Aharonov-Bohm effect in symmetry protected states


Santos, L. (2014). Aharonov-Bohm effect in symmetry protected states. Perimeter Institute. https://pirsa.org/14020126


Santos, Luiz. Aharonov-Bohm effect in symmetry protected states. Perimeter Institute, Feb. 10, 2014, https://pirsa.org/14020126


          @misc{ pirsa_PIRSA:14020126,
            doi = {10.48660/14020126},
            url = {https://pirsa.org/14020126},
            author = {Santos, Luiz},
            keywords = {},
            language = {en},
            title = {Aharonov-Bohm effect in symmetry protected states},
            publisher = {Perimeter Institute},
            year = {2014},
            month = {feb},
            note = {PIRSA:14020126 see, \url{https://pirsa.org}}

Luiz Santos Emory University


Symmetry protected topological (SPT) states are generalizations of topological band insulators to interacting systems. They possess a gapped bulk spectrum together with symmetry protected edge states, with no topological order. There has been recently an intense effort to classify SPT states both in terms of group cohomology as well as from the point of view of effective field theories. An interesting related question is to understand the structute of lattice models that realize SPT physics. In this talk, I shall present a class of lattice models describing the egde of non-chiral two-dimensional bosonic SPT states protected by Z_N symmetry. A crucial aspect of the construction relies on finding the correct non-trivial Z_N symmetry realizations on the edge consistent with all the possible classes of SPT states. Then I shall discuss the Aharonov-Bohm effect on the many-body SPT state by studying this many-body effect on the aforementioned gapless edge states. The effect of a Z_N gauge flux on the egde states is formulated in terms of twisted boundary conditions of the lattice models. The low energy spectral shifts due to the gauge flux are shown to depend on each of the SPT classes in a predictable way. I shall, in the course of this talk, present numerical results of exact diagonalization of our lattice Hamiltonians that support this analysis. This work is done in collaboration with Juven Wang and
appears in arXiv:1310.8291.