PIRSA:20020018

Lattice homotopy: the physics of moving things around and calling them the same

APA

Po, H.C. (2020). Lattice homotopy: the physics of moving things around and calling them the same. Perimeter Institute. https://pirsa.org/20020018

MLA

Po, Hoi Chun. Lattice homotopy: the physics of moving things around and calling them the same. Perimeter Institute, Feb. 25, 2020, https://pirsa.org/20020018

BibTex

          @misc{ pirsa_20020018,
            doi = {},
            url = {https://pirsa.org/20020018},
            author = {Po, Hoi Chun},
            keywords = {Condensed Matter},
            language = {en},
            title = {Lattice homotopy: the physics of moving things around and calling them the same},
            publisher = {Perimeter Institute},
            year = {2020},
            month = {feb},
            note = {PIRSA:20020018 see, \url{https://pirsa.org}}
          }
          

Abstract

While the concept of topology is often introduced by contrasting oranges with bagels, the idea of topologically distinct quantum phases of matter is far more abstract. In this talk, we will focus on a more tangible form of topology that also arises in quantum condensed matter system: when the sites in a lattice are dragged around in a symmetric manner, what attributes of the lattice would remain unchanged? Such deformation can be viewed as the lattice analog of the familiar (mental) exercise of transforming a bagel into a coffee mug. We will first introduce the mathematical framework for identifying the topological classes of lattices, and then discuss how these invariants can constrain and inform the more abstract notion of topological phases of matter that emerge.