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arXiv:2407.15242 · Physical review. B./Physical review. B

Low-energy interband Kondo bound states in orbital-selective Mott phases

Jiaming Wang, Yin Chen, Yi-Heng Tian, Rong-Qiang He, Zhong-Yi Lu

Published Apr 3, 2025• 2 citations
arXivHTMLPDF

Abstract

Low-energy excitations in correlated electron systems may show intricate behaviors and provide essential insights into the dynamics of quantum states and phase transitions. Here, we study a typical half-filled two-orbital Hubbard model featuring the so-called holon-doublon (HD) low-energy excitations in the orbital-selective Mott phase (OSMP), where the principal form of the low-energy excitations has been considered to be a HD bound state. We employ standard single-site dynamical mean-field theory (DMFT), using NORG as an improved impurity solver to calculate the spectral functions at zero temperature. We show that the HD bound state gives an incomplete or even wrong picture for the low-energy excitations. Instead, the excitations are composed of a Kondo-like state in the wide band and a doublon in the narrow band, termed as interband Kondo-like (IBK) bound states. Remarkably, we find that, as the bandwidths of the two bands approach each other, anomalous IBK bound-state excitations appear in the metallic wide band. Our study provides a new picture for the low-energy excitations in the OSMP.

DOI
10.1103/physrevb.111.155107

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Low-energy excitations in correlated electron systems may show intricate behaviors and provide essential insights into the dynamics of quantum states and phase transitions. Here, we study a typical half-filled two-orbital Hubbard model featuring the so-called holon-doublon (HD) low-energy excitations in the orbital-selective Mott phase (OSMP), where the principal form of the low-energy excitations has been considered to be a HD bound state. We employ standard single-site dynamical mean-field theory (DMFT), using NORG as an improved impurity solver to calculate the spectral functions at zero temperature. We show that the HD bound state gives an incomplete or even wrong picture for the low-energy excitations. Instead, the excitations are composed of a Kondo-like state in the wide band and a doublon in the narrow band, termed as interband Kondo-like (IBK) bound states. Remarkably, we find that, as the bandwidths of the two bands approach each other, anomalous IBK bound-state excitations appear in the metallic wide band. Our study provides a new picture for the low-energy excitations in the OSMP.
Multiorbital interactions have the capacity to produce an interesting kind of doublon-holon bound state that consists of a single-hole state in one band and a doubly occupied state in another band. Interband doublon-holon pair excitations in the two-orbital Hubbard model are studied by using dynamical mean-field theory with the Lanczos method as the impurity solver. We find that the interband bound states may provide several in-gap quasiparticle peaks in the density of states of the narrow band in the orbital-selective Mott phase with a small Hund's rule coupling (JJJ). There exists a corresponding energy relation between the in-gap states of the narrow band and the peaks in the excitation spectrum of the doublon for the wide band. We also find that the spin-flip and pair-hopping Hund interactions can divide one quasiparticle peak into two peaks, where the splitting energy increases linearly with increasing JJJ. Strong Hund's rule coupling can move the interband doublon-holon pair excitations outside the Mott gap and restrict the bound states by suppressing the orbital selectivity of the doubly occupied and single-hole states.
A repulsive Coulomb interaction between electrons in different orbitals in correlated materials can give rise to bound quasiparticle states. We study the nonhybridized two-orbital Hubbard model with intra- (inter)orbital interaction U(U12)U\phantom{\rule{4pt}{0ex}}({U}_{12})U(U12​) and different bandwidths using an improved dynamical mean-field theory numerical technique which leads to reliable spectra on the real energy axis directly at zero temperature. We find that a finite density of states at the Fermi energy in one band is correlated with the emergence of well-defined quasiparticle states at excited energies $\mathrm{\ensuremath{\Delta}}=U\ensuremath{-}{U}_{12}$ in the other band. These excitations are interband holon-doublon bound states. At the symmetric point U=U12U={U}_{12}U=U12​, the quasiparticle peaks are located at the Fermi energy, leading to a simultaneous and continuous Mott transition settling a long-standing controversy.
