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.

arXiv comment18 pages, 11 figures; v3 (expanded conclusion and appendix, additional minor changes)

References in corpus (66)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Quantum Spin Liquids
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Topological Superconductivity in Twisted Multilayer Graphene
• Quantum orders in an exact soluble model
• Orbital order and fluctuations in Mott insulators
• The Flux-Phase of the Half-Filled Band
• Dynamics of a two-dimensional quantum spin liquid: signatures of emergent Majorana fermions and fluxes
• Spin-orbital frustrations and anomalous metallic state in iron-pnictide superconductors
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Model for Metal-Insulator Transition in Graphene Superlattices and Beyond
• Quantum Melting of Magnetic Order due to Orbital Fluctuations
• SU(4) Theory for Spin Systems with Orbital Degeneracy
• Orbital liquid in three dimensional Mott insulator: $LaTi{O}_3$
• Exotic phases induced by strong spin-orbit coupling in ordered double perovskites
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Thermal fractionalization of quantum spins in a Kitaev model: $T$-linear specific heat and coherent transport of Majorana fermions
• Disordered Topological Insulators via $C^{\ast }$-Algebras
• Orbital Liquid in Perovskite Transition-Metal Oxides
• Spin-orbital quantum liquid on the honeycomb lattice
• Correlations and electronic order in a two-orbital honeycomb lattice model for twisted bilayer graphene
• Valence bond glass on an fcc lattice in the double perovskite Ba2YMoO6
• Spin-S Kitaev model: Classical Ground States, Order by Disorder and Exact Correlation Functions
• On the number of Nambu-Goldstone bosons and its relation to charge densities
• Magnetic properties of the geometrically frustrated S=1/2 antiferromagnets, La2LiMoO6 and Ba2YMoO6, with the B-site ordered double perovskite structure: Evidence for a Collective Spin Singlet Ground State
• Algebraic spin liquid in an exactly solvable spin model
• Heisenberg-Kitaev physics in magnetic fields
• Orbital ordering and frustrations
• Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice
• Fermionic magnons, non-Abelian spinons, and spin quantum Hall effect from an exactly solvable Kitaev Hamiltonian with SU(2) symmetry
• Microscopic models for Kitaev's sixteenfold way of anyon theories
• Confinement transition of ${\mathbb{Z}}_2$ gauge theories coupled to massless fermions: emergent QCD${}_3$ and $SO(5)$ symmetry
• Orbital degeneracy as a source of frustration in LiNiO${}_2$
• New Fermionic Description of Quantum S = 1/2 Antiferromargnet
• Emergent $\mathrm{SU}(4)$ Symmetry in $\alpha$-ZrCl${}_3$ and Crystalline Spin-Orbital Liquids
• One Proximate Kitaev Spin Liquid in the $K$-$J$-$\Gamma$ Model on the Honeycomb Lattice
• The SU(N) Heisenberg model on the square lattice: a continuous-N quantum Monte Carlo study
• Bridging Hubbard Model Physics and Quantum Hall Physics in Trilayer Graphene/h-BN moiré superlattice
• Competing phases of interacting electrons on triangular lattices in moiré heterostructures
• A $\Gamma$-matrix generalization of the Kitaev model
• A Z${}_2$ spin-orbital liquid state in the square lattice Kugel-Khomskii model
• Triplet and in-gap magnetic states in the ground state of the quantum frustrated FCC antiferromagnet Ba2YMoO6
• Three-dimensional topological phase on the diamond lattice
• Toward Kitaev's sixteenfold way in a honeycomb lattice model
• SU(2)-invariant spin liquids on the triangular lattice with spinful Majorana excitations
• Spontaneous plaquette formation in the SU(4) Spin-Orbital ladder
• Classical and quantum spin dynamics of the honeycomb $\Gamma$ model
• Fractionalized fermionic quantum criticality in spin-orbital Mott insulators
• Plaquette Ground State in the Two-dimensional SU(4) Spin-Orbital Model
• Spin-valley density wave in moiré materials
• Spin-Peierls Instability of Three-Dimensional Spin Liquids with Majorana Fermi Surfaces
• Chiral spin-orbital liquids with nodal lines
• SU(4) Heisenberg model on the honeycomb lattice with exchange-frustrated perturbations: implications for twistronics and Mott insulators
• Vison Crystals in an Extended Kitaev Model on the Honeycomb Lattice
• Majorana Fermion Representation For An Antiferromagnetic Spin-1/2 Chain
• Ferromagnetism and Spin-Valley liquid states in Moiré Correlated Insulators
• Time-reversal symmetric Kitaev model and topological superconductor in two dimensions
• Edge magnetization and spin transport in an SU(2)-symmetric Kitaev spin liquid
• Low-temperature spin dynamics of a valence bond glass in Ba2YMoO6
• Tuning topological orders by a conical magnetic field in the Kitaev model
• Dynamics of a two-dimensional quantum spin-orbital liquid: spectroscopic signatures of fermionic magnons
• Spin Liquids and Pseudogap Metals in $SU(4)$ Hubbard Model in Moiré Superlattice
• Partial flux ordering and thermal Majorana metals in (higher-order) spin liquids

Cited by in corpus (26)

• 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
• 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
• A Kitaev-type spin liquid on a quasicrystal
• 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
• Non-Hermitian generalizations of the Yao-Lee model augmented by SO(3)-symmetry-breaking terms
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• 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
• Quantum Loop States in Spin-Orbital Models on the Honeycomb Lattice
• 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
• 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
• Exactly solvable spin liquids in Kitaev bilayers and moiré superlattices
• Three-dimensional spin-orbital liquids