Entanglement spectrum of geometric states

Understand

The reduced density matrix of a given subsystem, denoted by $\rho_A$, 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 $\rho_{A,m}$ associated with an eigenvalue $\lambda$ 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 $\lambda_0$ which can be seen as an approximate state of $\rho_A$.