Chiral spin liquid with spinon Fermi surfaces in spin-$1/2$ triangular Heisenberg model

Abstract

We study the interplay of competing interactions in spin-$1/2$ triangular Heisenberg model through tuning the first- ($J_1$), second- ($J_2$), and third-neighbor ($J_3$) couplings. Based on large-scale density matrix renormalization group calculation, we identify a quantum phase diagram of the system and discover a new {\it gapless} chiral spin liquid (CSL) phase in the intermediate $J_2$ and $J_3$ regime. This CSL state spontaneously breaks time-reversal symmetry with finite scalar chiral order, and it has gapless excitations implied by a vanishing spin triplet gap and a finite central charge on the cylinder. Moreover, the central charge grows rapidly with the cylinder circumference, indicating emergent spinon Fermi surfaces. To understand the numerical results we propose a parton mean-field spin liquid state, the $U(1)$ staggered flux state, which breaks time-reversal symmetry with chiral edge modes by adding a Chern insulator mass to Dirac spinons in the $U(1)$ Dirac spin liquid. This state also breaks lattice rotational symmetries and possesses two spinon Fermi surfaces driven by nonzero $J_2$ and $J_3$, which naturally explains the numerical results. To our knowledge, this is the first example of a gapless CSL state with coexisting spinon Fermi surfaces and chiral edge states, demonstrating the rich family of novel phases emergent from competing interactions in triangular-lattice magnets.

arXiv comment4 pages, 4 figures, with Supplemental Material

References in corpus (50)

• Anyons in an exactly solved model and beyond
• Entanglement Entropy and Quantum Field Theory
• Quantum Spin Liquids
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Quantum Spin Liquid States
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Spin Liquid State in an Organic Mott Insulator with Triangular Lattice
• Quantum Orders and Symmetric Spin Liquids
• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• Inversion symmetry breaking in noncollinear magnetic phase of a triangular lattice antiferromagnet CuFeO2
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in κ-(ET)_2 Cu_2 (CN)_3
• Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4
• Rare-earth triangular lattice spin liquid: a single-crystal study of YbMgGaO${}_4$
• Mott Transition from a Spin Liquid to a Fermi Liquid in the Spin-Frustrated Organic Conductor kappa-(ET)2Cu2(CN)3
• Is 1T-TaS${}_2$ a 40 year old quantum spin liquid?
• Spin-driven ferroelectricity and possible antiferroelectricity in triangular lattice antiferromagnets ACrO2 (A = Cu, Ag, Li, or Na)
• Spin liquid nature in the Heisenberg $J_1$-$J_2$ triangular antiferromagnet
• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• The Non-Abelian Density Matrix Renormalization Group Algorithm
• Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
• Competing Spin Liquid States in the Spin-$1/2$ Heisenberg Model On Triangular Lattice
• Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model
• Spin-Liquid phase of the Multiple-Spin Exchange Hamiltonian on the Triangular Lattice
• A new high-temperature quantum spin liquid with polaron spins
• Topography of Spin Liquids on a Triangular Lattice
• Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
• Dirac Spin Liquid on the Spin-1/2 Triangular Heisenberg Antiferromagnet
• Fractionalization in the cuprates: Detecting the topological order
• Gapless spin-liquid phase in an extended spin 1/2 triangular Heisenberg model
• The half-filled Landau level: the case for Dirac composite fermions
• Spin Bose-Metal phase in a spin-1/2 model with ring exchange on a two-leg triangular strip
• Unifying Description of Competing Orders in Two Dimensional Quantum Magnets
• Spinon Fermi surface in a cluster Mott insulator model on a triangular lattice and possible application to 1T-TaS${}_2$
• Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension
• Projective symmetry group classification of chiral spin liquids
• Magnetic Interaction in the Geometrically Frustrated Triangular Lattice Antiferromagnet $\mathrm{CuFe}{\mathrm{O}}_2$
• Gapless excitations in the ground state of 1T-TaS${}_2$
• A Quantum Dipolar Spin Liquid
• Quasiclassical magnetic order and its loss in a spin-1/2 Heisenberg antiferromagnet on a triangular lattice with competing bonds
• Interaction-Driven Spontaneous Quantum Hall Effect on Kagome Lattice
• Spin Bose-Metal and Valence Bond Solid phases in a spin-1/2 model with ring exchanges on a four-leg triangular ladder
• The Spinon Fermi Surface U(1) Spin Liquid in a Spin-Orbit-Coupled Triangular Lattice Mott Insulator YbMgGaO4
• Hierarchy of exchange interactions in the triangular-lattice spin-liquid YbMgGaO${}_4$
• Symmetry fractionalization in the topological phase of the spin-$\frac{1}{2}$ $J_1$-$J_2$ triangular Heisenberg model
• Fractionalized excitations in the partially magnetized spin liquid candidate YbMgGaO4
• Symmetric $Z_2$ spin liquids and their neighboring phases on triangular lattice
• Heat transport study of the spin liquid candidate 1T-TaS2
• Spin Liquid versus Spin Orbit Coupling on the Triangular Lattice
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS

