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

Journal of the Physical Society of Japan

Partial Ferromagnetism in a Two-Band Hubbard Model with Semimetallic Bands: Numerical Evidences and a Rigorous Result

Koichi Kusakabe, Shinji Watanabe, Yoshio Kuramoto

Published Jan 1, 2002• 2 citations
Publisher

Abstract

Role of the double exchange for appearance of partial ferromagnetism in a semimetal is explored for a semimetallic two-band Hubbard model in one-dimension. In a strong coupling limit, a ferromagnetic exchange interaction between two neighboring triplet excitons becomes dominant compared with anti-ferromagnetic couplings and a partial spin polarization is shown to appear. Exact evaluation of magnetization is possible for the partially ferromagnetic ground state in this limit. Obtained phase diagram has a doping dependence similar to our DMRG results for finite interactions. The ferromagnetism is favored in semimetallic systems by the interplay of the intra-orbital Coulomb repulsion and the inter-orbital Hund-rule coupling.

DOI
10.1143/jpsjs.71s.311

Related papers

Ferromagnetism in the one-dimensional Hubbard model with orbital degeneracy: From low to high electron density

Harumi Sakamoto, Tsutomu Momoi, Kenn Kubo

We studied ferromagnetism in the one-dimensional Hubbard model with doubly degenerate atomic orbitals by means of the density-matrix renormalization-group method and obtained the ground-state phase diagrams. It was found that ferromagnetism is stable from low to high $(0<n<1.75)$ electron density when the interactions are sufficiently strong. The quasi-long-range order of triplet superconductivity coexists with the ferromagnetic order for a strong Hund coupling region, where the interorbital interaction ${U}^{\ensuremath{'}}\ensuremath{-}J$ is attractive. At quarter-filling $(n=1),$ the insulating ferromagnetic state appears, accompanying orbital quasi-long-range order. For low densities $(n<1),$ ferromagnetism occurs owing to the ferromagnetic exchange interaction caused by virtual hoppings of electrons, the same as in the quarter-filled system. This comes from separation of the charge and spin-orbital degrees of freedom in the strong-coupling limit. This ferromagnetism is fragile against variation of band structure. For high densities $(n>1),$ the phase diagram of the ferromagnetic phase is similar to that obtained in infinite dimensions. In this case, the double exchange mechanism is operative for stabilizing the ferromagnetic order and this long-range order is robust against variation of the band dispersion. A partially polarized state appears in the density region $1.68\ensuremath{\lesssim}n\ensuremath{\lesssim}1.75$ and phase separation occurs for n just below the half-filling $(n=2).$

arXiv:cond-mat/0104223•Physical review. B, Condensed matter•May 17, 2002•39 citations

Ferromagnetism and Superconductivity in the Multi-orbital Hubbard Model: Hund's Rule Coupling versus Crystal-Field Splitting

Kazuhiro Sano, Yoshiaki Ōno

The multi-orbital Hubbard model in one dimension is studied using the numerical diagonalization method. Due to the effect of the crystal-field splitting $Δ$, the fully polarized ferromagnetism which is observed in the strong coupling regime becomes unstable against the partially polarized ferromagnetism when the Hund's rule coupling $J$ is smaller than a certain critical value of order of $Δ$. In the vicinity of the partially polarized ferromagnetism, the orbital fluctuation develops due to the competition between the Hund's rule coupling and the crystal-field splitting. The superconducting phase with the Luttinger liquid parameter $K_ρ>1$ is observed for the singlet ground state in this region.

arXiv:cond-mat/0304620•Journal of the Physical Society of Japan•Aug 15, 2003•18 citations

Superconductivity in a model of two Hubbard chains coupled with ferromagnetic exchange interaction

