Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0405410 · Physical Review B

Single Mott transition in the multiorbital Hubbard model

A. Liebsch

Published Oct 12, 2004• 82 citations
arXivHTMLPDF

Abstract

The Mott transition in a multiorbital Hubbard model involving subbands of different widths is studied within the dynamical mean-field theory. Using the iterated perturbation theory for the quantum impurity problem it is shown that at low temperatures interorbital Coulomb interactions give rise to a single first-order transition rather than a sequence of orbital selective transitions. Impurity calculations based on the Quantum Monte Carlo method confirm this qualitative behavior. Nevertheless, at finite temperatures, the degree of metallic or insulating behavior of the subbands differs greatly. Thus, on the metallic side of the transition, the narrow band can exhibit quasi-insulating features, whereas on the insulating side the wide band exhibits pronounced bad-metal behavior. This complexity might partly explain contradictory results between several previous works.

DOI
10.1103/physrevb.70.165103

Related papers

Orbital-selective Mott-Hubbard transition in the two-band Hubbard model

Ryotaro Arita, Karsten Held

Recent advances in the field of quantum Monte Carlo simulations for impurity problems allow---within dynamical mean field theory---for a more thorough investigation of the two-band Hubbard model with a narrow-wide band and SU(2)-symmetric Hund's exchange. The nature of this transition has been controversial, and we establish that an orbital-selective Mott-Hubbard transition exists. The wide band still shows metallic behavior after the narrow band became insulating---not a pseudogap as for an Ising Hund's exchange. The coexistence of two solutions with a metallic wide band and an insulating or metallic narrow band indicates, in general, first-order transitions.

arXiv:cond-mat/0504040•Physical Review B•Nov 29, 2005•79 citations

Mott transition in three-orbital Hubbard model with orbital splitting

Tomoko Kita, Takuma Ohashi, Norio Kawakami

We study the Mott transition in the three-orbital Hubbard model. To investigate how the orbital level splitting and the Ising-type Hund's coupling affect the Mott transition in the case of two electrons per site, we use the dynamical mean-field theory combined with continuous-time quantum Monte Carlo simulations. The calculation of the double occupancy reveals that the critical interaction strength separating a metallic phase and two kinds of insulating phases shows a nonmonotonic behavior as a function of the level splitting. We find that this behavior is characteristic for $1/3$ filling, in comparison with the preceding results for different fillings and for two-orbital models. Strong competition between the two insulators results in an intriguing first-order transition to an insulating phase having intermediate characters between Mott and band insulators. It is also found that the two insulators show different behaviors in the phase boundary with the metallic phase in the interaction-temperature plane, which is reflected in a difference in the quasiparticle behavior around the transition. We also discuss the orbital selective Mott transition for larger Hund's coupling, which is compared with previous study at zero temperature.

Physical Review B•Nov 28, 2011•26 citations

Orbital-selective Mott transition in multiband systems: Slave-spin representation and dynamical mean-field theory

Luca de’ Medici, Antoine Georges, Silke Biermann

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 $J$ when the bandwidth ratio is small and only beyond a critical value of $J$ when the bandwidth ratio is larger. Dynamical mean-field theory partially confirms these findings, but the intermediate phase at $J=0$ 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 $V$ and replaced at small $V$ by a state with a large effective mass (and a low quasiparticle coherence scale) for the narrower band.

arXiv:cond-mat/0503764•Physical Review B•Nov 22, 2005•242 citations

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

Nayara G. Gusmão, G. G. Blesio, Armando A. Aligia +3 more

We investigate the Mott transition in a two-band Hubbard-Kanamori model using dynamical mean-field theory with the density matrix renormalization group and the numerical renormalization group (NRG) as impurity solvers. The study focuses on the case where the intraorbital and interorbital Coulomb interactions are equal ($U={U}_{2}$) and the Hund's coupling is absent ($J=0$). Our spectral analysis for this case confirms the absence of an orbital-selective Mott transition (OSMT) even in systems with very distinct bandwidths (${t}_{1}$ and ${t}_{2}$ parameters for wide and narrow band, respectively) indicating a simultaneous Mott transition occurring in both bands. Notably, the NRG results show the emergence of a pseudo-gap-like feature and a central peak in the narrow band, whose characteristics depend on the hopping parameter ${t}_{2}$. These spectral features may act as precursors to OSMT in more realistic systems with finite Hund's coupling ($J>0$). Furthermore, in the Mott insulating phase, the self-energies for both bands diverge, indicating that the Mott transition represents a topological phase transition for both bands. Our results underscore the importance of accurate impurity solvers in capturing the density of states and detailed spectral structures.

