Dyonic Lieb-Shultz-Mattis Theorem and Symmetry Protected Topological Phases in Decorated Dimer Models

Understand

We consider 2+1D lattice models of interacting bosons or spins, with both magnetic flux and fractional spin in the unit cell.

• We propose and prove a modified Lieb-Shultz Mattis (LSM) theorem in this setting, which applies even when the spin in the enlarged magnetic unit cell is integral.
• There are two nontrivial outcomes for gapped ground states that preserve all symmetries.
• In the first case, one necessarily obtains a symmetry protected topological (SPT) phase with protected edge states.