Constraints on topological order in mott insulators

Physical Review Letters
Michael P Zaletel, Ashvin Vishwanath

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.

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Citations

Nov 9, 2016·Reports on Progress in Physics·Lucile Savary, Leon Balents
Jan 18, 2018·Physical Review Letters·Chenjie Wang, Michael Levin
Aug 18, 2018·Physical Review Letters·Yan-Cheng WangZi Yang Meng
Aug 23, 2020·Nature Communications·Zhida SongYang Qi
Nov 26, 2015·Proceedings of the National Academy of Sciences of the United States of America·Haruki WatanabeMichael Zaletel

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