PIRSA:19010065

Many-Body Invariants for Electric Multipoles in Higher-Order Topology

Cho, G.Y. (2019). Many-Body Invariants for Electric Multipoles in Higher-Order Topology . Perimeter Institute. https://pirsa.org/19010065

Cho, Gil Young. Many-Body Invariants for Electric Multipoles in Higher-Order Topology . Perimeter Institute, Jan. 18, 2019, https://pirsa.org/19010065 

          @misc{ pirsa_PIRSA:19010065,
            doi = {10.48660/19010065},
            url = {https://pirsa.org/19010065},
            author = {Cho, Gil Young},
            keywords = {Condensed Matter},
            language = {en},
            title = {Many-Body Invariants for Electric Multipoles in Higher-Order Topology },
            publisher = {Perimeter Institute},
            year = {2019},
            month = {jan},
            note = {PIRSA:19010065 see, \url{https://pirsa.org}}
          }

Gil Young Cho Pohang University of Science and Technology

DOI 10.48660/19010065
Collection
Talk Type Scientific Series
Subject

Abstract

In crystals, quantum electrons can be spatially distributed in a way that the bulk solid supports macroscopic electric multipole moments, which are deeply 

related with emergence of topology insulators in condensed matter systems. However, unlike the classical electric multipoles in open space, 

defining electric multipoles in crystals is a non-trivial task. So far, only the dipolar moment, namely polarization, has been successfully defined and served as a classic example of topological insulators. 

In this talk, we propose the general definition, i.e., many-body invariants, for electric multipoles in crystals, which are related with recently-discovererd higher-order topological insulators. 

Our invariants are designed to measure the distribution of electron charge in unit cells and thus can detect multipole moments purely from the bulk ground state wavefunctions. 

We provide analytic as well as numerical proofs for our invariants. Application of our invariants to spin systems as well as various other aspects of the many-body invariants will be briefly discussed.