  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 $\rho_A$. The
parameter $\lambda_0$ is obtained in the two examples. For a general geometric
state, the approximate microcanonical ensemble state also exists. The parameter
$\lambda_0$ is associated with the entanglement entropy of $A$ and R\'enyi
entropy in the limit $n\to \infty$. 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.