Tomonori Shirakawa, Satoshi Nishimoto, Y. Ohta

We study the ground-state properties of the double-chain Hubbard model coupled with ferromagnetic exchange interaction by using the weak-coupling theory, density-matrix renormalization-group technique, and Lanczos exact-diagonalization method. We determine the ground-state phase diagram in the parameter space of the ferromagnetic exchange interaction and band filling. We find that, in high electron-density regime, the spin gap opens and the spin-singlet ${d}_{xy}$-wave-like pairing correlation is most dominant, whereas in low electron-density regime, the fully-polarized ferromagnetic state is stabilized where the spin-triplet ${p}_{y}$-wave-like pairing correlation is most dominant.

arXiv:0803.2590•Physical Review B•Jun 24, 2008•7 citations

Nagaoka Ferromagnetism in Two-Band Hubbard Model

Deping Zhang, Guang-Shan Tian, Hai‐Qing Lin

In the present paper, we investigate the existence of ferromagnetism in a two-band Hubbard model, by applying a recently-introduced method by us to study ferromagnetism in metallic clusters. We prove rigorously that the ground state of this model is ferromagnetic if the intra-orbital Coulomb repulsion between electrons is infinitely strong and only one hole exists in the system. Our theorem improves a previous result. Furthermore, our method can also be applied to deal with the case of multiple holes.

Communications in Theoretical Physics•Feb 1, 2015•1 citation

Spin-Triplet Pairing Induced by Hund's Rule Exchange in Orbitally Degenerate Systems: Hartree-Fock Approximation

M. Zegrodnik, Józef Spałek

We discuss the spin-triplet pairing mechanism induced by the Hund rule ferromagnetic exchange.We include explicitly the eect of interband hybridization and treat the problem by starting from an extended Hubbard model for a doubly degenerate band, making the simplest HartreeFock approximation for the part involving the pairing and the Hubbard interaction.The conditions of stability of various phases are determined as a function of both band lling and microscopic parameters.The phase diagram contains regions of stability of the spin-triplet superconducting phase coexisting with either saturated or non-saturated ferromagnetism.Phase diagrams for the cases of constant density of states and that of square lattice have been provided.The inuence of hybridization on the stability of considered phases, as well as the temperature dependences of magnetic moment and the superconducting gap are also discussed.

Acta Physica Polonica A•May 1, 2012•2 citations

Superconductivity in the one-dimensional two-orbital Hubbard model with finite band splitting

Using the numerical diagonalization method, we investigate superconductivity and related ferromagnetism in the one-dimensional two-orbital Hubbard model with a finite band splitting at less than half filling. We obtain superconducting (SC) region with the Luttinger liquid parameter Kρ > 1 and confirm anomalous flux quantization in the SC state. It is found that the SC phase appears near partially polarized ferromagnetic phase. We also calculate various pairing correlation functions to clarify the nature of the SC phase. Detailed analysis of these functions indicates that the triplet pairing between the nearest neighbor sites is relevant to the superconductivity. It suggests that the ferromagnetic fluctuation plays an important role for the superconductivity.

