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We examine the metal-insulator transition in a half-filled Hubbard model of electrons with random and all-to-all hopping and exchange, and an on-site non-random repulsion, the Hubbard $U$. We argue that recent numerical results of Cha et al. (arXiv:2002.07181) can be understood in terms of a deconfined critical point between a disordered Fermi liquid and an insulating spin glass. We find a deconfined critical point in a previously proposed large $M$ theory which generalizes the SU(2) spin symmetry to SU($M$), and obtain exponents for the electron and spin correlators which agree with those of Cha et al. We also present a renormalization group analysis, and argue for the presence of an additional metallic spin glass phase at half-filling and small $U$.
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In contrast to the Hubbard model, the extended Hubbard model, which additionally accounts for non-local interactions, lacks systemic studies of thermodynamic properties especially across the metal-insulator transition. Using a variational principle, we perform such a systematic study and describe how non-local interactions screen local correlations differently in the Fermi-liquid and in the insulator. The thermodynamics reveal that non-local interactions are at least in parts responsible for first-order metal-insulator transitions in real materials.
In this work we study the two-orbital Hubbard model on a square lattice in the presence of hybridization between nearest-neighbor orbitals and a crystal-field splitting. We use a highly reliable numerical technique based on the density matrix renormalization group to solve the dynamical mean field theory self-consistent impurity problem. We find that the orbital mixing always leads to a finite local density states at the Fermi energy in both orbitals when at least one band is metallic. When one band is doped, and the chemical potential lies between the Hubbard bands in the other band, the coherent quasiparticle peak in this orbital has an exponential behavior with the Hubbard interaction $U$.
In this article, we discuss the non-trivial collective charge excitations (plasmons) of the extended square-lattice Hubbard model. Using a fully non-perturbative approach, we employ the hybrid Monte Carlo algorithm to simulate the system at half-filling. A modified Backus-Gilbert method is introduced to obtain the spectral functions via numerical analytic continuation. We directly compute the single-particle density of states which demonstrates the formation of Hubbard bands in the strongly-correlated phase. The momentum-resolved charge susceptibility is also computed on the basis of the Euclidean charge density-density correlator. In agreement with previous EDMFT studies, we find that at large strength of the electron-electron interaction, the plasmon dispersion develops two branches.
We have investigated the half-filling two-orbital Hubbard model on a triangular lattice by means of the dynamical mean-field theory (DMFT). The densities of states and optical conductivity clearly show the occurence of metal-insulating transition (MIT) at U$_{c}$, U$_{c}$=18.2, 16.8, 6.12 and 5.85 for J=0, 0.01U, U/4 and U/3, respectively. The distinct continuities of double occupation of electrons, local square moments and local susceptibility of the charge, the spin and the orbital at J > 0 suggest that the MIT is the first-order; however at J=0, the MIT is the second-order in the half-filling two-orbital Hubbard model on triangular lattices. We attribute the first-order nature of the MIT to the low symmetry of the systems with finite Hunds coupling J.
The temperature ($T$) dependent metal-insulator transition (MIT) in VO$_2$ is investigated using bulk sensitive hard x-ray ($sim$ 8 keV) valence band, core level, and V 2$p-3d$ resonant photoemission spectroscopy (PES). The valence band and core level spectra are compared with full-multiplet cluster model calculations including a coherent screening channel. Across the MIT, V 3$d$ spectral weight transfer from the coherent ($d^1underbar{it {C}}$ final) states at Fermi level to the incoherent ($d^{0}+d^1underbar{it {L}}$ final) states, corresponding to the lower Hubbard band, lead to gap-formation. The spectral shape changes in V 1$s$ and V 2$p$ core levels as well as the valence band are nicely reproduced from a cluster model calculations, providing electronic structure parameters. Resonant-PES finds that the $d^1underbar{it{L}}$ states resonate across the V 2$p-3d$ threshold in addition to the $d^{0}$ and $d^1underbar{it {C}}$ states. The results support a Mott-Hubbard transition picture for the first order MIT in VO$_2$.
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