Chiral spin liquid phase of the triangular lattice Hubbard model: a density matrix renormalization group study

Abstract

Motivated by experimental studies that have found signatures of a quantum spin liquid phase in organic crystals whose structure is well described by the two-dimensional triangular lattice, we study the Hubbard model on this lattice at half filling using the infinite-system density matrix renormalization group (iDMRG) method. On infinite cylinders with finite circumference, we identify an intermediate phase between observed metallic behavior at low interaction strength and Mott insulating spin-ordered behavior at strong interactions. Chiral ordering from spontaneous breaking of time-reversal symmetry, a fractionally quantized spin Hall response, and characteristic level statistics in the entanglement spectrum in the intermediate phase provide strong evidence for the existence of a chiral spin liquid in the full two-dimensional limit of the model.

arXiv commentv2: 15 pages, 13 figures, plus 30 pages (38 figures) Supplemental Material. Substantial additional data supporting the original conclusions: additional cylinder geometries; flux insertion; MPS transfer matrix spectra; analysis of the metal-insulator transition; and analysis of domain walls between the two chiralities. v1:7 pages, 4 figures, plus 15 pages (22 figures) Supplementary Material

References in corpus (70)

• The density-matrix renormalization group in the age of matrix product states
• Entanglement Entropy and Quantum Field Theory
• Topological entanglement entropy
• 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
• Entanglement spectrum of a topological phase in one dimension
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Spin Liquid State in an Organic Mott Insulator with Triangular Lattice
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• An Area Law for One Dimensional Quantum Systems
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in κ-(ET)_2 Cu_2 (CN)_3
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Neel order in square and triangular lattice Heisenberg models
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Is 1T-TaS${}_2$ a 40 year old quantum spin liquid?
• Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States
• Scaling of entanglement support for Matrix Product States
• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• Nonmagnetic Insulating States near the Mott Transitions on Lattices with Geometrical Frustration and Implications for $\kappa$-(ET)${}_2$Cu${}_2(CN{)}_3$
• Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
• Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model
• Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians
• Characterizing topological order by studying the ground states of an infinite cylinder
• Mott Transition, Antiferromagnetism, and d-wave Superconductivity in Two-Dimensional Organic Conductors
• Competing Spin Liquid States in the Spin-$1/2$ Heisenberg Model On Triangular Lattice
• Variational description of Mott insulators
• Topography of Spin Liquids on a Triangular Lattice
• Dirac Spin Liquid on the Spin-1/2 Triangular Heisenberg Antiferromagnet
• Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice
• The Hubbard model on the triangular lattice: Spiral order and spin liquid
• Gapless spin-liquid phase in an extended spin 1/2 triangular Heisenberg model
• Emergence of inhomogeneous moments from spin liquid in the triangular-lattice Mott insulator $\kappa$-(ET)${}_2$Cu${}_2$(CN)${}_3$
• The half-filled Landau level: the case for Dirac composite fermions
• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• The phase diagram of the anisotropic spin-2 XXZ model: an infinite system DMRG study
• Chiral Spin Liquid and Quantum Criticality in Extended $S=1/2$ Heisenberg Models on the Triangular Lattice
• Spin Bose-Metal phase in a spin-1/2 model with ring exchange on a two-leg triangular strip
• Fractionalization, topological order, and quasiparticle statistics
• Global phase diagram and quantum spin liquids in spin-1/2 triangular antiferromagnet
• Weak Mott insulators on the triangular lattice: possibility of a gapless nematic quantum spin liquid
• Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
• Theory of a competitive spin liquid state for weak Mott insulators on the triangular lattice
• Ground state phase diagram of the triangular lattice Hubbard model by density matrix renormalization group method
• Phase diagram of the Hubbard model on the anisotropic triangular lattice
• Absence of magnetic thermal conductivity in the quantum spin liquid candidate EtMe3Sb[Pd(dmit)2]2 -- revisited
• Characterization and stability of a fermionic ν=1/3 fractional Chern insulator
• Transfer Matrices and Excitations with Matrix Product States
• Spin Bose-Metal and Valence Bond Solid phases in a spin-1/2 model with ring exchanges on a four-leg triangular ladder
• Density matrix renormalization group on a cylinder in mixed real and momentum space
• Spin-liquid versus spiral-order phases in the anisotropic triangular lattice
• Thermal conductivity of the quantum spin liquid candidate EtMe3Sb[Pd(dmit)2]2: No evidence of mobile gapless excitations
• Fractionalized excitations in the partially magnetized spin liquid candidate YbMgGaO4
• Spin-liquid and magnetic phases in the anisotropic triangular lattice: the case of $\kappa$-(ET)${}_2$X
• Constraints on topological order in Mott Insulators
• Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice
• Error estimates for extrapolations with matrix-product states
• Critical Spin Liquid versus Valence Bond Glass in Triangular Lattice Organic $\kappa$-(ET)${}_2$Cu${}_2$(CN)${}_3$
• The effect of spin-orbit coupling on the effective-spin correlation in YbMgGaO4
• Strong-Coupling Phases of Frustrated Bosons on a 2-leg Ladder with Ring Exchange
• Detection and characterization of symmetry-broken long-range orders in the spin-$\frac{1}{2}$ triangular Heisenberg model
• A continuous Mott transition between a metal and a quantum spin liquid
• Mott transition and magnetism of the triangular-lattice Hubbard model with next-nearest-neighbor hopping
• Measuring space-group symmetry fractionalization in Z${}_2$ spin liquids
• Edge Excitations of the $\nu =2/3$ Spin-Singlet Quantum Hall State
• Metal-insulator transitions, superconductivity, and magnetism in the two-band Hubbard model
• Electron energy spectrum of the spin-liquid state in a frustrated Hubbard model
• Classical phase diagram of the stuffed honeycomb lattice

