From Spinon Band Topology to the Symmetry Quantum Numbers of Monopoles in Dirac Spin Liquids

The interplay of symmetry and topology has been at the forefront of recent progress in quantum matter. Here, we uncover an unexpected connection between band topology and the description of competing orders in a quantum magnet. Specifically, we show that aspects of band topology protected by crystal...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. X 2020-02, Vol.10 (1), p.011033, Article 011033
Main Authors: Song, Xue-Yang, He, Yin-Chen, Vishwanath, Ashvin, Wang, Chong
Format: Article
Language:English
Subjects:
Absolute zero
Angular momentum
Antiferromagnetism
Band theory
Condensed matter physics
Excitation
Fermions
Gauge theory
High temperature
Insulators
Kagome lattice
Liquids
Magnetic flux
Magnetic monopoles
Magnetic properties
Magnetism
Magnets
Quantum electrodynamics
Quantum numbers
Spin liquid
Superconductivity
Symmetry
Topology
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The interplay of symmetry and topology has been at the forefront of recent progress in quantum matter. Here, we uncover an unexpected connection between band topology and the description of competing orders in a quantum magnet. Specifically, we show that aspects of band topology protected by crystalline symmetries determine key properties of the Dirac spin liquid (DSL), which can be defined on the honeycomb, square, triangular, and kagome lattices. At low energies, the DSL on all of these lattices is described by an emergent quantum electrodynamics (QED3) withNf=4flavors of Dirac fermions coupled to aU(1)gauge field. However, the symmetry properties of the magnetic monopoles, an important class of critical degrees of freedom, behave very differently on different lattices. In particular, we show that the lattice momentum and angular momentum of monopoles can be determined from the charge (or Wannier) centers of the corresponding spinon insulator. We also show that for DSLs on bipartite lattices, there always exists a monopole that transforms trivially under all microscopic symmetries owing to the existence of a parentSU(2)gauge theory. We connect our results to generalized Lieb-Schultz-Mattis theorems and also derive the time-reversal and reflection properties of monopoles. Our results indicate that recent insights into free-fermion band topology can also guide the description of strongly correlated quantum matter.
ISSN:2160-3308
2160-3308
DOI:10.1103/PhysRevX.10.011033