Abstract
In this work we study the time evolutions of (Renyi) entanglement entropy of locally excited states in two dimensional conformal field theories (CFTs) at finite temperature. We consider excited states created by acting with local operators on thermal states and give both field theoretic and holographic calculations. In free field CFTs, we find that the growth of Renyi entanglement entropy at finite temperature is reduced compared to the zero temperature result by a small quantity proportional to the width of the localized excitations. On the other hand, in finite temperature CFTs with classical gravity duals, we find that the entanglement entropy approaches a characteristic value at late time. This behaviour does not occur at zero temperature. We also study the mutual information between the two CFTs in the thermofield double (TFD) formulation and give physical interpretations of our results.
Highlights
There are two asymptotic AdS boundaries dual to two copies of conformal field theories (CFTs) in the thermofield formulation of finite temperature CFT
In this work we study the time evolutions of (Renyi) entanglement entropy of locally excited states in two dimensional conformal field theories (CFTs) at finite temperature
In free field CFTs, we find that the growth of Renyi entanglement entropy at finite temperature is reduced compared to the zero temperature result by a small quantity proportional to the width of the localized excitations
Summary
Consider two non-interacting CFTs, say CFTL and CFTR, in two dimensions with isomorphic Hilbert spaces HL,R. A particular entangled state in the total Hilbert space. Where Z(β) = n e−βEn is the standard partition function in one of the Hilbert spaces. The reduced density matrix of (2.1) on either Hilbert space equals to a thermal state. Any correlation functions of observables OR acting on HR will equal thermal correlation functions. Even in the absence of interactions, quantum entanglement is responsible for the existence of non-trivial correlations between HL and HR. These correlations are encoded in two-sided correlation functions involving operators OL,R acting on each Hilbert space.
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