Twisting the Hubbard model into the Momentum-Mixing Hatsugai-Kohmoto Model
arXiv:2401.08746 · doi:10.1038/s41567-025-03095-1
Abstract
The Hubbard model is a standard theoretical tool for studying materials with strong electron-electron interactions, such as the cuprate superconductors. Unfortunately, interaction-driven phenomena such as the transition into the strongly correlated Mott insulator phase are difficult to treat with established theoretical techniques. However, the exactly solvable Hatsugai-Kohmoto model displays similar Mott physics. Here we show how the Hatsugai-Kohmoto model can be deformed continuously into the Hubbard model. The trick is to systematically re-introduce all the momentum mixing the original Hatsugai-Kohmoto model omits. This can be accomplished by grouping -momenta into a cell and hybridizing them resulting in the momentum-mixing Hatsugai-Kohmoto (MMHK) model. We recover the Bethe ansatz ground state energy of the one-dimensional Hubbard model to within 1 from only ten mixed momenta. Overall the convergence scales as as opposed to the inverse linear behaviour of standard finite-cluster techniques. Our results for a square lattice reproduce all known features from state-of-the-art simulations also with only a few mixed momenta. Consequently, we believe the MMHK model offers an alternative tool for strongly correlated quantum matter.
arXiv comment7 pages + supplement (greatly expanded revision)
References in corpus (36)
- Quantum Cluster Theories
- Stripe order in the underdoped region of the two-dimensional Hubbard model
- Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
- Superconductivity and the Pseudogap in the two-dimensional Hubbard model
- Cluster Dynamical Mean Field Theory of the Mott Transition
- Bad metallic transport in a cold atom Fermi-Hubbard system
- How bad metals turn good: spectroscopic signatures of resilient quasiparticles
- Fermi arcs and the hidden zeros of the Green's function in the pseudogap state
- Anomalous superconductivity and its competition with antiferromagnetism in doped Mott insulators
- Mottness: Identifying the Propagating Charge Modes in doped Mott Insulators
- Pseudogap opening and formation of Fermi arcs as an orbital-selective Mott transition in momentum space
- Stripe order from the perspective of the Hubbard model
- Strange metallicity in the doped Hubbard model
- Characteristic Crossing Points in Specific Heat Curves of Correlated Systems
- Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method
- Exact Superconducting Instability in a Doped Mott Insulator
- Two-stage metal-insulator transition in the 2D Hubbard model: momentum selectivity in the 8-site dynamical cluster approximation
- Hidden Fermi Liquid, Scattering Rate Saturation and Nernst Effect: a DMFT Perspective
- Stripe order enhanced superconductivity in the Hubbard model
- Topological Mott Insulator at Quarter Filling in the Interacting Haldane Model
- Intertwined spin, charge and pair correlations in the two-dimensional Hubbard model in the thermodynamic limit
- Specific Heat of the 2D Hubbard Model
- Failure of Topological Invariants in Strongly Correlated Matter
- Doped Mott Insulators Break Symmetry of a Fermi Liquid: Stability of Strongly Coupled Fixed Points
- Dynamical vertex approximation for the two-dimensional Hubbard model
- 1/4 is the new 1/2 when topology is intertwined with Mottness
- Ground state stability, symmetry, and degeneracy in Mott insulators with long range interactions
- Solvable Periodic Anderson Model with Infinite-Range Hatsugai-Kohmoto Interaction: Ground-states and beyond
- Symmetry constraints and spectral crossing in a Mott insulator with Green's function zeros
- Topological Mott insulator in the odd-integer filled Anderson lattice model with Hatsugai-Kohmoto interactions
- Fermi and Luttinger arcs: two concepts, realized on one surface
- Robust charge-density wave correlations in the electron-doped single-band Hubbard model
- Magnon heat transport in a two-dimensional Mott insulator
- Brillouin-zone integration scheme for many-body density of states: Tetrahedron method combined with cluster perturbation theory
- Real-space analysis of Hatsugai-Kohmoto interaction
- Single-Particle Dispersion and Density of States of the Half-Filled 2D Hubbard Model