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We study R\'enyi entropy of locally excited states with considering thethermal and boundary effects respectively in two dimensional conformal fieldtheories (CFTs). Firstly we consider locally excited states obtained by actingprimary operators on a thermal state in low temperature limit. The R\'enyientropy is summation of contribution from thermal effect and local excitation.Secondly, we mainly study the R\'enyi entropy of locally excited states in 2DCFT with a boundary. We show that the evolution of R\'enyi entropy does notdepend on the choice of boundary conditions and boundary will change the timeevolution of R\'enyi entropy. Moreover, in 2D rational CFTs with a boundary, weshow that the R\'enyi entropy always coincides with the log of quantumdimension of the primary operator during some periods of the evolution. We makeuse of a quasi-particle picture to understand this phenomenon. In terms ofquasi-particle interpretation, the boundary behaves as an infinite potentialbarrier which reflects any energy moving towards the boundary.

R\'enyi entropy of locally excited states with thermal and boundary effect in 2D CFTs