Haldane-Hubbard Mott Insulator: From Tetrahedral Spin Crystal to Chiral Spin Liquid

Abstract

Motivated by cold atom experiments on Chern insulators, we study the honeycomb lattice Haldane-Hubbard Mott insulator of spin-$1/2$ fermions using exact diagonalization and density matrix renormalization group methods. We show that this model exhibits various chiral magnetic orders including a wide regime of triple-Q tetrahedral order. Incorporating third-neighbor hopping frustrates and ultimately melts this tetrahedral spin crystal. From analyzing low energy spectra, many-body Chern numbers, entanglement spectra, and modular matrices, we identify the molten state as a chiral spin liquid (CSL) with gapped semion excitations. We formulate and study the Chern-Simons-Higgs field theory of the exotic CSL-to-tetrahedral spin crystallization transition.

4 pages, Supplemental Material (3 pages). Revised following referee comments. Published version

References in corpus (30)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• "Deconfined" quantum critical points
• Observation of Weyl nodes in TaAs
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator
• Discovery of a Weyl Fermion semimetal state in NbAs
• Scalar spin chirality and quantum Hall effect on a triangular lattice
• Precise quantization of anomalous Hall effect near zero magnetic field
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Characterizing topological order by studying the ground states of an infinite cylinder
• Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Coupled wire construction of chiral spin liquids
• Nature of chiral spin liquids on the kagome lattice
• Variational Monte Carlo study of chiral spin liquid in the extended Heisenberg model on the Kagome lattice
• Chiral Spin Liquids in Arrays of Spin Chains
• Plaquette valence-bond ordering in J_1-J_2 Heisenberg antiferromagnet on the honeycomb lattice
• Chiral topological spin liquids with projected entangled pair states
• Chiral spin liquids on the kagome Lattice
• Continuous Preparation of a Fractional Chern Insulator
• Chern-Simons theory of the magnetization plateaus of the spin-1/2 quantum XXZ Heisenberg model on Kagome Lattice
• Detecting crystal symmetry fractionalization from the ground state: Application to ${\mathbb{Z}}_2$ spin liquids on the kagome lattice
• Magnetic Order Driven Topological Transition in the Haldane-Hubbard Model
• Competing Chiral Orders in the Topological Haldane-Hubbard Model of Spin-1/2 Fermions and Bosons
• Chiral spin density wave order on frustrated honeycomb and bilayer triangle lattice Hubbard model at half-filling
• Classification and detection of symmetry fractionalization in chiral spin liquids
• Numerical detection of symmetry enriched topological phases with space group symmetry

Cited by in corpus (54)

• Topological Bands for Ultracold Atoms
• Band geometry, Berry curvature and superfluid weight
• Chiral Spin Liquid and Quantum Criticality in Extended $S=1/2$ Heisenberg Models on the Triangular Lattice
• Dynamical Time-Reversal Symmetry Breaking and Photo-Induced Chiral Spin Liquids in Frustrated Mott Insulators
• Global phase diagram and quantum spin liquids in spin-1/2 triangular antiferromagnet
• Topological phase transitions in the repulsively interacting Haldane-Hubbard model
• Probing and controlling spin chirality in Mott insulators by circularly polarized laser
• Thermal Hall effects in quantum magnets
• Controlling the Floquet state population and observing micromotion in a periodically driven two-body quantum system
• Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
• Emergence of Chiral Spin Liquids via Quantum Melting of Non-Coplanar Magnetic Orders
• First order topological phase transition of the Haldane--Hubbard model
• Phase diagram topology of the Haldane-Hubbard-Coulomb model
• Topological Sachdev-Ye-Kitaev Model
• Fate of a topological invariant for correlated lattice electrons at finite temperature
• Two-component quantum Hall effects in topological flat bands
• Non-Coplanar Magnetic Orders in Classical Square-Kagome Antiferromagnets
• Coexistence of non-Abelian chiral spin liquid and magnetic order in a spin-1 antiferromagnet
• Emergent Chiral Spin State in the Mott Phase of a Bosonic Kane-Mele-Hubbard Model
• Spin chain network construction of chiral spin liquids
• Non-coplanar magnetism, topological density wave order and emergent symmetry at half-integer filling of moiré Chern bands
• Chiral Spin Order in Kondo-Heisenberg systems
• Polarization as a tuning parameter for Floquet engineering: magnetism in the honeycomb, square, and triangular Mott insulators
• Quantum phase diagram and chiral spin liquid in the extended spin-$\frac{1}{2}$ honeycomb XY model
• Noncoplanar orders and quantum disordered states in maple-leaf (anti)ferromagnets
• Spectrum of conformal gauge theories on a torus
• A Scaling Behavior of Bloch Oscillation in Weyl Semimetals
• Phase diagram and topological phases in the triangular lattice Kitaev-Hubbard model
• Emergent topology and symmetry-breaking order in correlated quench dynamics
• Determining non-Abelian topological order from infinite projected entangled pair states
• Chiral Broken Symmetry Descendants of the Kagomé Lattice Chiral Spin Liquid
• On the origin of the possible chiral spin liquid state of the triangular lattice Hubbard model
• Quantum spin liquids of Rydberg excitations in a honeycomb lattice induced by density-dependent Peierls phases
• Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model
• Determining topological order from infinite projected entangled pair states
• Generalized Gibbs Ensemble Description of Real Space Entanglement Spectra of (2+1)-dimensional Chiral Topological Systems with $SU(2)$ Symmetry
• Topological phase transition and nontrivial thermal Hall signatures in honeycomb lattice magnets
• Bilayer Haldane model: From trivial band insulator to fractionalized quantum anomalous Hall insulator
• Anomalous valley Hall effect in monolayer chromium-based triple-Q magnets
• Quantum cluster approach to the topological invariants in correlated Chern insulators
• Electric field control of a quantum spin liquid in weak Mott insulators
• Fractional Spin Quantum Hall Effect in Weakly Coupled Spin Chain Arrays
• Topological order in the Haldane model with spin-spin on-site interactions
• Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet
• Magnetic field induced partially polarized chiral spin liquid in a transition metal dichalcogenide moiré system
• Chiral spin liquid phase in an optical lattice at mean-field level
• Chiral Spin Liquid and Quantum Phase Transition in the Triangular Lattice Hofstadter-Hubbard Model
• Diagnosing electronic phases of matter using photonic correlation functions
• Emergence of charge density wave and superconducting phase transitions through Lorentz-invariant interactions in the Haldane-Hubbard model
• Quantum Magnetism in Wannier-Obstructed Mott Insulators
• Variational methods for characterizing matrix product operator symmetries
• Tuning magnetic interactions with nonequilibrium optical phonon populations: a theoretical study
• Schwinger-Boson mean-field study of spin-1/2 $J_1$-$J_2$-$J_{\chi }$ model in honeycomb lattice: thermal Hall signature
• Persistent Haldane Phase in Carbon Tetris Chains