Constraints on topological order in Mott Insulators

Abstract

We point out certain symmetry induced constraints on topological order in Mott Insulators (quantum magnets with an odd number of spin $\frac{1}{2}$ 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.

5 pages plus appendices

References in corpus (16)

• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Identifying Topological Order by Entanglement Entropy
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• 17O NMR study of the intrinsic magnetic susceptibility and spin dynamics of the quantum kagome antiferromagnet ZnCu3(OH)6Cl2
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Dzyaloshinsky-Moriya Anisotropy in the Spin-1/2 Kagomé Compound ZnCu${}_3$(OH)${}_6$Cl${}_2$
• Quantum phase transition induced by Dzyaloshinskii-Moriya in the kagome antiferromagnet
• Dynamic Scaling in the Susceptibility of the Spin-1\2 Kagome Lattice Antiferromagnet Herbertsmithite
• Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model
• Fractionalization, topological order, and quasiparticle statistics
• Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets
• Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros
• Quantum criticality of the kagome antiferromagnet with Dzyaloshinskii-Moriya interactions
• Double Semion Phase in an Exactly Solvable Quantum Dimer Model on the Kagome Lattice
• Semionic resonating valence bond states

Cited by in corpus (1)

• Phase diagram of the J1-J2 Heisenberg model on the kagome lattice