PIRSA:16050054

Reduction of the classification of topological insulators and superconductors by quartic interactions

(2016). Reduction of the classification of topological insulators and superconductors by quartic interactions. Perimeter Institute. https://pirsa.org/16050054

Reduction of the classification of topological insulators and superconductors by quartic interactions. Perimeter Institute, May. 31, 2016, https://pirsa.org/16050054 

          @misc{ pirsa_PIRSA:16050054,
            doi = {10.48660/16050054},
            url = {https://pirsa.org/16050054},
            author = {},
            keywords = {Condensed Matter},
            language = {en},
            title = {Reduction of the classification of topological insulators and superconductors by quartic interactions},
            publisher = {Perimeter Institute},
            year = {2016},
            month = {may},
            note = {PIRSA:16050054 see, \url{https://pirsa.org}}
          }
Talk number
PIRSA:16050054
Collection
Talk Type
Subject
Abstract

I will discuss the stability and breakdown of the topological classification of gapped ground states of non-interacting fermions, the tenfold way, in the presence of quartic fermion-fermion interactions.  In our approach [1], the effects of interactions on the boundary gapless modes are encoded in terms of boundary dynamical masses. Breakdown of the non-interacting topological classification occurs when the quantum nonlinear sigma models for the boundary dynamical masses favor quantum disordered phases.  The non-interacting topological classification $Z$ in odd spatial dimensions is unstable and reduces to $Z_N$ that can be identified explicitly for any dimension and any defining symmetries.
[1] T. Morimoto, A. Furusaki, and C. Mudry, Phys. Rev. B 91, 235111 (2015).