement Properties of Boundary State and Thermalization. https://doi.org/10.1007/jhep06(2018)044

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