Abstract
We discuss the regularized boundary state {e}^{-{tau}_0H}Big|{left.Brightrangle}_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/τ0 works as a mass scale. The other concerns with its time evolution, i.e., {e}^{-itH}{e}^{-{tau}_0H}Big|{left.Brightrangle}_a . We investigate the Kubo-Martin-Schwinger (KMS) condition on correlation function of local operators to detect the thermal properties. Interestingly we find the correlation functions in the initial state {e}^{-{tau}_0H}Big|{left.Brightrangle}_a also partially satisfy the KMS condition. In the limit t → ∞, 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 τ0 limit the thermal property of 2-point function in {e}^{-{tau}_0H}Big|{left.Brightrangle}_a also appears.
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