Compass 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. A simple illustrative example is furnished by the 90 • compass model on a square lattice in which only couplings of the form τ x i τ x j (where {τ a i }a denote Pauli operators at site i) are associated with nearest neighbor sites i and j separated along the x axis of the lattice while τ y i τ y j couplings appear for sites separated by a lattice constant along the y axis. Such compass-type interactions can appear in diverse physical systems. This includes 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, vacancy centers and cold atomic gases. 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. This is complemented by a survey of numerical results.

Spin-orbital entangled molecular jeff states in lacunar spinel compounds

“…In addition to the Heisenberg term, the Hamiltonian contains the bond-dependent and Ising-like pseudodipolar interaction, called as a Heisenberg-compass model 37 . It can be further reduced to distinct 2D spin models in thin-film geometries.…”

Quantum entanglement in the one-dimensional spin-orbitalSU(2)⊗XXZmodel

“…In both these cases the orbital exchange (orbital-flip) processes are blocked and orbital interaction are of a classical Ising-like form. Such Ising interactions are frustrated when they emerge in higher dimension, as in the well-studied orbital compass model [73][74][75] and in Kitaev model [76], see also a recent review on the compass model [77]. It is now intriguing to ask what happens to the SOE in this case.…”

Field-induced quantum criticality in the Kitaev system α−RuCl3

“…Mott insulator with a layered structure of edge-sharing RuCl 6 octahedra arranged in a honeycomb lattice [1][2][3][4][5][6][7][8]. It has been suggested [9,10] that strongly spin-orbit-coupled Mott insulators with that lattice geometry realize bond-dependent magnetic "compass" interactions [11], which, if dominant, would lead to a quantum spin-liquid (QSL) ground state as discussed by Kitaev [12]. This exotic spin-disordered state displays an emergent Z 2 gauge field and fractionalized Majorana-fermion excitations relevant for topological quantum computation [12][13][14][15].…”