Cited by in corpus (51)

• The Hubbard Model
• Four-Spin Terms and the Origin of the Chiral Spin Liquid in Mott Insulators on the Triangular Lattice
• SU(4) chiral spin liquid, exciton supersolid and electric detection in moiré bilayers
• Spin liquids in geometrically perfect triangular antiferromagnets
• Thermal Hall effects in quantum magnets
• Quantum Spin Liquid with Emergent Chiral Order in the Triangular-lattice Hubbard Model
• Topological superconductivity in the doped chiral spin liquid on the triangular lattice
• Modular commutator in gapped quantum many-body systems
• Spontaneous antiferromagnetic skyrmion/antiskyrmion lattice and spiral spin liquid states in the frustrated triangular lattice
• Spectral function of the $J_1-J_2$ Heisenberg model on the triangular lattice
• Non-linear magnons and exchange Hamiltonians of delafossite proximate quantum spin liquids
• Dynamical Signatures of Symmetry Broken and Liquid Phases in an $S=1/2$ Heisenberg Antiferromagnet on the Triangular Lattice
• Superconductivity in the doped quantum spin liquid on the triangular lattice
• Quantum Skyrmion Lattices in Heisenberg Ferromagnets
• Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet
• Anyon Superconductivity from Topological Criticality in a Hofstadter-Hubbard Model
• Floquet engineering correlated materials with unpolarized light
• Spin liquid state in a rare-earth hyperkagome lattice
• Nature of quantum spin liquids of the S=1/2 Heisenberg antiferromagnet on the triangular lattice: A parallel DMRG study
• Unquantized thermal Hall effect in quantum spin liquids with spinon Fermi surfaces
• The Hubbard model on triangular $N$-leg cylinders: chiral and non-chiral spin liquids
• Quantum phase diagram and chiral spin liquid in the extended spin-$\frac{1}{2}$ honeycomb XY model
• Arc-shaped structure factor in the $J_1$-$J_2$-$J_3$ classical Heisenberg model on the triangular lattice
• Cavity Moiré Materials: Controlling Magnetic Frustration with Quantum Light-Matter Interaction
• Ground-state and thermodynamic properties of the spin-$\frac{1}{2}$ Heisenberg model on the anisotropic triangular lattice
• Polarization as a tuning parameter for Floquet engineering: magnetism in the honeycomb, square, and triangular Mott insulators
• Noncoplanar orders and quantum disordered states in maple-leaf (anti)ferromagnets
• Simulating Spin Dynamics of Supersolid States in a Quantum Ising Magnet
• Intertwining SU($N$) symmetry and frustration on a honeycomb lattice
• Spontaneous Chiral-Spin Ordering in Spin-Orbit Coupled Honeycomb Magnets
• On the origin of the possible chiral spin liquid state of the triangular lattice Hubbard model
• Electric field control of a quantum spin liquid in weak Mott insulators
• Engineering frustrated Rydberg spin models by graphical Floquet modulation
• Interplay of Kitaev Interaction and Off-diagonal Exchanges: Exotic Phases and Quantum Phase Diagrams
• Detection of chiral spin fluctuations driven by frustration in Mott insulators
• Magnetic field induced partially polarized chiral spin liquid in a transition metal dichalcogenide moiré system
• Partially disordered Heisenberg antiferromagnet with short-range stripe correlations
• From strong to weak correlations in breathing-mode kagome van der Waals materials: Nb${}_3$(F,Cl,Br,I)${}_8$ as a robust and versatile platform for many-body engineering
• Emergent Quantum Phenomena of Noncentrosymmetric Charge-Density Wave in 1T-Transition Metal Dichalcogenides
• Majorana Fermi surface state in a network of quantum spin chains
• Magnetic field-temperature phase diagram of spin-1/2 triangular lattice antiferromagnet KYbSe${}_2$
• Recent progress in quantum spin liquids, fractional magnetization plateaus, and unconventional superconductivity in kagome lattices
• The Finite-Temperature Behavior of a Triangular Heisenberg Antiferromagnet
• Fermi-Hubbard model on non-bipartite lattices: flux problem and emergent chirality
• Density-Matrix Mean-Field Theory
• 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
• Itinerant magnetism in Hubbard models with long-range interactions
• Finite Spinon Density-of-States in Triangular-Lattice Delafossite TlYbSe${}_2$
• Competing states in the $S=1/2$ triangular-lattice $J_1$-$J_2$ Heisenberg model: a dynamical density-matrix renormalization group study
• Quantum spin liquid ground state with the evidence of roton-like excitations at elevated temperatures in the triangular-lattice delafossite YbCuSe${}_2$