Cited by in corpus (140)

• Quantum Criticality in Twisted Transition Metal Dichalcogenides
• Provably efficient machine learning for quantum many-body problems
• Band topology, Hubbard model, Heisenberg model, and Dzyaloshinskii-Moriya interaction in twisted bilayer WSe${}_2$
• Hartree-Fock study of the moiré Hubbard model for twisted bilayer transition metal dichalcogenides
• Mott insulating states with competing orders in the triangular lattice 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
• Stripes, Antiferromagnetism, and the Pseudogap in the Doped Hubbard Model at Finite Temperature
• Site-resolved imaging of ultracold fermions in a triangular-lattice quantum gas microscope
• Non-local interactions in moiré Hubbard systems
• High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks
• Doped Mott Insulators in the Triangular Lattice Hubbard Model
• Phase diagram of the anisotropic triangular lattice Hubbard model
• Metal-insulator transition in transition metal dichalcogenide heterobilayer moiré superlattices
• A two-dimensional programmable tweezer array of fermions
• Fractional quantum Hall states for moiré superstructures in the Hofstadter regime
• Quantum Spin Liquid with Emergent Chiral Order in the Triangular-lattice Hubbard Model
• Gate-tunable heavy fermion quantum criticality in a moiré Kondo lattice
• Ultrafast renormalization of the onsite Coulomb repulsion in a cuprate superconductor
• Topological superconductivity in the doped chiral spin liquid on the triangular lattice
• Doping the chiral spin liquid -- topological superconductor or chiral metal?
• Dynamical Mean Field Theory of Moiré Bilayer Transition Metal Dichalcogenides: Phase Diagram, Resistivity, and Quantum Criticality
• Competing magnetic states in transition metal dichalcogenide moiré materials
• TMDs as a platform for spin liquid physics: A strong coupling study of twisted bilayer WSe${}_2$
• Hubbard ladders at small $U$ revisited
• Evidence of Dirac Quantum Spin Liquid in YbZn2GaO5
• Spectral function of the $J_1-J_2$ Heisenberg model on the triangular lattice
• Abelian SU$(N{)}_1$ Chiral Spin Liquids on the Square Lattice
• Quantum Phase Diagram and Spontaneously Emergent Topological Chiral Superconductivity in Doped Triangular-Lattice Mott Insulators
• Topological chiral and nematic superconductivity by doping Mott insulators on triangular lattice
• Triangular lattice Hubbard model physics at intermediate temperatures
• Hole Spectral Function of a Chiral Spin Liquid in the Triangular Lattice Hubbard Model
• Gapless spin liquid and pair density wave of the Hubbard model on three-leg triangular cylinders
• Tunable Stripe Order and Weak Superconductivity in the Moiré Hubbard Model
• Chiral Pseudo Spin Liquids in Moire Heterostructures
• Quantum Electrodynamics in 2+1 Dimensions as the Organizing Principle of a Triangular Lattice Antiferromagnet
• Quantum Phases of Transition Metal Dichalcogenide Moiré Systems
• Thermodynamic properties of an $S=1/2$ ring-exchange model on the triangular lattice
• Electrically tuned topology and magnetism in twisted bilayer MoTe${}_2$ at ${\nu }_h=1$
• Witnessing nonequilibrium entanglement dynamics in a strongly correlated fermionic chain
• Mott transition, Widom line and pseudogap in the half-filled triangular lattice Hubbard model
• Deconfined metallic quantum criticality: A $U(2)$ gauge-theoretic approach
• Metal-insulator transition and intermediate phases in the kagome lattice Hubbard model
• Magnetic and spin-liquid phases in the frustrated $t-t^{\prime }$ Hubbard model on the triangular lattice
• Kagome chiral spin liquid in transition metal dichalcogenide moiré bilayers
• Singlet, Triplet and Pair Density Wave Superconductivity in the Doped Triangular-Lattice Moiré System
• Holes and magnetic polarons in a triangular lattice antiferromagnet
• Quantum gas microscopy of a geometrically frustrated Hubbard system
