Low-energy structure and topology of the two-band Hubbard-Kanamori model

TL;DR

The study examines the two-band Hubbard-Kanamori model at half filling with $U=U_2$ and $J=0$ using DMFT supplemented by NRG and DMRG impurity solvers. It demonstrates the absence of an orbital-selective Mott transition, even for large bandwidth disparity $t_1\neq t_2$, and reveals a pseudogap-like structure with a central Kondo-like peak in the narrow band near the Mott boundary. Both orbitals undergo a Mott transition simultaneously at a common critical interaction $U_c$, with the transition exhibiting topological characteristics evidenced by the divergence of self-energies and winding-number arguments. The results underscore the importance of high-precision impurity solvers to capture subtle spectral features and have implications for understanding multi-band correlated materials where Hund coupling is weak or absent.

Abstract

We investigate the Mott transition in a two-band Hubbard-Kanamori model using Dynamical Mean-Field Theory (DMFT) with the Density Matrix Renormalization Group (DMRG) and the Numerical Renormalization Group (NRG) as impurity solvers. Our study focuses on the case where the intraorbital and interorbital Coulomb interactions are equal (U = U2) and the Hund's coupling is absent (J = 0). Spectral analysis confirms the absence of an orbital-selective Mott transition (OSMT), even in systems with significantly different bandwidths (t1 and t2 for the wide and narrow bands, respectively), indicating a simultaneous Mott transition in both bands. Notably, the NRG results reveal the emergence of a pseudo-gap-like feature and a central peak in the narrow band, whose characteristics depend on the hopping parameter t2. These spectral features may serve as precursors to OSMT in more realistic systems with finite Hund's coupling (J > 0). Furthermore, in the Mott insulating phase, the self-energies of both bands diverge, suggesting that the Mott transition represents a topological phase transition. Our results highlight the crucial role of accurate impurity solvers in capturing the density of states and detailed spectral structures.

Figures (6)

• Figure 1: (a) Illustration of the orbital-selective behaviour in a two-orbital model, depicting three distinct situations: I) At small $U$, both bands are metallic; II) At intermediate $U$, the NB presents an in-gap structure with quasiparticle (QP) states; III) At large $U$, both bands become insulating, featuring the Lower Hubbard Band (LHB) and Upper Hubbard Band (UHB). If an orbital-selective Mott transition (OSMT) exists, it would occur between (II) and (III). (b) Schematic representation of the Hubbard-Kanamori Hamiltonian for two orbitals, illustrating the formation of the holon-doublon (HD) state, characterized by an empty site in one orbital combined with a doubly occupied site in another orbital. Additionally, the diagram depicts the electronic configurations corresponding to different interaction terms in the model: the intraorbital Coulomb interaction $U$, the interorbital Coulomb interaction $U_2$. The narrow band (NB) is associated with a smaller bandwidth, while the wide band (WB) has a larger bandwidth.
• Figure 2: Electronic DOS in a metallic configuration for different values of $t_2$ with $U = U_2 = 1$ obtained using NRG as impurity solver. Panels a), b), and c) show the DOS for $t_2=0.02$, $t_2=0.1$, and $t_2=0.15$, respectively, highlighting the presence of the central peak in the NB and the broadening of the dips around it as $t_2$ decreases. Panel d) presents a zoom on the central peak of the NB, comparing the three cases and showing the influence of $t_2$ on the intensity of the DOS at $\omega = 0$. Notably, even for very small values of $t_2$, the DOS remains finite, indicating the absence of an orbital-selective Mott transition (OSMT).
• Figure 3: DOS near the Mott metal-insulator transition with $U = U_2 = 3$ and different $t_2$ values. Results were obtained using DMRG (left) and NRG (right) as the impurity solver. The insets show a broader omega region than that in the main panels. Both NB and WB exhibit signatures of the upper and lower Hubbard bands. Between these, a central Kondo-like peak emerges, with shape and spectral weight in the NB changing as $t_2$ varies.
• Figure 4: Real (top) and imaginary (bottom) parts of the self-energy for both orbitals, calculated with NRG as a function of energy, for $t_2 = 0.1$ and interaction strengths $U = 3$ and $U = 3.5$. The inset highlights the low-energy behavior near $\omega = 0$.
• Figure 5: DOS near the metal-insulator transition with DMRG for $t_2=0.1$. We see the formation of the gap between a) $U = 3.5$ and b) $U = 4$ for both bands, confirming the absence of an OSMT. The inset in a) highligths the central peak for $U=3.5$.