The shift in the spectral weight distribution under doping is termed the spectral weight transfer (SWT) and is a key indicator of strongly correlated physics. The static SWT (
t=0) for doping fraction
x scales as
x for semiconductors and as
2x for Mott insulators. The SWT receives corrections in
t/U due to the noncommutativity of the kinetic and interaction terms in the Hamiltonian, termed the dynamic SWT. We compute explicitly the low-energy spectral weight (LESW) in the lower Hubbard band using the orbital Hatsugai-Kohmoto (OHK) model. We show that the dynamical mixing enters the LESW with a universal slope independent of the number of orbitals. This independence on orbital number corroborates the rapid convergence of the OHK model to the Hubbard model. As a result, OHK is an effective simulator of Hubbard physics.
Multiband superconductivity gives rise to a rich landscape of possible pairing states. Here we study superconductivity emerging from a half-filled normal state in a two-orbital extension of the Hatsugai-Kohmoto model, an exactly solvable model of correlated electrons with momentum-local interactions, which provides a minimal framework to explore the interplay of strong correlations, orbital structure and pairing symmetry. For a system with point-group symmetry
D4h, we classify the symmetry-allowed superconducting gap structures, taking into account spin, orbital and momentum degrees of freedom. We further compute the critical temperature and the superconducting order parameter for selected pairing channels as functions of interaction and pairing strength within a mean-field treatment. Our results provide a systematic framework for analyzing superconductivity in the orbital Hatsugai-Kohmoto model and extend symmetry-based approaches to correlated multiband settings.
The all-to-all momentum coupling of the Hubbard interaction makes interacting lattice models generically unsolvable. In many settings, however, from Peierls instabilities to Moiré superlattice physics, the low-energy behavior is dominated by scattering at a few characteristic wavevectors. We exploit this by constructing a momentum-space clustering scheme that retains only a chosen subset of interaction channels. Our scheme can be considered a generalization of twist-averaged boundary conditions. In proving this, we also prove that our scheme can be considered as a generalization of Hatsugai-Kohmoto (HK) models, and all versions of the HK model previously considered in the literature arise as special cases. This shows that the surprising phenomenological success of HK models arises from their correspondence to the finite-site Hubbard model. In particular, the recently introduced "Momentum-Mixing HK" model corresponds to a specific choice of clustering limit, which is equal to the original finite-site Hubbard model with twist-averaged boundary conditions. Our scheme becomes particularly powerful when a spatially varying potential selects the dominant momentum channels. We demonstrate this on the one-dimensional analogue of interacting moiré systems: the Aubry-André-Hubbard model. We show that for sufficiently strong onsite potential, clusters as small as two sites can recover the ground state energy to below 1% error relative to DMRG benchmarks. This establishes that physically motivated momentum-space truncations can yield accurate low-energy descriptions at feasible computational cost, opening a path toward tractable interacting models of Moiré systems in two dimensions. Code for reproducing all numerical results is available at https://github.com/chainik1125/decomposing-hubbard.
From the condensed matter physics perspective, the most natural single orbital tight-binding Hamiltonians, and hence the most widely studied, contain two fermionic species, corresponding to spin up and spin down electrons. In cold atom systems, however, SU(N) symmetry, in which
N>2 fermionic species reside within a single band, also occurs. In order to understand such experiments, the SU(N) Hubbard model has been increasingly studied. Here we present determinant Quantum Monte Carlo simulations of the SU(N) {\it Holstein} Hamiltonian, in which
N fermionic species couple to a single local phonon mode. We show that at half filling it has an insulating charge density wave phase (CDW) at low temperatures, in which empty sites alternate with sites with
N particles. We determine the
N=3 CDW phase diagram in the temperature,
T, versus electron-phonon coupling,
α, plane at fixed phonon frequency
ω0 and half-filling
ρ=1.5. The critical temperature
Tc for
N=3 can be as high as twice the maximum attainable for
N=2. We also obtain the
N dependence of
Tc for a representative, fixed,
ω0 and
α.
The Hatsugai-Kohmoto interaction model has gained a lot of attention in recent years, due to the fact it is exactly solvable in momentum space in any dimension while capturing some key features of the Mott phase. Here a one-dimensional lattice model with this interaction is approached from the real-space perspective, to explore how breaking the translation invariance of a lattice affects the intuition built by studying the exact solution in
k space. The ground state properties of chains with periodic and open boundary conditions are calculated and compared with both the exact solution in momentum space as well as with analogous solutions of the Hubbard model. The results show that introducing hard edges enhances the ferromagnetic correlations and the system undergoes a magnetic transition before reaching the strong coupling limit. Understanding the impact of hard edges is a crucial step toward answering the looming question of the existence of edge states and other topological phenomena in systems with this type of interaction.