2020/08/31 by Wu-zhong Guo
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Canonical ensemble #Cosmology and Gravitation Theories #Density matrix #Eigenvalues and eigenvectors #Entropy (arrow of time) #Mathematical physics #Mathematics #Microcanonical ensemble #Physics #Quantum #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Squashed entanglement #Statistical physics #Statistics #Theoretical physics #hep-th #quant-ph
paper · pdf · doi:10.1007/jhep02(2021)085
references added
arxiv created 2020/09/25 · openalex publication_date 2021/02/10 · arxiv updated 2021/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A bstract The reduced density matrix of a given subsystem, denoted by ρ A , contains the information on subregion duality in a holographic theory. We may extract the information by using the spectrum (eigenvalue) of the matrix, called entanglement spectrum in this paper. We evaluate the density of eigenstates, one-point and two-point correlation functions in the microcanonical ensemble state ρ A,m associated with an eigenvalue λ for some examples, including a single interval and two intervals in vacuum state of 2D CFTs. We find there exists a microcanonical ensemble state with λ 0 which can be seen as an approximate state of ρ A . The parameter λ 0 is obtained in the two examples. For a general geometric state, the approximate microcanonical ensemble state also exists. The parameter λ 0 is associated with the entanglement entropy of A and Rényi entropy in the limit n → ∞ . As an application of the above conclusion we reform the equality case of the Araki-Lieb inequality of the entanglement entropies of two intervals in vacuum state of 2D CFTs as conditions of Holevo information. We show the constraints on the eigenstates. Finally, we point out some unsolved problems and their significance on understanding the geometric states.