Entanglement spectrum of geometric states

The reduced density matrix of a given subsystem, denoted by $\rho_A$, contains the information on subregion duality in holographic theory. We may extract using spectrum (eigenvalue) matrix, called entanglement this paper. evaluate eigenstates, one-point and two-point correlation functions microcanonical ensemble state $\rho_{A,m}$ associated with an eigenvalue $\lambda$ for some examples, including single interval two intervals vacuum 2D CFTs. find there exists $\lambda_0$ which can be seen as approximate $\rho_A$. parameter is obtained examples. For general geometric state, also exists. entropy $A$ R\'enyi limit $n\to \infty$. As application above conclusion we reform equality case Araki-Lieb inequality entropies CFTs conditions Holevo information. show constraints eigenstates. Finally, point out unsolved problems their significance understanding states.