Flux crystals, Majorana metals, and flat bands in exactly solvable spin-orbital liquids

Abstract

Spin-orbital liquids are quantum disordered states in systems with entangled spin and orbital degrees of freedom. We study exactly solvable spin-orbital models in two dimensions with selected Heisenberg-, Kitaev-, and $\Gamma$-type interactions, as well as external magnetic fields. These models realize a variety of spin-orbital-liquid phases featuring dispersing Majorana fermions with Fermi surfaces, nodal Dirac or quadratic band touching points, or full gaps. In particular, we show that Zeeman magnetic fields can stabilize nontrivial flux patterns and induce metamagnetic transitions between states with different topological character. Solvable nearest-neighbor biquadratic spin-orbital perturbations can be tuned to stabilize zero-energy flat bands. We discuss in detail the examples of $\mathrm{SO}(2)$- and $\mathrm{SO}(3)$-symmetric spin-orbital models on the square and honeycomb lattices, and use group-theoretical arguments to generalize to $\mathrm{SO}(\nu )$-symmetric models with arbitrary integer $\nu >1$. These results extend the list of exactly solvable models with spin-orbital-liquid ground states and highlight the intriguing general features of such exotic phases. Our models are thus excellent starting points for more realistic modellings of candidate materials.

18 pages, 11 figures; v3 (expanded conclusion and appendix, additional minor changes)

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Cited by in corpus (25)

• Unveiling the S=3/2 Kitaev Honeycomb Spin Liquids
• Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids
• Topological Disorder Parameter
• Quantum phases of two-dimensional ${\mathbb{Z}}_2$ gauge theory coupled to single-component fermion matter
• Order Fractionalization in a Kitaev-Kondo model
• Kitaev spin-orbital bilayers and their moiré superlattices
• A Kitaev-type spin liquid on a quasicrystal
• Vison crystals, chiral and crystalline phases in the Yao-Lee model
• Quantum liquids of the S=3/2 Kitaev honeycomb and related Kugel-Khomskii models
• Microscopic Roadmap to a Yao-Lee Spin-Orbital Liquid
• Phase diagrams of SO($N$) Majorana-Hubbard models: Dimerization, internal symmetry breaking, and fluctuation-induced first-order transitions
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• Non-Hermitian generalizations of the Yao-Lee model augmented by SO(3)-symmetry-breaking terms
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains
• Fractionalized fermionic multicriticality in anisotropic Kitaev spin-orbital liquids
• The spin-orbital Kitaev model: from kagome spin ice to classical fractons
• Magnetic order through Kondo coupling to quantum spin liquids
• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
• Projectively implemented altermagnetism in an exactly solvable quantum spin liquid
• Even-odd effect in multilayer Kitaev honeycomb magnets
• Three-dimensional spin-orbital liquids
• Exactly solvable spin liquids in Kitaev bilayers and moiré superlattices
• Thermal and quantum fluctuations in extended Kitaev-Yao-Lee spin-orbital model
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands