Entanglement spectrum in one-dimensional systems

Abstract

We derive the distribution of eigenvalues of the reduced density matrix of a block of length $\ensuremath{\ell}$ in a one-dimensional system in the scaling regime. The resulting ``entanglement spectrum'' is described by a universal scaling function depending only on the central charge of the underlying conformal field theory. This prediction is checked against exact results for the $XX$ chain. We also show how the entanglement gap closes when $\ensuremath{\ell}$ is large.