The Hubbard model: A computational perspective

Abstract

The Hubbard model is the simplest model of interacting fermions on a lattice and is of similar importance to correlated electron physics as the Ising model is to statistical mechanics or the fruit fly to biomedical science. Despite its simplicity, the model exhibits an incredible wealth of phases, phase transitions, and exotic correlation phenomena. While analytical methods have provided a qualitative description of the model in certain limits, numerical tools have shown impressive progress in achieving quantitative accurate results over the last years. This article gives an introduction to the model, motivates common questions, and illustrates the progress that has been achieved over the last years in revealing various aspects of the correlation physics of the model.

arXiv commentSubmitted to Annual Reviews, Comments are welcome

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Cited by in corpus (59)

• The Hubbard Model
• Ground State Phase Diagram of the $t$-$t^{\prime }$-$J$ model
• Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer
• Stripe order enhanced superconductivity in the Hubbard model
• Intertwined spin, charge and pair correlations in the two-dimensional Hubbard model in the thermodynamic limit
• Magnetic correlations in infinite-layer nickelates: an experimental and theoretical multi-method study
• Tangent Space Approach for Thermal Tensor Network Simulations of the 2D Hubbard Model
• Automatic differentiation applied to excitations with Projected Entangled Pair States
• Enhanced superconductivity by near-neighbor attraction in the doped Hubbard model
• Temperature Dependence of Spin and Charge Orders in the Doped Two-Dimensional Hubbard Model
• Universal thermodynamics of an SU($N$) Fermi-Hubbard Model
• Origin and fate of the pseudogap in the doped Hubbard model
• Efficient MPS methods for extracting spectral information on rings and cylinders
• Explaining the pseudogap through damping and antidamping on the Fermi surface by imaginary spin scattering
• Single boson exchange representation of the functional renormalization group for strongly interacting many-electron systems
• Triangular lattice Hubbard model physics at intermediate temperatures
• Fast and scalable quantum Monte Carlo simulations of electron-phonon models
• Traces of Electron-Phonon Coupling in One-Dimensional Cuprates
• Universality and Critical Exponents of the Fermion Sign Problem
• Non-perturbative intertwining between spin and charge correlations: A "smoking gun" single-boson-exchange result
• Mott transition, Widom line and pseudogap in the half-filled triangular lattice Hubbard model
• Fragmented Cooper pair condensation in striped superconductors
• Fluctuating intertwined stripes in the strange metal regime of the Hubbard model
• Bootstrap Embedding on a Quantum Computer
• Fermi Arcs From Dynamical Variational Monte Carlo
• Towards learning optimized kernels for complex Langevin
• Strongly correlated superconductivity with long-range spatial fluctuations
• Single domain stripe order in a high-temperature superconductor
• Phase transitions in partial summation methods: Results from the 3D Hubbard model
• Spectral properties of 1D extended Hubbard model from bosonization and time-dependent variational principle: applications to 1D cuprate
• Phase Diagram, $d$-Wave Superconductivity, and Pseudogap of the $t$-$t^{\prime }$-$J$ Model at Finite Temperature
• The Wiedemann-Franz law in doped Mott insulators without quasiparticles
• Exact eigenstates of multicomponent Hubbard models: SU($N$) magnetic $\eta$ pairing, weak ergodicity breaking, and partial integrability
• Competing orders in the honeycomb lattice $t$-$J$ model
• Robust charge-density wave correlations in the electron-doped single-band Hubbard model
• Stripes in the extended $t-t^{\prime }$ Hubbard model: A Variational Monte Carlo analysis
• Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling
• Improved effective vertices in the multi-orbital Two-Particle Self-Consistent method from Dynamical Mean-Field Theory
• Renormalized Perturbation Theory for Fast Evaluation of Feynman Diagrams on the Real Frequency Axis
• Hidden, one-dimensional, strongly nested, and almost half-filled Fermi surface in Ba${}_2$CuO${}_{3+y}$ superconductors
• Comparative study of charge order in undoped infinite-layer nickelate superconductors
• Geometry of Degeneracy in Potential and Density Space
• 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
• Balls and Walls: A Compact Unary Coding for Bosonic States
• Robust d-wave superconductivity from the Su-Schrieffer-Heeger-Hubbard model: possible route to high-temperature superconductivity
• Lee-Yang theory of quantum phase transitions with neural network quantum states
• $\pi$-Phase shift across stripes in a charge density wave system
• Three-body problem in a multiband Hubbard model
• Stability of $(N+1)$-body fermion clusters in multiband Hubbard model
• The Weak, the Strong and the Long Correlation Regimes of the Two-Dimensional Hubbard Model at Finite Temperature
• Effect of hole doping on the 120 degree order in the triangular lattice Hubbard model: A Hartree-Fock revisit
• The fate of pairing and spin-charge separation in the presence of long-range antiferromagnetism
• On the pure state $v$-representability of density matrix embedding theory
• Single- and two-particle finite size effects in interacting lattice systems
• The cumulant Green's functions method for the Hubbard model
• A lattice pairing-field approach to ultracold Fermi gases
• Nonpertubative Many-Body Theory for the Two-Dimensional Hubbard Model at Low Temperature: From Weak to Strong Coupling Regimes
• Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials