Entanglement of low-energy excitations in Conformal Field Theory

TL;DR

This paper extends the understanding of entanglement entropy in quantum critical chains by relating excited states' Renyi entropies to correlators in conformal field theory, revealing a new connection between quantum information and CFT.

Contribution

It generalizes the relation between entanglement entropy and CFT from ground states to excited states associated with primary fields.

Findings

Renyi entropy for excited states linked to 2n-point correlators of primary fields

Verification of the relation in XX and XXZ chains

Uncovers a new connection between quantum information theory and CFT

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.