In a quantum critical chain, the scaling regime of the energy and momentum of the ground state and low-lying excitations are described by conformal field theory (CFT). The same holds true for the von Neumann and Rényi entropies of the ground state, which display a universal logarithmic behavior depending on the central charge. In this Letter we generalize this result to those excited states of the chain that correspond to primary fields in CFT. It is shown that the $n$th Rényi entropy is related to a $2n$-point correlator of primary fields. We verify this statement for the critical $XX$ and $XXZ$ chains. This result uncovers a new link between quantum information theory and CFT.

• Received 31 January 2011

DOI:https://doi.org/10.1103/PhysRevLett.106.201601