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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser

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Constraints on topological order in mott insulators.

Michael P Zaletel^1,2, Ashvin Vishwanath¹

¹Department of Physics, University of California, Berkeley, California 94720, USA.

Physical Review Letters

|March 13, 2015

Summary

Symmetry constraints rule out double-semion topological order in Mott insulators, refining understanding of quantum magnets. This finding impacts theories for 2D quantum magnets and kagome lattice antiferromagnets.

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Area of Science:

Condensed Matter Physics
Quantum Magnetism
Topological Phases of Matter

Background:

Mott insulators, characterized by an odd number of spin 1/2 moments per unit cell, can exhibit topological order.
The Hastings-Oshikawa-Lieb-Schultz-Mattis theorem states that fully symmetric gapped 2D quantum magnets must be topologically ordered.
Previous work has not specified which topological orders are permissible under specific symmetries.

Purpose of the Study:

To investigate symmetry-induced constraints on topological order in Mott insulators.
To determine the compatibility of specific topological orders with fundamental symmetries like time-reversal and translation.
To refine the understanding of topological order in 2D quantum magnets.

Main Methods:

Theoretical analysis of symmetry properties in Mott insulators.
Investigating the compatibility of double-semion topological order with time-reversal and translation symmetry.
Applying findings to specific lattice models like the kagome lattice.

Main Results:

The double-semion topological order is shown to be incompatible with time-reversal and translation symmetry in Mott insulators.
This result sharpens the Hastings-Oshikawa-Lieb-Schultz-Mattis theorem by excluding certain topological orders.
For the kagome lattice quantum antiferromagnet, the double-semion topological order is ruled out as a possible ground state.

Conclusions:

Symmetry plays a crucial role in dictating the possible topological orders in Mott insulators.
The findings provide a more precise characterization of topological order in 2D quantum magnets.
This work clarifies the nature of the ground state in systems like the kagome lattice antiferromagnet.