The Hubbard Model

Abstract

The repulsive Hubbard model has been immensely useful in understanding strongly correlated electron systems, and serves as the paradigmatic model of the field. Despite its simplicity, it exhibits a strikingly rich phenomenology which is reminiscent of that observed in quantum materials. Nevertheless, much of its phase diagram remains controversial. Here, we review a subset of what is known about the Hubbard model, based on exact results or controlled approximate solutions in various limits, for which there is a suitable small parameter. Our primary focus is on the ground state properties of the system on various lattices in two spatial dimensions, although both lower and higher dimensions are discussed as well. Finally, we highlight some of the important outstanding open questions.

To appear in Annual Reviews of Condensed Matter Physics

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Cited by in corpus (258)

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• Extended Bose-Hubbard model with dipolar excitons
• Emergent Superconductivity and Competing Charge Orders in Hole-Doped Square-Lattice $t$-$J$ Model
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• Temperature Dependence of Spin and Charge Orders in the Doped Two-Dimensional Hubbard Model
• A neutral-atom Hubbard quantum simulator in the cryogenic regime
• Origin and fate of the pseudogap in the doped Hubbard model
• Quantum Phase Diagram and Spontaneously Emergent Topological Chiral Superconductivity in Doped Triangular-Lattice Mott Insulators
• Triangular lattice Hubbard model physics at intermediate temperatures
• Topological chiral and nematic superconductivity by doping Mott insulators on triangular lattice
• Superconductivity in the Bilayer Two-orbital Hubbard Model
• Fast and scalable quantum Monte Carlo simulations of electron-phonon models
• Superconducting stripes in the hole-doped three-band Hubbard model
• Comprehensive mean-field analysis of magnetic and charge orders in the two-dimensional Hubbard model
• Traces of Electron-Phonon Coupling in One-Dimensional Cuprates
• Hofstadter states and reentrant charge order in a semiconductor moiré lattice
• Altermagnetism on the Shastry-Sutherland lattice
• Twisted bilayer graphene revisited: minimal two-band model for low-energy bands
• Magnetic properties and pseudogap formation in infinite-layer nickelates: insights from the single-band Hubbard model
• Cavity engineering of solid-state materials without external driving
• Superconducting valence bond fluid in lightly doped 8-leg $t$-$J$ cylinders
• Anyon Superconductivity from Topological Criticality in a Hofstadter-Hubbard Model
• Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
• Global Phase Diagram of D-wave Superconductivity in the Square-Lattice $t\text{-}J$ Model
• Metal-insulator transition and quantum magnetism in the SU(3) Fermi-Hubbard Model: Disentangling Nesting and the Mott Transition
• Universality and Critical Exponents of the Fermion Sign Problem
• Ab-initio variational wave functions for the time-dependent many-electron Schrödinger equation
• Mott transition, Widom line and pseudogap in the half-filled triangular lattice Hubbard model
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• Dynamical vortex transitions in a gate-tunable Josephson junction array
• Fragmented Cooper pair condensation in striped superconductors
• Full counting statistics in the many-body Hatano-Nelson model
• Fluctuating intertwined stripes in the strange metal regime of the Hubbard model
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• Neural network approach to quasiparticle dispersions in doped antiferromagnets
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• Phase transitions in partial summation methods: Results from the 3D Hubbard model
• Accurate Simulation of the Hubbard Model with Finite Fermionic Projected Entangled Pair States
• Broken-symmetry magnetic phases in two-dimensional triangulene crystals
• Phase Diagram, $d$-Wave Superconductivity, and Pseudogap of the $t$-$t^{\prime }$-$J$ Model at Finite Temperature
• Magnetic, thermodynamic, and dynamical properties of the three-dimensional fermionic Hubbard model: A comprehensive Monte Carlo study
