Entanglement of low-energy excitations in Conformal Field Theory

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.

4 pages, 3 figures

References in corpus (5)

• Entanglement entropy of two disjoint intervals in conformal field theory II
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• Entanglement entropy of two disjoint blocks in XY chains
• Universal corrections to scaling for block entanglement in spin-1/2 XX chains
• Finite Size Corrections to Entanglement in Quantum Critical Systems

Cited by in corpus (7)

• Thermodynamical Property of Entanglement Entropy for Excited States
• The entanglement entropy of one-dimensional gases
• Shell-Filling Effect in the Entanglement Entropies of Spinful Fermions
• Entanglement evolution across defects in critical anisotropic Heisenberg chains
• Entanglement Entropy of the Low-Lying Excited States and Critical Properties of an Exactly Solvable Two-Leg Spin Ladder with Three-Spin Interactions
• Symmetric Orbifolds and Entanglement Entropy for Primary Excitations in Two Dimensional CFT
• Holographic Entanglement Entropy for Excited States in Two Dimensional CFT