•Mar 23, 2007•0 citations
Role of the double exchange for appearance of partial ferromagnetism in a semimetal is explored for a semimetallic two-band Hubbard model in one-dimension. In a strong coupling limit, a ferromagnetic exchange interaction between two neighboring triplet excitons becomes dominant compared with anti-ferromagnetic couplings and a partial spin polarization is shown to appear. Exact evaluation of magnetization is possible for the partially ferromagnetic ground state in this limit. Obtained phase diagram has a doping dependence similar to our DMRG results for finite interactions. The ferromagnetism is favored in semimetallic systems by the interplay of the intra-orbital Coulomb repulsion and the inter-orbital Hund-rule coupling.
We studied ferromagnetism in the one-dimensional Hubbard model with doubly degenerate atomic orbitals by means of the density-matrix renormalization-group method and obtained the ground-state phase diagrams. It was found that ferromagnetism is stable from low to high (0<n<1.75)(0<n<1.75)(0<n<1.75) electron density when the interactions are sufficiently strong. The quasi-long-range order of triplet superconductivity coexists with the ferromagnetic order for a strong Hund coupling region, where the interorbital interaction ${U}^{\ensuremath{'}}\ensuremath{-}J$ is attractive. At quarter-filling (n=1),(n=1),(n=1), the insulating ferromagnetic state appears, accompanying orbital quasi-long-range order. For low densities (n<1),(n<1),(n<1), ferromagnetism occurs owing to the ferromagnetic exchange interaction caused by virtual hoppings of electrons, the same as in the quarter-filled system. This comes from separation of the charge and spin-orbital degrees of freedom in the strong-coupling limit. This ferromagnetism is fragile against variation of band structure. For high densities (n>1),(n>1),(n>1), the phase diagram of the ferromagnetic phase is similar to that obtained in infinite dimensions. In this case, the double exchange mechanism is operative for stabilizing the ferromagnetic order and this long-range order is robust against variation of the band dispersion. A partially polarized state appears in the density region $1.68\ensuremath{\lesssim}n\ensuremath{\lesssim}1.75$ and phase separation occurs for n just below the half-filling (n=2).(n=2).(n=2).
The multi-orbital Hubbard model in one dimension is studied using the numerical diagonalization method. Due to the effect of the crystal-field splitting ΔΔΔ, the fully polarized ferromagnetism which is observed in the strong coupling regime becomes unstable against the partially polarized ferromagnetism when the Hund's rule coupling JJJ is smaller than a certain critical value of order of ΔΔΔ. In the vicinity of the partially polarized ferromagnetism, the orbital fluctuation develops due to the competition between the Hund's rule coupling and the crystal-field splitting. The superconducting phase with the Luttinger liquid parameter Kρ>1K_ρ>1Kρ​>1 is observed for the singlet ground state in this region.
We study the ground-state properties of the double-chain Hubbard model coupled with ferromagnetic exchange interaction by using the weak-coupling theory, density-matrix renormalization-group technique, and Lanczos exact-diagonalization method. We determine the ground-state phase diagram in the parameter space of the ferromagnetic exchange interaction and band filling. We find that, in high electron-density regime, the spin gap opens and the spin-singlet dxy{d}_{xy}dxy​-wave-like pairing correlation is most dominant, whereas in low electron-density regime, the fully-polarized ferromagnetic state is stabilized where the spin-triplet py{p}_{y}py​-wave-like pairing correlation is most dominant.
In the present paper, we investigate the existence of ferromagnetism in a two-band Hubbard model, by applying a recently-introduced method by us to study ferromagnetism in metallic clusters. We prove rigorously that the ground state of this model is ferromagnetic if the intra-orbital Coulomb repulsion between electrons is infinitely strong and only one hole exists in the system. Our theorem improves a previous result. Furthermore, our method can also be applied to deal with the case of multiple holes.
We discuss the spin-triplet pairing mechanism induced by the Hund rule ferromagnetic exchange.We include explicitly the eect of interband hybridization and treat the problem by starting from an extended Hubbard model for a doubly degenerate band, making the simplest HartreeFock approximation for the part involving the pairing and the Hubbard interaction.The conditions of stability of various phases are determined as a function of both band lling and microscopic parameters.The phase diagram contains regions of stability of the spin-triplet superconducting phase coexisting with either saturated or non-saturated ferromagnetism.Phase diagrams for the cases of constant density of states and that of square lattice have been provided.The inuence of hybridization on the stability of considered phases, as well as the temperature dependences of magnetic moment and the superconducting gap are also discussed.
Using the numerical diagonalization method, we investigate superconductivity and related ferromagnetism in the one-dimensional two-orbital Hubbard model with a finite band splitting at less than half filling. We obtain superconducting (SC) region with the Luttinger liquid parameter Kρ > 1 and confirm anomalous flux quantization in the SC state. It is found that the SC phase appears near partially polarized ferromagnetic phase. We also calculate various pairing correlation functions to clarify the nature of the SC phase. Detailed analysis of these functions indicates that the triplet pairing between the nearest neighbor sites is relevant to the superconductivity. It suggests that the ferromagnetic fluctuation plays an important role for the superconductivity.