Renyi entropy of locally excited states with thermal and boundary effect in 2D CFTs

We study Renyi entropy of locally excited states with considering the thermal and boundary effects respectively in two dimensional conformal field theories (CFTs). Firstly, we consider locally excited states obtained by acting primary operators on a thermal state in low temperature limit. The Renyi entropy is summation of contribution from thermal effect and local excitation. Secondly, we mainly study the Renyi entropy of locally excited states in 2D CFT with a boundary. We show that the time evolution of Renyi entropy is affected by the boundary, but does not depend on the boundary condition. Moreover, we show that the maximal value of Renyi entropy always coincides with the log of quantum dimension of the primary operator. In terms of quasi-particle interpretation, the boundary behaves as an infinite potential barrier which reflects any energy moving towards it.