Entanglement of excited states in critical spin chians

TL;DR

This paper extends the universal law relating entanglement entropy in critical spin chains to excited states, providing an alternative derivation and numerical verification across models, including oscillation phenomena.

Contribution

It offers a new derivation of entanglement scaling laws for excited states in critical spin chains and confirms these results numerically in various models.

Findings

Universal entanglement law applies to excited states.

Numerical verification in models with c=1 and 1/2 universality classes.

Oscillations in Renyi entropy for excited and descendant states.

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.