Tensor networks for LGT: beyond 1D

          @misc{ scivideos_PIRSA:20110020,
            doi = {10.48660/20110020},
            url = {https://pirsa.org/20110020},
            author = {Banuls, Mari-Carmen},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Tensor networks for LGT: beyond 1D},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2020},
            month = {nov},
            note = {PIRSA:20110020 see, \url{https://scivideos.org/pirsa/20110020}}
          }
          

Abstract

The suitability of tensor network ansatzes for the description of physically relevant states in one dimensional lattice gauge theories (LGT) has been demonstrated in the last years by a large amount of systematic studies, including abelian and non-abelian LGTs, and including scenarios where traditional Monte Carlo approaches fail due to a sign problem. While this establishes a solid motivation to extend the program to higher dimensions, a similar systematic study in two dimensions using PEPS requires dealing with specific considerations. Besides a larger computational costs associated to the higher spatial dimension, the presence of plaquette terms in LGTs hinders the efficiency of the most up-to-date PEPS algorithms. With a newly developed update strategy, nevertheless, such terms can be treated by the most efficient techniques. We have used this method to perform the first ab initio iPEPS study of a LGT in 2+1 dimensions: a Z3 invariant model, for which we have determined the phase diagram.