Constraints on Topological Order in Mott Insulators

2014/10/31 by Michael P. Zaletel, Ashvin Vishwanath · 5 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Business #Combinatorics #Condensed matter physics #Mathematics #Mott insulator #Order (exchange) #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Theoretical physics #Topological insulator #Topology (electrical circuits) #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevlett.114.077201

published as Phys. Rev. Lett. 114, 077201 (2015) · 5 pages plus appendices

openalex publication_date 2015/02/18 · arxiv created 2015/04/18 · arxiv updated 2015/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We point out certain symmetry induced constraints on topological order in Mott insulators (quantum magnets with an odd number of spin 1/2 moments 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 about which topological order is permitted. Our result applies to the kagome lattice quantum antiferromagnet, where recent numerical calculations of the entanglement entropy indicate a ground state compatible with either toric code or double-semion topological order. Our result rules out the latter possibility.

Citations

• Topological properties of Abelian and non-Abelian quantum Hall states classified using patterns of zeros
• Spin Dynamics of the Spin-1/2Kagome Lattice AntiferromagnetZnCu3(OH)6Cl2
• Fractionalization, Topological Order, and Quasiparticle Statistics
• Dynamic Scaling in the Susceptibility of the Spin-12Kagome Lattice Antiferromagnet Herbertsmithite
• Entanglement spectrum of a topological phase in one dimension
• String-net condensation: A physical mechanism for topological phases
• Two soluble models of an antiferromagnetic chain
• Anyons in an exactly solved model and beyond
• Quantum orders and symmetric spin liquids

Cited by

• Thermodynamics of spin-1/2 Kagomé Heisenberg antiferromagnet: algebraic paramagnetic liquid and finite-temperature phase diagram
• Phase diagram of theJ1−J2Heisenberg model on the kagome lattice
• Symmetry fractionalization in the topological phase of the spin-12J1−J2triangular Heisenberg model
• Translational Symmetry and Microscopic Constraints on Symmetry-Enriched Topological Phases: A View from the Surface
• Competing spin-liquid states in the spin-12Heisenberg model on the triangular lattice