Entanglement Entropy, the Multi-scale Entanglement Renormalisation Ansatz and Lifshitz Field Theories

Abstract

In this thesis we will summarise recent developments in tensor network methods and extend results for entanglement entropy using cMERA in Lifshitz field theories. After a brief recounting of the important aspects of entanglement entropy we will present a description of pertinent tensor networks. This will include both matrix product states (MPS) and the multi-scale entanglement renormalisation ansatz (MERA). We will recount previous area law results for the entanglement entropy in these ansatze. Following this we will continue to discuss MERA and in particular its continuous realisation (cMERA). Finally we apply this cMERA framework to free field theories and extend known results to the case of field theories with anisotropic scaling, that is, Lifshitz field theories. In particular we find a new result for the entanglement entropy of fermionic theories with anisotropic scaling.