• Frustrated extended Bose-Hubbard model and deconfined quantum critical points with optical lattices at the anti-magic wavelength
• Noncoplanar magnetic orders and gapless chiral spin liquid on the kagome lattice with staggered scalar spin chirality
• Lee-Yang theory of the two-dimensional quantum Ising model
• Coexistence of non-Abelian chiral spin liquid and magnetic order in a spin-1 antiferromagnet
• Metal-Insulator Transition with Charge Fractionalization
• Electronic Correlation and Geometrical Frustration in Molecular Solids -- A Systematic ab initio Study of ${\beta }^{\prime }$-$X$[Pd(dmit)${}_2$]${}_2$
• Electromagnetic signatures of chiral quantum spin liquid
• From observations to complexity of quantum states via unsupervised learning
• The Hubbard model on triangular $N$-leg cylinders: chiral and non-chiral spin liquids
• Cavity Moiré Materials: Controlling Magnetic Frustration with Quantum Light-Matter Interaction
• Emergence of Competing Orders and Possible Quantum Spin Liquid in SU(N) Fermions
• Quantum Melting of Generalized Wigner Crystals in Transition Metal Dichalcogenide Moiré Systems
• Quantum Hall spin liquids and their possible realization in moiré systems
• Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice
• Low-depth simulations of fermionic systems on square-grid quantum hardware
• Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator
• Probing magnetism in moiré heterostructures with quantum twisting microscopes
• Chiral spin liquid and quantum phase diagram of spin-$1/2$ $J_1$-$J_2$-$J_{\chi }$ model on the square lattice
• Magnetic excitations, phase diagram and order-by-disorder in the extended triangular-lattice Hubbard model
• Spectra of a Gapped Quantum Spin Liquid with a Strong Chiral Excitation on the Triangular Lattice
• Mott insulators in moiré transition metal dichalcogenides at fractional fillings: Slave-rotor mean-field theory
• Proximity-driven ferromagnetism and superconductivity in the triangular Rashba-Hubbard model
• How quantum phases on cylinders approach the 2d limit
• 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
• Chiral Broken Symmetry Descendants of the Kagomé Lattice Chiral Spin Liquid
• Spin Vortex Crystal Order in Organic Triangular Lattice Compound
• Superconductivity in doped triangular Mott insulators: the roles of parent spin backgrounds and charge kinetic energy
• Magnetic phases of the anisotropic triangular lattice Hubbard model
• Comparative study of the density matrix embedding theory for the Hubbard models
• Kitaev-Heisenberg model on the star lattice: From chiral Majorana fermions to chiral triplons
• Chiral superconductivity in the doped triangular-lattice Fermi-Hubbard model in two dimensions
• Hydrodynamics of quantum spin liquids
• Doping the Mott insulating state of the triangular-lattice Hubbard model reveals the Sordi transition
• Phase diagram of a bilinear-biquadratic spin-1 model on the triangular lattice from density matrix renormalization group simulations
• Unconventional ferromagnetism and spin-triplet superconductivity in the imbalanced Kagome-lattice Hubbard model
• Pomeranchuk Effect and Tunable Quantum Phase Transitions in 3L-MoTe2/WSe2
• Tunable moire spinons in magnetically encapsulated twisted van der Waals quantum spin-liquids
• Linked Cluster Expansions via Hypergraph Decompositions
• Particle-hole asymmetric ferromagnetism and spin textures in the triangular Hubbard-Hofstadter model
• Pressure-tuned many-body phases through $\Gamma$-K valleytronics in moiré bilayer WSe${}_2$
• Charge and spin properties of a generalized Wigner crystal realized in the moiré WSe${}_2$/WS${}_2$ heterobilayer
• Electric field control of a quantum spin liquid in weak Mott insulators
• Performance of the rigorous renormalization group for first order phase transitions and topological phases
• A Multi-Purpose Platform for Analog Quantum Simulation
