Comprehensive mean-field analysis of magnetic and charge orders in the two-dimensional Hubbard model

Abstract

We present an unbiased mean-field analysis of magnetic and charge orders in the two-dimensional Hubbard model on a square lattice, both at zero and finite temperatures. Unrestricted Hartree-Fock calculations on large finite lattices are complemented by solutions restricted to Néel and circular spiral order in the thermodynamic limit. The magnetic states are classified by a systematic scheme based on the dominant Fourier components of the spin texture. On finite lattices a whole zoo of ordering patterns appears. We show that many of these states are finite size artifacts related to the limited choice of ordering wave vectors on a finite lattice. In the thermodynamic limit only three classes of states with a relatively simple structure survive: Néel, circular spiral, and stripe states. Stripes involve also charge order and can be unidirectional or bidirectional, with horizontal and/or vertical orientation. We present complete phase diagrams in the plane spanned by electron density and temperature, for a moderate Hubbard interaction and various choices of the next-nearest neighbor hopping amplitude.

15 pages, 14 figures

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• Inversion-asymmetric itinerant antiferromagnets by the space group symmetry
• Fractionalized Fermi liquids and the cuprate phase diagram
• Charge density wave solutions of the Hubbard model in the composite operator formalism
• Canted magnetism and ${\mathbb{Z}}_2$ fractionalization in metallic states of the Lieb lattice Hubbard model near quarter filling
• Mean-field analysis of a Hubbard interaction on Bernal Bilayer Graphene
• Effects of the pseudogap and the Fermi surface on the rapid Hall-coefficient changes in cuprates
• Altermagnetism in an interacting model of Kagome materials
• Thermopower across Fermi-volume-changing quantum phase transitions without translational symmetry breaking
• Unit-density SU(3) Fermi-Hubbard Model with Spin Flavor Imbalance
• Spin susceptibility in a pseudogap state with fluctuating spiral magnetic order
• Geometric Frustration Assisted Kinetic Ferromagnetism in Doped Mott Insulators
• Nonpertubative Many-Body Theory for the Two-Dimensional Hubbard Model at Low Temperature: From Weak to Strong Coupling Regimes
• Update of Hartree--Fock theory for Hubbard-like models
• Variational Monte Carlo study of stripes as a function of doping in the $t-t^{\prime }$ Hubbard model
• Frequency dependence of temporal spin stiffness and short-range magnetic order in the doped two-dimensional Hubbard model
• Engineering Hubbard models with gated two-dimensional moiré systems