Classification and characterization of interacting crystalline insulators in (2+1)D

          @misc{ scivideos_PIRSA:24030121,
            doi = {10.48660/24030121},
            url = {https://pirsa.org/24030121},
            author = {Calvera Ciguenas, Francisco Vladimir},
            keywords = {Quantum Matter},
            language = {en},
            title = {Classification and characterization of interacting crystalline insulators in (2+1)D},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2024},
            month = {mar},
            note = {PIRSA:24030121 see, \url{https://scivideos.org/pirsa/24030121}}
          }
          

Abstract

In this presentation, I will discuss our latest efforts to classify and characterize insulators in two spatial dimensions in the presence of interactions. I will focus on two examples, both on the square lattice. The first example is of bosonic insulators with symmetry G = p4m x K, where K is an internal symmetry group taken to be U(1), SO(3) or Z_N. The second example is of fermionic insulators with G= p4 x U(1)^f. In both scenarios, we propose a set of invariants that reproduce the classification anticipated through real space constructions and topological field theory (TFT). In doing so, we relate these invariants to coefficients appearing in the response action obtained from TFT. For the fermionic case, we propose a map from the non-interacting classification to the interacting classification.

This talk is based on work done with Naren Manjunath and Maissam Barkeshli.

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