PIRSA:14110132

Fractionalization from Crystallography

(2014). Fractionalization from Crystallography. Perimeter Institute. https://pirsa.org/14110132

Fractionalization from Crystallography. Perimeter Institute, Nov. 18, 2014, https://pirsa.org/14110132 

          @misc{ pirsa_PIRSA:14110132,
            doi = {10.48660/14110132},
            url = {https://pirsa.org/14110132},
            author = {},
            keywords = {Condensed Matter},
            language = {en},
            title = {Fractionalization from Crystallography},
            publisher = {Perimeter Institute},
            year = {2014},
            month = {nov},
            note = {PIRSA:14110132 see, \url{https://pirsa.org}}
          }
DOI 10.48660/14110132
Collection
Talk Type Scientific Series
Subject

Abstract

A featureless insulator is a gapped phase of matter that does not exhibit fractionalization or other exotic physics, and thus has a unique ground state. The classic albeit non-interacting example is an electronic band insulator. A standard textbook argument tells us that band insulators require an even number of electrons -- an integer number for each spin -- per unit cell. I will explore the converse question: given such an 'integer filling', is a featureless insulating state possible?  I will demonstrate that in most three-dimensional crystals, an insulating ground state cannot be unique -- and hence cannot be featureless -- except at certain special fillings fixed by the crystalline space group. This result, which remains valid more generally for interacting systems of fermions, bosons, or spins (as long as they have a conserved U(1) charge), relies on a combination of topological 'flux insertion' arguments and elementary crystallographic ideas. I will explore its implications through examples ranging from band theory, where it leads to the identification of protected semimetals, to frustrated magnetism, where it suggests new venues for spin liquid physics.

References: S.A. Parameswaran, A.M. Turner, D.P. Arovas and A. Vishwanath, Nature Physics 9, 299 (2013).
(see also related work in PNAS 110, 16378 (2013) and Phys. Rev. Lett. 110, 125301 (2013).)