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arXiv:2605.24927

Strong Correlation Effect and In-gap State in the Doped Electron-Hole Two-Band Hubbard Model Based on the Dynamical Mean-Field Theory

Masashi Akiyama, Yusuke Inokuma, Yoshiaki Ōno

Published May 24, 2026• 0 citations
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Abstract

We investigate the strong correlation effect in the spinless electron-hole two-band Hubbard model using the dynamical mean-field theory. At half filling, both the renormalization factor $Z$ and the number of conduction electrons (valence holes) $n_c$ decrease with increasing the interband Coulomb interaction $U$ down to $Z\sim 0.15$ and $n_c\sim 0.1$ for $U_c \sim \mbox{bandwidth}$ at which the first-order Lifshitz transition occurs from a correlated semimetal with a large effective mass $m^*/m=Z^{-1}$ to a band insulator with a finite gap due to the Hartree shift. A slight hole doping $x$ in the band insulator with a large $U>U_c$ yields a remarkable correlated semimetal with $Z\sim 0.1$ at $x\sim 0.01$, where in-gap states emerge above the valence band top and those weights increase with increasing $x$ together with the increase in $Z$ similar to the in-gap states observed in doped Mott insulators.

DOI
10.48550/arxiv.2605.24927

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We study a two-band Hubbard model using the dynamical mean-field theory combined with the exact diagonalization method. At the electron density n=2n=2n=2, a transition from a band-insulator to a correlated semimetal occurs when the on-site Coulomb interaction UUU is varied for a fixed value of the charge-transfer energy ΔΔΔ. At low temperature, the correlated semimetal shows ferromagnetism or superconductivity. With increasing doping ∣n−2∣|n-2|∣n−2∣, the ferromagnetic transition temperature rapidly decreases and finally becomes zero at a critical value of nnn. The second-order phase transition occurs at high temperature, while a phase separation of ferromagnetic and paramagnetic states takes place at low temperature. The superconducting transition temperature gradually decreases and finally becomes zero near n=1n=1n=1 (n=3n=3n=3) where the system is Mott insulator which shows antiferromagnetism at low temperature.
We study a model of a covalent band insulator with on-site Coulomb repulsion at half filling using dynamical mean-field theory. Upon increasing the interaction strength the system undergoes a discontinuous transition from a correlated band insulator to a Mott insulator with hysteretic behavior at low temperatures. Increasing the temperature in the band insulator close to the insulator-insulator transition we find a crossover to a Mott insulator at elevated temperatures. Remarkably, correlations decrease the energy gap in the correlated band insulator. The gap renormalization can be traced to the low-frequency behavior of the self-energy, analogously to the quasiparticle renormalization in a Fermi liquid. While the uncorrelated band insulator is characterized by a single gap for both charge and spin excitations, the spin gap is smaller than the charge gap in the correlated system.
We study by dynamical mean-field theory the ground state of a quarter-filled Hubbard model of two bands with different bandwidths. At half-filling, this model is known to display an orbital selective Mott transition, with the narrower band undergoing Mott localization while the wider one being still itinerant. At quarter-filling, the physical behavior is different and to some extent reversed. The interaction generates an effective crystal field splitting, absent in the Hamiltonian, that tends to empty the narrower band in favor of the wider one, which also become more correlated than the former at odds with the orbital selective paradigm. Upon increasing the interaction, the depletion of the narrower band can continue till it empties completely and the system undergoes a topological Lifshitz transition into a half-filled single-band metal that eventually turns insulating. Alternatively, when the two bandwidths are not too different, a first order Mott transition intervenes before the Lifshitz's one. The properties of the Mott insulator are significantly affected by the interplay between spin and orbital degrees of freedom.
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