arXiv:2504.01269•Physical review. B./Physical review. B•Sep 5, 2025•0 citations

On the nature of the Mott transition in multiorbital systems

Jorge I. Facio, Verónica Laura Vildosola, Daniel J. García +1 more

We analyze the nature of a Mott metal-insulator transition in multiorbital systems using dynamical mean-field theory. The auxiliary multiorbital quantum impurity problem is solved using continuous-time quantum Monte Carlo and the rotationally invariant slave-boson (RISB) mean-field approximation. We focus our analysis on the Kanamori Hamiltonian and find that there are two markedly different regimes determined by the nature of the lowest-energy excitations of the atomic Hamiltonian. The RISB results at $T\ensuremath{\rightarrow}0$ suggest the following rule of thumb for the order of the transition at zero temperature: a second-order transition is to be expected if the lowest-lying excitations of the atomic Hamiltonian are charge excitations, while the transition tends to be first order if the lowest-lying excitations are in the same charge sector as the atomic ground state. At finite temperatures, the transition is first order and its strength, as measured, e.g., by the jump in the quasiparticle weight at the transition, is stronger in the parameter regime where the RISB method predicts a first-order transition at zero temperature. Interestingly, these results seem to apply to a wide variety of models and parameter regimes.

arXiv:1605.08652•Physical review. B./Physical review. B•Feb 16, 2017•14 citations

Effect of crystal-field splitting and interband hybridization on the metal-insulator transitions of strongly correlated systems

A. I. Poteryaev, Michel Ferrero, Antoine Georges +1 more

We investigate a quarter-filled two-band Hubbard model involving a crystal-field splitting, which lifts the orbital degeneracy as well as an interorbital hopping (interband hybridization). Both terms are relevant to the realistic description of correlated materials such as transition-metal oxides. The nature of the Mott metal-insulator transition is clarified and is found to depend on the magnitude of the crystal-field splitting. At large values of the splitting, a transition from a two-band to a one-band metal is first found as the on-site repulsion is increased and is followed by a Mott transition for the remaining band, which follows the single-band (Brinkman-Rice) scenario well documented previously within dynamical mean-field theory. At small values of the crystal-field splitting, a direct transition from a two-band metal to a Mott insulator with partial orbital polarization is found, which takes place simultaneously for both orbitals. This transition is characterized by a vanishing of the quasiparticle weight for the majority orbital but has a first-order character for the minority orbital. It is pointed out that finite-temperature effects may easily turn the metallic regime into a bad metal close to the orbital polarization transition in the metallic phase.

