Entanglement of excited states in critical spin chians

Abstract

Renyi and von Neumann entropies quantifying the amount of entanglement in ground states of critical spin chains are known to satisfy a universal law which is given by the Conformal Field Theory (CFT) describing their scaling regime. This law can be generalized to excitations described by primary fields in CFT, as was done in reference (Alcaraz et. al., Phys. Rev. Lett. 106, 201601 (2011)), of which this work is a completion. An alternative derivation is presented, together with numerical verifications of our results in different models belonging to the c=1,1/2 universality classes. Oscillations of the Renyi entropy in excited states and descendant fields are also discussed.

23 pages, 13 figures

References in corpus (7)

• Entanglement of low-energy excitations in Conformal Field Theory
• Mutual Information and Boson Radius in c=1 Critical Systems in One Dimension
• The entanglement entropy of one-dimensional gases
• Entanglement Entropy and Twist Fields
• Unusual Corrections to Scaling in Entanglement Entropy
• Exact relationship between the entanglement entropies of XY and quantum Ising chains
• Finite Size Corrections to Entanglement in Quantum Critical Systems

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