• The Wiedemann-Franz law in doped Mott insulators without quasiparticles
• Complex magnetic and spatial symmetry breaking from correlations in kagome flat bands
• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
• Phase fluctuations in two-dimensional superconductors and pseudogap phenomenon
• Spectral properties of 1D extended Hubbard model from bosonization and time-dependent variational principle: applications to 1D cuprate
• Seven Useful Questions in Density Functional Theory
• Exact eigenstates of multicomponent Hubbard models: SU($N$) magnetic $\eta$ pairing, weak ergodicity breaking, and partial integrability
• Cavity Moiré Materials: Controlling Magnetic Frustration with Quantum Light-Matter Interaction
• Finite Projected Entangled Pair States for the Hubbard model
• Reexamining doped two-legged Hubbard ladders
• Thermodynamics of the metal-insulator transition in the extended Hubbard model from determinantal quantum Monte Carlo
• Exploring the role of nonlocal Coulomb interactions in perovskite transition metal oxides
• Deconfined criticalities and dualities between chiral spin liquid, topological superconductor and charge density wave Chern insulator
• Nagaoka ferromagnetism in doped Hubbard models in optical lattices
• Mott transition and pseudogap of the square-lattice Hubbard model: results from center-focused cellular dynamical mean-field theory
• Precision Many-Body Study of the Berezinskii-Kosterlitz-Thouless Transition and Temperature-Dependent Properties in the Two-Dimensional Fermi Gas
• Sign structure of the $t$-$t^{\prime }$-$J$ model and its physical consequences
• Pseudogap metal and magnetization plateau from doping moiré Mott insulator
• Switching between Mott-Hubbard and Hund physics in moiré quantum simulators
• Robust charge-density wave correlations in the electron-doped single-band Hubbard model
• Spectral structure and doublon dissociation in the two-particle non-Hermitian Hubbard model
• Observation of emergent scaling of spin-charge correlations at the onset of the pseudogap
• Minimal pole representation and analytic continuation of matrix-valued correlation functions
• Dichotomy of heavy and light pairs of holes in the $t-J$ model
• From non-metal to strange metal at the stripe-percolation transition in La${}_{2-x}$Sr${}_x$CuO${}_4$
• Quantifying hole-motion-induced frustration in doped antiferromagnets by Hamiltonian reconstruction
• Magnetic excitations, phase diagram and order-by-disorder in the extended triangular-lattice Hubbard model
• Attractive Su-Schrieffer-Heeger-Hubbard Model on a Square Lattice Away from Half-Filling
• Quadratic scaling path integral molecular dynamics for fictitious identical particles and its application to fermion systems
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• Renormalized Perturbation Theory for Fast Evaluation of Feynman Diagrams on the Real Frequency Axis
• Delay Update in determinant quantum Monte Carlo
• Altermagnetism from coincident Van Hove singularities: application to $\kappa$-Cl
• Adaptive Time Stepping for the Two-Time Integro-Differential Kadanoff-Baym Equations
• Comparative study of charge order in undoped infinite-layer nickelate superconductors
• One- and two-particle properties of the weakly interacting two-dimensional Hubbard model in proximity to the van Hove singularity
• Spiral to stripe transition in the two-dimensional Hubbard model
• Two dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method
• Signatures of many-body localization of quasiparticles in a flat band superconductor
• Sign-Free Determinant Quantum Monte Carlo Study of Excitonic Density Orders in a Two-Orbital Hubbard-Kanamori Model
• Quantum information scrambling in two-dimensional Bose-Hubbard lattices
• Magnetic phase diagram of the three-dimensional doped Hubbard model
• Experimental Demonstration of Break-Even for the Compact Fermionic Encoding
• Pairing at a single Van Hove point
• Splitting and Parallelizing of Quantum Convolutional Neural Networks for Learning Translationally Symmetric Data
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• Superconductivity in doped triangular Mott insulators: the roles of parent spin backgrounds and charge kinetic energy
