Topological Insulators and Quantum Spin Liquids

Abstract

In this paper we review some connections recently discovered between topological insulators and certain classes of quantum spin liquids, focusing on two and three spatial dimensions. In two dimensions we show the integer quantum Hall effect plays a key role in relating topological insulators and chiral spin liquids described by fermionic excitations, and we describe a procedure for "generating" a certain class of topological states. In three dimensions we discuss interesting relationships between certain quantum spin liquids and interacting "exotic" variants of topological insulators. We focus attention on better understanding interactions in topological insulators, and the phases nearby in parameter space that might result from moderate to strong interactions in the presence of strong spin-orbit coupling. We stress that oxides with heavy transition metal ions, which often host a competition between electron interactions and spin-orbit coupling, are an excellent place to search for unusual topological phenomena and other unconventional phases.

Invited article (Review); 19 pages, 15 figures, Stated more precisely under which conditions we expect a TI-QSL correspondence to hold, updated references

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Cited by in corpus (25)

• Topological and magnetic phases of interacting electrons in the pyrochlore iridates
• Correlation effects in two-dimensional topological insulators
• Magnetic ordering phenomena of interacting quantum spin Hall models
• Topological order in a correlated three-dimensional topological insulator
• Entanglement Entropy and Spectra of the One-dimensional Kugel-Khomskii Model
• Interaction effects on topological phase transitions via numerically exact quantum Monte Carlo calculations
• Unusual magnetic phases in the strong interaction limit of two-dimensional topological band insulators in transition metal oxides
• The characterization of topological properties in Quantum Monte Carlo simulations of the Kane-Mele-Hubbard model
• Topological Invariant and Quantum Spin Models from Magnetic π Fluxes in Correlated Topological Insulators
• Time-reversal symmetric Kitaev model and topological superconductor in two dimensions
• Doping the Kane-Mele-Hubbard model: A Slave-Boson Approach
• An Exact Chiral Amorphous Spin Liquid
• Cellular dynamical mean-field theory study of an interacting topological honeycomb lattice model at finite temperature
• Dynamics of a j=3/2 quantum spin liquid
• Single magnetic impurities in the Kane-Mele model
• Hot-carrier transport and spin relaxation on the surface of topological insulator
• Quantum anomalous Hall state from spatially decaying interactions on the decorated honeycomb lattice
• Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice
• Critical quasiparticles in single-impurity and lattice Kondo models
• Spatially anisotropic kagome antiferromagnet with Dzyaloshinskii-Moriya interaction
• High-field charge transport on the surface of Bi${}_2$Se${}_3$
• From Frustrated to Unfrustrated: Coupling two triangular-lattice itinerant Quantum Magnets
• Fidelity of the Kitaev honeycomb model under a quench
• Simple model for the gap in the surface states of the antiferromagnetic topological insulator MnBi${}_2$Te${}_4$
• Enhancement of the superconducting transition temperature from the competition between electron-electron correlations and electron-phonon interactions