Abstract
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 Renyi entropies of
the ground state, which display a universal logarithmic behaviour 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 Renyi 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.
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