• Geometry of Degeneracy in Potential and Density Space
• Resonant Inelastic X-ray Scattering Study of Electron-Exciton Coupling in High-Tc Cuprates
• Collective density fluctuations of strange metals with critical Fermi surfaces
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• Flat-band-induced superconductivity in synthetic bilayer optical lattices
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• CDMFT+HFD : an extension of dynamical mean field theory for nonlocal interactions applied to the single band extended Hubbard model
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• Beyond-Hubbard pairing in a cuprate ladder
• Thermodynamic Stability at the Two-Particle Level
• Doping the Mott insulating state of the triangular-lattice Hubbard model reveals the Sordi transition
• Chiral superconductivity in the doped triangular-lattice Fermi-Hubbard model in two dimensions
• Real-space analysis of Hatsugai-Kohmoto interaction
• Self-consistent optimization of the trial wave-function in constrained path auxiliary field Quantum Monte Carlo using mixed estimators
• Nature of the mixed-parity pairing of attractive fermions with spin-orbit coupling in optical lattice
• Lee-Yang theory of quantum phase transitions with neural network quantum states
• Magnetism and Metallicity in Moiré Transition Metal Dichalcogenides
• Hubbard parameters for programmable tweezer arrays
• Phase Diagram of the Square-Lattice $t$-$J$-$V$ Model for Electron-Doped Cuprates
• On the Adequacy of the Dynamical Mean Field Theory for Low Density and Dirac Materials
• Intertwined Orders and the Physics of High Temperature Superconductors
• Theory of Coulomb driven nematicity in a multi-valley two-dimensional electron gas
• Charge Stripe Manipulation of Superconducting Pairing Symmetry Transition
• Robust d-wave superconductivity from the Su-Schrieffer-Heeger-Hubbard model: possible route to high-temperature superconductivity
• Superconductivity in a Topological Lattice Model with Strong Repulsion
• Tunable $t-t^{\prime }-U$ Hubbard models in twisted square homobilayers
• Finite-Temperature Kinetic Ferromagnetism in the Square Lattice Hubbard Model
• Fluctuating charge-density-wave correlations in the three-band Hubbard model
• Dynamic charge Kondo effect and a slave fermion approach to the Mott transition
• Boosting quantum Monte Carlo and alleviating sign problem by Gutzwiller projection
• Three-body problem in a multiband Hubbard model
• Polynomial Time Quantum Gibbs Sampling for Fermi-Hubbard Model at any Temperature
• Superconductivity in the two-dimensional Hubbard model with cellular dynamical mean-field theory: a quantum impurity model analysis
• Digital quantum simulation of lattice fermion theories with local encoding
• Correlation induced $d$-wave pairing in quantum dot square lattice
• Second-order phase transitions and divergent linear response in dynamical mean-field theory
• Spin and bond-charge excitation spectra in correlated electron systems near antiferromagnetic phase
• Preempting Fermion Sign Problem: Unveiling Quantum Criticality through Nonequilibrium Dynamics in Imaginary Time
• Boosting Determinant Quantum Monte Carlo with Submatrix Updates: Unveiling the Phase Diagram of the 3D Hubbard Model
• Quantitative assessment of the universal thermopower in the Hubbard model
• Efficiently measuring $d$-wave pairing and beyond in quantum gas microscopes
• Correlated states in super-moiré materials with a kernel polynomial quantics tensor cross interpolation algorithm
• Ising phase transitions and thermodynamics of correlated fermions in a two-dimensional spin-dependent lattice potential
• Random singlet-like phase of disordered Hubbard chains
• Efficient simulation of inhomogeneously correlated systems using block interaction product states
• The significance of "stripes" in the physics of the cuprates, the Hubbard model, and other highly correlated electronic systems
• Two-doublon Bloch oscillations in the mass-imbalanced extended Fermi-Hubbard model
• Dynamical exchange-correlation potential formalism for spin-$\frac{1}{2}$ Heisenberg and Hubbard chains: the antiferromagnetic/half-filled case
