Constraints on topological order in Mott Insulators

TL;DR

This paper establishes symmetry-based constraints on topological order in Mott insulators, ruling out certain orders like double semion in specific lattice models, thereby refining the understanding of possible quantum phases.

Contribution

It demonstrates that certain topological orders, such as double semion, are incompatible with symmetries in Mott insulators, sharpening existing theorems about topological phases.

Findings

Double semion order is incompatible with time reversal and translation symmetry.

The results exclude double semion order in Kagome lattice antiferromagnets.

Supports the possibility of toric code order in symmetric Mott insulators.

Abstract

We point out certain symmetry induced constraints on topological order in Mott Insulators (quantum magnets with an odd number of spin $\tfrac{1}{2}$ per unit cell). We show, for example, that the double semion topological order is incompatible with time reversal and translation symmetry in Mott insulators. This sharpens the Hastings-Oshikawa-Lieb-Schultz-Mattis theorem for 2D quantum magnets, which guarantees that a fully symmetric gapped Mott insulator must be topologically ordered, but is silent on which topological order is permitted. An application of our result is the Kagome lattice quantum antiferromagnet where recent numerical calculations of entanglement entropy indicate a ground state compatible with either toric code or double semion topological order. Our result rules out the latter possibility.