Entanglement properties of boundary state and thermalization

Abstract

Abstract We discuss the regularized boundary state $$ {e}^{-{\tau}_0H}\Big|{\left.B\right\rangle}_a $$ e − τ 0 H | B 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., $$ {e}^{-itH}{e}^{-{\tau}_0H}\Big|{\left.B\right\rangle}_a $$ e − i t H e − τ 0 H | B 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 $$ {e}^{-{\tau}_0H}\Big|{\left.B\right\rangle}_a $$ e − τ 0 H | B 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 τ 0 limit the thermal property of 2-point function in $$ {e}^{-{\tau}_0H}\Big|{\left.B\right\rangle}_a $$ e − τ 0 H | B a also appears.