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• Two $T$-linear scattering rate regimes in the triangular lattice Hubbard model
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• The Fractal-Lattice Hubbard Model
• Quantum Transport Theory of Strongly Correlated Matter
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• Effect of hole doping on the 120 degree order in the triangular lattice Hubbard model: A Hartree-Fock revisit
• Inversion symmetry breaking in bilayer multi-orbital Hubbard model with impurity approximation
• Frustration induced Itinerant Ferromagnetism of Fermions in Optical Lattice
• The Influence of Extended Interactions on Spin Dynamics in One-dimensional Cuprates
• Quantum-assisted variational Monte Carlo
• Experimental demonstration of optimal measurement for unambiguously discriminating asymmetric qudit states
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• Half-filled stripe to N$\acute{e}$el antiferromagnetism transition in the $t^{\prime }$-Hubbard model on honeycomb lattice
• Quantum phase transition driven by competing intralayer and interlayer hopping in bilayer nickelates
• Pairing tendencies in the doped Kitaev-Heisenberg model
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• Diagnosing electronic phases of matter using photonic correlation functions
• Classical Benchmarks for Variational Quantum Eigensolver Simulations of the Hubbard Model
• Probing Green's Function Zeros by Co-tunneling through Mott Insulators
• Tuning competition between charge order and superconductivity in the square-lattice $t$-$t^{\prime }$-$J$ model
• Attraction versus repulsion between doublons or holons in Mott-Hubbard systems
• Enhanced pair-density-wave vertices in a bilayer Hubbard model at half-filling
• Ferromagnetism and Skyrmions in the Hofstadter-Fermi-Hubbard Model
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• The SU(N) Fermi-Hubbard Model on two sites: Bethe Ansatz solution and Quantum Phase Transition of the Lipkin-Meshkov-Glick Model in the large-N limit
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• Parameters dependent superconducting transition temperature in high temperature superconductors
• Many-body tunneling in a double-well potential
• Universality of mean-field antiferromagnetic order in an anisotropic 3D Hubbard model at half-filling
• Lee-Yang formalism for phase transitions of interacting fermions using tensor networks
• Structural complexity of snapshots of 2D Fermi-Hubbard systems
• Simulating the Fermi-Hubbard model with long-range hopping on a quantum computer
• Relaxation to persistent currents in a Hubbard trimer coupled to fermionic baths
• Chern numbers for the two-body Hofstadter-Hubbard butterfly
• Mean-field analysis of a Hubbard interaction on Bernal Bilayer Graphene
• Extracting the spin excitation spectrum of a fermionic system using a quantum processor
• Dynamical structure factor and a new method to measure the pairing gap in two-dimensional attractive Fermi-Hubbard model
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• $\eta$-pairing states in the Hubbard model with non-uniform Hubbard interaction
• Accelerating ground-state auxiliary-field quantum Monte Carlo simulations by delayed update and block force-bias update
• Partial suppression of magnetism in the square lattice SU(3) Hubbard model
• A Pseudo-Fermion Propagator Approach to the Fermion Sign Problem
• Signatures of superconducting pairing driven by electron-electron interactions in moiré WSe${}_2$/WSe${}_2$ homobilayer modelled by Hubbard Hamiltonian
• Thermal Tensor Network Simulations of Lattice Fermions with Fixed Filling
• The cumulant Green's functions method for the Hubbard model
• Mean Field Study of Superconductivity in the Square Lattice $t$-$J$ Model with Three-Site Hopping
• Unveiling Stripe-shaped Charge Density Modulations in Doped Mott Insulators
• Robust correlated magnetic moments in end-modified graphene nanoribbons
• Semiclassical analysis of spin dynamics in the non-Hermitian Hubbard model
• Density Matrix Renormalization Group simulations of the SU(N) Fermi-Hubbard chain implementing the full SU(N) symmetry via Semi-Standard Young Tableaux and Unitary Group Subduction Coefficients
