MERA and CFT

          @misc{ pirsa_PIRSA:11100098,
            doi = {10.48660/11100098},
            url = {https://pirsa.org/11100098},
            author = {Evenbly, Glen},
            keywords = {},
            language = {en},
            title = {MERA and CFT},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {oct},
            note = {PIRSA:11100098 see, \url{https://pirsa.org}}
          }
          

Abstract

The MERA offers a powerful variational approach to quantum field theory. While the continuous MERA may allow us to directly address field theories in the continuum, the MERA on the lattice has already demonstrated its ability to characterize conformal field theories. In this talk I will explain how to extract the conformal data (central charge, primary fields, and their scaling dimensions and OPE) of a CFT from a quantum spin chain at a quantum critical point. I will consider both homogeneous systems (translation invariant) and systems with an impurity (where translation invariance is explicitly broken). Key to the success of the MERA is the exploitation of both scale and translation invariance. I will show how translation invariance can still be exploited even in the presence of an impurity, even if the system is no longer translation invariant. This follows from an intriguing "causality principle" in the RG flow. I will also discuss the relation of these results with Wilson's famous resolution of the Kondo impurity problem.