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.

Submitted 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
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• 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
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• Fluctuating intertwined stripes in the strange metal regime of the Hubbard model
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