PIRSA:17020128

Boundary Hamiltonian theory for gapped topological phases on an open surface

(2017). Boundary Hamiltonian theory for gapped topological phases on an open surface. Perimeter Institute. https://pirsa.org/17020128

Boundary Hamiltonian theory for gapped topological phases on an open surface. Perimeter Institute, Feb. 21, 2017, https://pirsa.org/17020128 

          @misc{ pirsa_PIRSA:17020128,
            doi = {10.48660/17020128},
            url = {https://pirsa.org/17020128},
            author = {},
            keywords = {Condensed Matter},
            language = {en},
            title = {Boundary Hamiltonian theory for gapped topological phases on an open surface},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {feb},
            note = {PIRSA:17020128 see, \url{https://pirsa.org}}
          }
Talk number
PIRSA:17020128
Collection
Talk Type
Subject
Abstract

In this talk we propose a Hamiltonian approach to 2+1D gapped topological phases on an open surface with boundary. The bulk part is

(Levin-Wen) string-net models arising from a unitary fusion category (can be viewed as Hamiltonian approach to extended Turaev-Viro TQFT), while the boundary Hamiltonian is constructed using any Frobenius algebra in the input category. The combined Hamiltonian is exactly solvable and gives rise to a gapped energy spectrum which is topologically protected.

Our boundary Hamiltonians can be used to characterize and classify boundary conditions that give rise to gapped topological phase. We study the ground states and boundary excitations. Particularly, we show a correspondence between elementary excitations and the ground states on a cylinder system. Both are characterized by the category of bimodules over the Frobenius algebra that defines the  boundary Hamiltonian.