2017/08/31 by Wu-zhong Guo
Physics and Astronomy · #Algorithm #Black Holes and Theoretical Physics #Computer science #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1007/jhep06(2018)044
published as JHEP 1806 (2018) 044 · JHEP version, some conclusions are modified
openalex publication_date 2018/06/01 · arxiv created 2018/06/20 · arxiv updated 2018/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A bstract We discuss the regularized boundary state e^-τ0H|.B⟩a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>τ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mi>H</mml:mi> </mml:mrow> </mml:msup> <mml:mo>|</mml:mo> <mml:msub> <mml:mfenced> <mml:mi>B</mml:mi> </mml:mfenced> <mml:mi>a</mml:mi> </mml:msub> </mml:math> 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-itHe^-τ0H|.B⟩a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mi>i</mml:mi> <mml:mi>t</mml:mi> <mml:mi>H</mml:mi> </mml:mrow> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>τ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mi>H</mml:mi> </mml:mrow> </mml:msup> <mml:mo>|</mml:mo> <mml:msub> <mml:mfenced> <mml:mi>B</mml:mi> </mml:mfenced> <mml:mi>a</mml:mi> </mml:msub> </mml:math> . 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^-τ0H|.B⟩a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>τ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mi>H</mml:mi> </mml:mrow> </mml:msup> <mml:mo>|</mml:mo> <mml:msub> <mml:mfenced> <mml:mi>B</mml:mi> </mml:mfenced> <mml:mi>a</mml:mi> </mml:msub> </mml:math> 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^-τ0H|.B⟩a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>τ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mi>H</mml:mi> </mml:mrow> </mml:msup> <mml:mo>|</mml:mo> <mml:msub> <mml:mfenced> <mml:mi>B</mml:mi> </mml:mfenced> <mml:mi>a</mml:mi> </mml:msub> </mml:math> also appears.