arXiv:0801.4356•Physical Review B•Jul 23, 2008•63 citations
The Mott transition in a multiorbital Hubbard model involving subbands of different widths is studied within the dynamical mean-field theory. Using the iterated perturbation theory for the quantum impurity problem it is shown that at low temperatures interorbital Coulomb interactions give rise to a single first-order transition rather than a sequence of orbital selective transitions. Impurity calculations based on the Quantum Monte Carlo method confirm this qualitative behavior. Nevertheless, at finite temperatures, the degree of metallic or insulating behavior of the subbands differs greatly. Thus, on the metallic side of the transition, the narrow band can exhibit quasi-insulating features, whereas on the insulating side the wide band exhibits pronounced bad-metal behavior. This complexity might partly explain contradictory results between several previous works.
Recent advances in the field of quantum Monte Carlo simulations for impurity problems allow---within dynamical mean field theory---for a more thorough investigation of the two-band Hubbard model with a narrow-wide band and SU(2)-symmetric Hund's exchange. The nature of this transition has been controversial, and we establish that an orbital-selective Mott-Hubbard transition exists. The wide band still shows metallic behavior after the narrow band became insulating---not a pseudogap as for an Ising Hund's exchange. The coexistence of two solutions with a metallic wide band and an insulating or metallic narrow band indicates, in general, first-order transitions.
We study the Mott transition in the three-orbital Hubbard model. To investigate how the orbital level splitting and the Ising-type Hund's coupling affect the Mott transition in the case of two electrons per site, we use the dynamical mean-field theory combined with continuous-time quantum Monte Carlo simulations. The calculation of the double occupancy reveals that the critical interaction strength separating a metallic phase and two kinds of insulating phases shows a nonmonotonic behavior as a function of the level splitting. We find that this behavior is characteristic for 1/31/31/3 filling, in comparison with the preceding results for different fillings and for two-orbital models. Strong competition between the two insulators results in an intriguing first-order transition to an insulating phase having intermediate characters between Mott and band insulators. It is also found that the two insulators show different behaviors in the phase boundary with the metallic phase in the interaction-temperature plane, which is reflected in a difference in the quasiparticle behavior around the transition. We also discuss the orbital selective Mott transition for larger Hund's coupling, which is compared with previous study at zero temperature.
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 investigate the Mott transition in a two-band Hubbard-Kanamori model using dynamical mean-field theory with the density matrix renormalization group and the numerical renormalization group (NRG) as impurity solvers. The study focuses on the case where the intraorbital and interorbital Coulomb interactions are equal (U=U2U={U}_{2}U=U2​) and the Hund's coupling is absent (J=0J=0J=0). Our spectral analysis for this case confirms the absence of an orbital-selective Mott transition (OSMT) even in systems with very distinct bandwidths (t1{t}_{1}t1​ and t2{t}_{2}t2​ parameters for wide and narrow band, respectively) indicating a simultaneous Mott transition occurring in both bands. Notably, the NRG results show the emergence of a pseudo-gap-like feature and a central peak in the narrow band, whose characteristics depend on the hopping parameter t2{t}_{2}t2​. These spectral features may act as precursors to OSMT in more realistic systems with finite Hund's coupling (J>0J>0J>0). Furthermore, in the Mott insulating phase, the self-energies for both bands diverge, indicating that the Mott transition represents a topological phase transition for both bands. Our results underscore the importance of accurate impurity solvers in capturing the density of states and detailed spectral structures.
We analyze the nature of a Mott metal-insulator transition in multiorbital systems using dynamical mean-field theory. The auxiliary multiorbital quantum impurity problem is solved using continuous-time quantum Monte Carlo and the rotationally invariant slave-boson (RISB) mean-field approximation. We focus our analysis on the Kanamori Hamiltonian and find that there are two markedly different regimes determined by the nature of the lowest-energy excitations of the atomic Hamiltonian. The RISB results at $T\ensuremath{\rightarrow}0$ suggest the following rule of thumb for the order of the transition at zero temperature: a second-order transition is to be expected if the lowest-lying excitations of the atomic Hamiltonian are charge excitations, while the transition tends to be first order if the lowest-lying excitations are in the same charge sector as the atomic ground state. At finite temperatures, the transition is first order and its strength, as measured, e.g., by the jump in the quasiparticle weight at the transition, is stronger in the parameter regime where the RISB method predicts a first-order transition at zero temperature. Interestingly, these results seem to apply to a wide variety of models and parameter regimes.
We investigate a quarter-filled two-band Hubbard model involving a crystal-field splitting, which lifts the orbital degeneracy as well as an interorbital hopping (interband hybridization). Both terms are relevant to the realistic description of correlated materials such as transition-metal oxides. The nature of the Mott metal-insulator transition is clarified and is found to depend on the magnitude of the crystal-field splitting. At large values of the splitting, a transition from a two-band to a one-band metal is first found as the on-site repulsion is increased and is followed by a Mott transition for the remaining band, which follows the single-band (Brinkman-Rice) scenario well documented previously within dynamical mean-field theory. At small values of the crystal-field splitting, a direct transition from a two-band metal to a Mott insulator with partial orbital polarization is found, which takes place simultaneously for both orbitals. This transition is characterized by a vanishing of the quasiparticle weight for the majority orbital but has a first-order character for the minority orbital. It is pointed out that finite-temperature effects may easily turn the metallic regime into a bad metal close to the orbital polarization transition in the metallic phase.