Thermal Corrections to Entanglement Entropy

Abstract

This thesis deals with the study of quantum entanglement across spatial boundaries in conformal-invariant quantum eld theories (2d CFT) in two dimensions. In 2d CFT, R enyi entropy and entanglement entropy has been evaluated successfully using the replica method for non-compact systems at zero and non-zero temperatures and for compact systems at zero temperature (Ref.[2],[4]). However, for a compact system at nite temperature, an exact evaluation of the entropy measure using the replica trick has not been successfully performed. In order to gain more insights into the problem, calculations have been done by approximating the system to a compact system at zero temperature and expanding about it to obtain the leading order correction term to the entropy measure (Ref.[6]). In this thesis we propose a method to calculate the second correction term and eventually a general approach for calculating higher order correction terms to R enyi entropy and entanglement entropy at low temperature expansion for a spatially compacti ed 1d system.