Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands

Abstract

Fractional excitations hold immense promise for both fundamental physics and quantum technologies. However, constructing lattice models for their dynamics under gauge fields remains a formidable challenge due to inherent obstructions. Here, we introduce a novel and systematic framework for deriving low-energy lattice models of fractional orbitals coupled to tight-binding gauge fields. Departing from conventional geometric approaches, our method systematically eliminates the high-energy states via virtual hopping, thereby deriving the gauge potential and quantum metric through a superexchange-like mechanism. We demonstrate the framework by constructing Wannier orbitals for Majorana states and a tight-binding $Z_2$ gauge field across various flux crystalline phases in the Kitaev spin model on a honeycomb lattice. Our study reveals a striking phase transition between two non-trivial topological phases characterized by gapless flat-band with extensive degeneracy. Furthermore, we develop a gauge-invariant mean-field theory for interacting Majorana orbitals, leading to a correlation-induced fractional Chern state. Our work establishes a general framework for gauge-mediated tight-binding models and a gauge-invariant mean-field theory for interacting fractional orbitals that can be readily extended to $U(1)$, $SU(N)$ lattice gauge theories.

Accepted in PRX; 21 pages including references and supplementary material

References in corpus (57)

• "Deconfined" quantum critical points
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Wannier representation of Z_2 topological insulators
• Exponential localization of Wannier functions in insulators
• Exact results for spin dynamics and fractionization in the Kitaev Model
• Superfluidity and Quantum Geometry in Twisted Multilayer Systems
• Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis of Schwinger Boson States
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Review of Some Promising Fractional Physical Models
• The insulator/Chern-insulator transition in the Haldane model
• Gauging quantum states: from global to local symmetries in many-body systems
• Vortexability: A Unifying Criterion for Ideal Fractional Chern Insulators
• Superfluid weight bounds from symmetry and quantum geometry in flat bands
• A simple method to construct Flat Band lattices
• Compactly-supported Wannier functions and algebraic $K$-theory
• Classical Prethermal Phases of Matter
• Absent pinch points and emergent clusters: further neighbour interactions in the pyrochlore Heisenberg antiferromagnet
• Fundamental bound on topological gap
• Spin Dynamics in Pyrochlore Heisenberg Antiferromagnets
• Contrasting lattice geometry dependent versus independent quantities: ramifications for Berry curvature, energy gaps, and dynamics
• Vacancy-induced low-energy density of states in the Kitaev spin liquid
• STM as a single Majorana detector of Kitaev's chiral spin liquid
• Electrical Access to Ising Anyons in Kitaev Spin Liquids
• Spectroscopic fingerprints of gapped quantum spin liquids, both conventional and fractonic
• Continuous Preparation of a Fractional Chern Insulator
• The Heart of Entanglement: Chiral, Nematic, and Incommensurate Phases in the Kitaev-Gamma Ladder in a Field
• Topological Route to New and Unusual Coulomb Spin Liquids
• Pinwheel valence-bond-crystal ground state of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the $shuriken$ lattice
• Logarithmic entanglement growth from disorder-free localization in the two-leg compass ladder
• Flux crystals, Majorana metals, and flat bands in exactly solvable spin-orbital liquids
• Generic nearest-neighbour kagome model: XYZ & Dzyaloshinskii-Moriya, and comparison to pyrochlore
• A fractionalised "${\mathbb{Z}}_2$" classical Heisenberg spin liquid
• Thermodynamics of the spin-half square-kagome lattice antiferromagnet
• Combined approach to analyze and classify families of classical spin liquids
• Origin of band flatness and constraints of higher Chern numbers
• Order by disorder, without order, in a two-dimensional spin system with O(2) symmetry
• Further insights into the thermodynamics of the Kitaev honeycomb model
• Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model out of equilibrium
• Non-Coplanar Magnetic Orders in Classical Square-Kagome Antiferromagnets
• Signatures of fractional statistics in nonlinear pump-probe spectroscopy
• Majorana correlations in the Kitaev model with ordered-flux structures
• Magnetism of the $s=1/2$ $J_1$-$J_2$ square-kagome lattice antiferromagnet
• Flux mobility delocalization in the Kitaev spin ladder
• Flat bands and entanglement in the Kitaev ladder
• Ferromagnetic Coulomb phase in classical spin ice
• $\require{mhchem}$Quantum paramagnetism in the decorated square-kagome antiferromagnet $\ce{Na6Cu7BiO4(PO4)4Cl3}$
• Emergent glassiness in disorder-free Kitaev model: Density matrix renormalization group study on a one-dimensional ladder setting
• Classical spin liquids in stacked triangular lattice Ising antiferromagnets
• Static and resonant properties of decorated square kagome lattice compound KCu${}_7$(TeO${}_4$)(SO${}_4$)${}_5$Cl
• Protected Gapless Edge States In Trivial Topology
• The Classical Heisenberg Model on the Centred Pyrochlore Lattice
• Optimally Localized Wannier Functions for 2D Chern Insulators
• Field-driven spatiotemporal manipulation of Majorana zero modes in a Kitaev spin liquid
• Effective models for dense vortex lattices in the Kitaev honeycomb model
• Majorana Gap Formation in the Anisotropic Kitaev Model with Ordered Flux Configuration