Compass and Kitaev models -- Theory and Physical Motivations

Abstract

Compass models are theories of matter in which the couplings between the internal spin (or other relevant field) components are inherently spatially (typically, direction) dependent. Compass-type interactions appear in diverse physical systems including Mott insulators with orbital degrees of freedom (where interactions sensitively depend on the spatial orientation of the orbitals involved), the low energy effective theories of frustrated quantum magnets, systems with strong spin-orbit couplings (such as the iridates), vacancy centers, and cold atomic gases. Kitaev's models, in particular the compass variant on the honeycomb lattice, realize basic notions of topological quantum computing. The fundamental inter-dependence between internal (spin, orbital, or other) and external (i.e., spatial) degrees of freedom which underlies compass models generally leads to very rich behaviors including the frustration of (semi-)classical ordered states on non-frustrated lattices and to enhanced quantum effects prompting, in certain cases, the appearance of zero temperature quantum spin liquids. As a consequence of these frustrations, new types of symmetries and their associated degeneracies may appear. These intermediate symmetries lie midway between the extremes of global symmetries and local gauge symmetries and lead to effective dimensional reductions. We review compass models in a unified manner, paying close attention to exact consequences of these symmetries, and to thermal and quantum fluctuations that stabilize orders via order out of disorder effects. We review non-trivial statistics and the appearance of topological quantum orders in compass systems in which, by virtue of their intermediate symmetry standard orders do not arise. This is complemented by a survey of numerical results. Where appropriate theoretical and experimental results are compared.

Review, 111 pages, 58 figures

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Cited by in corpus (9)

• Quantum Spin Liquid States
• Kitaev interactions between j=1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations
• Quantum memories at finite temperature
• The impossibility of exactly flat non-trivial Chern bands in strictly local periodic tight binding models
• Spin-orbital Entangled Molecular $j_{\mathrm{eff}}$ States in Lacunar Spinel Compounds
• Non-Standard Finite-Size Scaling at First-Order Phase Transitions
• Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware
• Multicanonical analysis of the plaquette-only gonihedric Ising model and its dual
• Transmuted finite-size scaling at first-order phase transitions