We investigate the effects of crystal field splitting in a doped two-band Hubbard model with different bandwidths within dynamical mean-field theory (DMFT), using a quantum Monte Carlo impurity solver. In addition to an orbital-selective Mott phase (OSMP) of the narrow band, which is adiabatically connected with the well-studied OSMP in the half-filled case without crystal field splitting, we find, for sufficiently strong interaction and a suitable crystal field, also an OSMP of the wide band. We establish the phase diagram (in the absence of magnetic or orbital order) at moderate doping as a function of interaction strength and crystal field splitting and show that also the wide-band OSMP is associated with non-Fermi-liquid behavior in the case of Ising-type Hund rule couplings. Our numerical results are supplemented by analytical strong-coupling studies of spin order and spectral functions at integer filling.
We examine whether the Mott transition of a half-filled, two-orbital Hubbard model with unequal bandwidths occurs simultaneously for both bands or whether it is a two-stage process in which the orbital with narrower bandwith localizes first (giving rise to an intermediate ``orbital-selective'' Mott phase). This question is addressed using both dynamical mean-field theory and a representation of fermion operators in terms of slave quantum spins, followed by a mean-field approximation (similar in spirit to a Gutzwiller approximation). In the latter approach, the Mott transition is found to be orbital selective for all values of the Coulomb exchange (Hund) coupling JJJ when the bandwidth ratio is small and only beyond a critical value of JJJ when the bandwidth ratio is larger. Dynamical mean-field theory partially confirms these findings, but the intermediate phase at J=0J=0J=0 is found to differ from a conventional Mott insulator, with spectral weight extending down to arbitrary low energy. Finally, the orbital-selective Mott phase is found, at zero temperature, to be unstable with respect to an interorbital hybridization VVV and replaced at small VVV by a state with a large effective mass (and a low quasiparticle coherence scale) for the narrower band.
We study the electronic spectral properties at zero temperature of the one-dimensional (1D) version of the degenerate two-orbital Kanamori-Hubbard model, one of the well-established frameworks to study transition metal compounds, using state-of-the-art numerical techniques based on the density matrix renormalization group. While the system is Mott insulating for the half-filled case, as expected for an interacting 1D system, we find interesting and rich structures in the single-particle density of states (DOS) for the hole-doped system. In particular, we find the existence of in-gap states which are pulled down to lower energies from the upper Hubbard band with increasing the interorbital Coulomb interaction VVV. We analyze the composition of the DOS by projecting it onto different local excitations, and we observe that for large dopings these in-gap excitations are formed mainly by interorbital holon-doublon (HD) states and their energies follow approximately the HD states in the atomic limit. We observe that the Hund interaction JJJ increases the width of the in-gap band, as expected from the two-particle fluctuations in the Hamiltonian. The observation of a finite density of states within the gap between the Hubbard bands for this extended 1D model indicates that these systems present a rich excitation spectra which could help us understand the microscopic physics behind multiorbital compounds.
We study the nondegenerate one-dimensional two-orbital Hubbard model with an interorbital Coulomb interaction. By means of the density-matrix renormalization group technique, we calculate the local single-particle density of states and the optical conductivity at zero temperature. We find that a finite interorbital Coulomb repulsion VVV generates a different class of states within the Mott-Hubbard band which has a large weight of holon-doublon pairs, which we hence call the holon-doublon band (HDB). When VVV is sufficiently large, the HDB specifies the gapless low-energy excitations, and the system becomes an unconventional correlated metal. Optical conductivity results resolve different metallic behaviors for zero and finite interaction VVV. Compared to the case without an interorbital interaction, the conductivity is strongly reduced in the correlated holon-doublon metal for finite VVV. In addition, the absorption spectrum is dominated by the HDB, which is clearly distinguishable from the Mott-Hubbard band.