• Kondo enabled transmutation between spinons and superconducting vortices: origin of magnetic memory in 4Hb-$\mathrm{Ta}{\mathrm{S}}_2$
• Effects of lattice geometry on thermopower properties of the repulsive Hubbard model
• Superconductivity in a Topological Lattice Model with Strong Repulsion
• Double exchange, itinerant ferromagnetism and topological Hall effect in moiré heterobilayer
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Continuous Wigner-Mott transition at $\nu =1/5$
• Detection of chiral spin fluctuations driven by frustration in Mott insulators
• Simulating chiral spin liquids with projected entangled-pair states
• Effect of hole doping on the 120 degree order in the triangular lattice Hubbard model: A Hartree-Fock revisit
• Chern number landscape of spin-orbit coupled chiral superconductors
• Classical and quantum spin liquids
• The Fractal-Lattice Hubbard Model
• Hamming Distance and the onset of quantum criticality
• Particle-Hole Asymmetry and Pinball Liquid in a Triangular-Lattice Extended Hubbard Model within Mean-Field Approximation
• Self-consistent evaluation of proximity and inverse proximity effects with pair-breaking in diffusive SN junctions
• Chiral Spin Liquid and Quantum Phase Transition in the Triangular Lattice Hofstadter-Hubbard Model
• A Promising Method for Strongly Correlated Electrons in Two Dimensions: Gutzwiller-Guided Density Matrix Renormalization Group
• Network of chiral one-dimensional channels and localized states emerging in a moiré system
• Continuous phase transition from a chiral spin state to collinear magnetic order in a zigzag chain with Kitaev interactions
• Quantum Spin Liquids in Weak Mott Insulators with a Spin-Orbit Coupling
• Ferromagnetism and Skyrmions in the Hofstadter-Fermi-Hubbard Model
• Magnetic field induced partially polarized chiral spin liquid in a transition metal dichalcogenide moiré system
• Metal-insulator transitions in pyrochlore oxides
• Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation
• Rainbow chains and numerical renormalisation group for accurate chiral conformal spectra
• Symmetry-deformed toric codes and the quantum dimer model
• Ground state energy and magnetization curve of a frustrated magnetic system from real-time evolution on a digital quantum processor
• Spiral magnetism and chiral superconductivity in Kondo-Hubbard triangular lattice model
• Fermi-Hubbard model on non-bipartite lattices: flux problem and emergent chirality
• Chiral Edge States Emerging on Anyon-Net
• Phase diagram of the J1-J2 Heisenberg second-order topological quantum magnet
• Correlation-driven non-trivial phases in single bi-layer Kagome intermetallics
• Gapped magnetic ground state in the spin-liquid candidate $\kappa$-(BEDT-TTF)${}_2$Ag${}_2$(CN)${}_3$ suggested by magnetic spectroscopy
• Quantum Hall to Chiral Spin Liquid transition in a Triangular Lattice Hofstadter-Hubbard Model
• Study of the triangular-lattice Hubbard model with constrained-path quantum Monte Carlo
• Kinetic Energy Driven Ferromagnetic Insulator
• Renormalization group analysis of weakly interacting van der Waals Fermi system
• The Frenkel line and the pseudogap: an analogy between classical and electronic fluids
• Entanglement Spectroscopy and probing the Li-Haldane Conjecture in Topological Quantum Matter
• Competing states in the $S=1/2$ triangular-lattice $J_1$-$J_2$ Heisenberg model: a dynamical density-matrix renormalization group study
• Site-resolved observables in the doped spin-imbalanced triangular Hubbard model
• Hubbard model on a triangular lattice at finite temperatures
• Functional renormalization of spinless triangular-lattice fermions: $N$-patch vs. truncated-unity scheme
• Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials
• SrCu(OH)${}_3$Cl, an ideal isolated equilateral triangle spin $S$ = 1/2 model system
• Triangular lattice models of the Kalmeyer-Laughlin spin liquid from coupled wires
• Itinerant magnetism in Hubbard models with long-range interactions