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In this work we study the time evolutions of (Renyi) entanglement entropy oflocally excited states in two dimensional conformal field theories (CFTs) atfinite temperature. We consider excited states created by acting with localoperators on thermal states and give both field theoretic and holographiccalculations. In free field CFTs, we find that the growth of Renyi entanglemententropy at finite temperature is reduced compared to the zero temperatureresult by a small quantity proportional to the width of the localizedexcitations. On the other hand, in finite temperature CFTs with classicalgravity duals, we find that the entanglement entropy approaches acharacteristic value at late time. This behaviour does not occur at zerotemperature. We also study the mutual information between the two CFTs in thethermofield double (TFD) formulation and give physical interpretations of ourresults.

Quantum Entanglement of Localized Excited States at Finite Temperature