• Spin susceptibility in a pseudogap state with fluctuating spiral magnetic order
• Trimers in the Extended Hubbard Model
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• Single-particle spectra and magnetic susceptibility in the Emery model: a dynamical mean-field perspective
• Shaping Magnetic Order by Local Frustration for Itinerant Fermions on a Graph
• Spin-stripes in the Hubbard model: a combined DMFT and Bethe-Salpeter analysis
• Disorder-induced decoupling of attracting identical fermions: transfer matrix approach
• Enhancing wave-particle duality
• Quantum Phase Transitions in Skewed Ladder Systems
• Locality bounds for quantum dynamics at low energy
• Infinite temperature spin dynamics in the asymmetric Hatsugai-Kohmoto model
• Disentangling real space fluctuations: the diagnostics of metal-insulator transitions beyond single-particle spectral functions
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• S. Vonsovsky and the dawn of the theory of strongly correlated systems
• Quantum Monte Carlo study of the metal-insulator crossover in the square-lattice Hubbard model
• Nesting-driven ferromagnetism of itinerant electrons
• Density Matrix Renormalization Group study of superconducting pairing near the quarter-filled Wigner crystal
• Grassmann tensor networks
• Survival of the metallic state in a single-hole multiband $p$-orbital molecular system
• Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials
• Error Interference in Quantum Simulation
• Site-selective correlations in interacting "flat-band" quasicrystals
• Insulating and metallic phases in the one-dimensional Hubbard-Su-Schrieffer-Heeger model: Insights from a backflow-inspired variational wave function
• Coherent pair injection as a route towards the enhancement of supersolid order in many-body bosonic models
• Ground-State-Based Model Reduction with Unitary Circuits
• Evolution of magnetic correlation in an inhomogeneous square lattice
• Itinerant magnetism in Hubbard models with long-range interactions
• Faster Quantum Algorithm for Multiple Observables Estimation in Fermionic Problems
• Polarization-Driven Charge Frustration and Emergent Phases in the One-Dimensional Extended Hubbard Model
• Probing quasiparticle excitations in a doped Mott insulator via Friedel oscillations
• Nonpertubative Many-Body Theory for the Two-Dimensional Hubbard Model at Low Temperature: From Weak to Strong Coupling Regimes
• Magnetic correlations in the $SU(3)$ triangular-lattice $t$-$J$ model at finite doping
• Enhanced superconducting correlations in the Emery model and its connections to strange metallic transport and normal state coherence
• Probing the pseudogap and beyond: Examining single-particle properties of the hole- and electron-doped Hubbard model
• Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods
• Inverted duality of Hubbard model and an equation for the Green's function
• Coupled Hubbard ladders at weak coupling: Pairing and spin excitations
• Probing dielectric breakdown in Mott insulators through current oscillations
• Magnetization of electronic ground states in frustrated superstable graphs
• Entanglement Complexity in Many-body Systems from Positivity Scaling Laws
• Anomalous Quantum Relaxation in the Infinite Temperature Hubbard Chain
• Transmission through multiple Mott insulator - semiconductor wells
• Comparing Symmetrized Determinant Neural Quantum States for the Hubbard Model
• Variational approach for the two-body problem in a multiband extended-Hubbard model
• Exact analysis of the interplay of charge order and unconventional pairings in the 2D Hatsugai-Kohmoto model
• Ground state energy and phase transitions of Long-range XXZ using VQE
• Dominant Excitonic Superconductivity in a Three-component Hubbard Chain
• Learning Minimal Representations of Fermionic Ground States
• Non-perturbative effects of short-range spatial correlations at the two-particle level
• Surface Functional Renormalization Group for Layered Quantum Materials
• Novel dynamical excitations and roton-based measurement of Cooper-pair momentum in a two-dimensional Fulde-Ferrell-Larkin-Ovchinnikov superfluid on optical lattices