MPS for Relativistic QFTs

          @misc{ pirsa_PIRSA:11100085,
            doi = {10.48660/11100085},
            url = {https://pirsa.org/11100085},
            author = {Haegeman, Jutho},
            keywords = {},
            language = {en},
            title = {MPS for Relativistic QFTs},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {oct},
            note = {PIRSA:11100085 see, \url{https://pirsa.org}}
          }
          

Abstract

In 1987, Feynman devoted one of his last lectures to highlighting three serious objections against the usefulness of the variational principle in the theory of relativistic quantum fields. In that same year, in a different branch of physics, Affleck, Kennedy, Lieb and Tasaki devised a quantum state that resulted in the development of a handful of different variational ansätze for lattice models over the last two decennia. These quantum states are known as tensor network states and invalidate at least two of Feynman's arguments. They could thus be used in a variational study of relativistic quantum field theories on a lattice. However, two classes of tensor network states, namely the matrix product state and the multi-scale entanglement renormalization ansatz, have recently been ported to the continuous setting, so that we now have direct access to variational wave functions for quantum field theories and are no longer restricted to a lattice regularization.