We derive the distribution of eigenvalues of the reduced density matrix of a block of length $\ell$ 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 $\ell$ is large.

• Received 20 June 2008

DOI:https://doi.org/10.1103/PhysRevA.78.032329