From spinon band topology to the symmetry quantum numbers of monopoles in Dirac spin liquids
Abstract
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 kagomé lattices. At low energies, the DSL on all these lattices is described by an emergent Quantum Electrodynamics (QED$_3$) with $N_f=4$ flavors of Dirac fermions coupled to a $U(1)$ 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 parent SU(2) gauge theory. We connect our results to generalized LiebSchultzMattis theorems and also derive the timereversal 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2018
 arXiv:
 arXiv:1811.11182
 Bibcode:
 2018arXiv181111182S
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Lattice;
 High Energy Physics  Theory
 EPrint:
 26 pages, 7 figures