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

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

Published Mar 23, 2007• 0 citations
OpenAlex

Abstract

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.

Related papers

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

Kazuhiro Sano, Yūichi Ono

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 and confirm anomalous flux quantization in the SC statenear 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.

Journal of Physics Condensed Matter•Mar 23, 2007•1 citation

Ferromagnetism and superconductivity in the one-dimensional multi-orbital Hubbard model

Using the numerical diagonalization method, we investigate the ferromagnetism and the superconductivity in the multi-orbital Hubbard model in one-dimension. To examine the superconductivity, we calculate the critical exponent Kρ based on the Luttinger liquid theory and the anomalous flux quantization in the superconducting region. Analyzing the value of Kρ, we obtain the phase diagram on the U′ - J parameter plane including the superconducting phase and the fully polarized ferromagnetic phase.

•Mar 1, 2007•0 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 the two-dimensional Hubbard model

J. Beenen, David M. Edwards

Quasiparticle bands of the two-dimensional Hubbard model are calculated using the Roth two-pole approximation to the one-particle Green's function. Excellent agreement is obtained with recent Monte Carlo calculations, including an anomalous volume of the Fermi surface near half-filling, which can possibly be explained in terms of a breakdown of Fermi liquid theory. The calculated bands are very flat around the (\ensuremath{\pi},0) points of the Brillouin zone in agreement with photoemission measurements of cuprate superconductors. With doping there is a shift in spectral weight from the upper band to the lower band. The Roth method is extended to deal with superconductivity within a four-pole approximation allowing electron-hole mixing. It is shown that triplet p-wave pairing never occurs. A self-consistent solution with singlet ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$-wave pairing is found and optimal doping occurs when the van Hove singularity, corresponding to the flat band part, lies at the Fermi level. Nearest-neighbor antiferromagnetic correlations play an important role in flattening the bands near the Fermi level and in favoring superconductivity. However, the mechanism for superconductivity is a local one, in contrast to spin-fluctuation exchange models. For reasonable values of the hopping parameter the transition temperature ${\mathit{T}}_{\mathit{c}}$ is in the range 10--100 K. The optimum doping ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$ lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and 2${\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$/${\mathit{kT}}_{\mathit{c}}$\ensuremath{\simeq}4.

arXiv:cond-mat/9503054•Physical review. B, Condensed matter•Nov 1, 1995•111 citations

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

Ferromagnetic transition and phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping

S. Daul, R. M. Noack

We study the phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping using exact diagonalization, the density-matrix renormalization group, the Edwards variational ansatz, and an adaptation of weak-coupling calculations on the two-chain Hubbard model. We find that a substantial region of the strong-coupling phase diagram is ferromagnetic, and that three physically different limiting cases are connected in one ferromagnetic phase. At a point in the phase diagram at which there are two Fermi points at weak coupling, we study carefully the phase transition from the paramagnetic state to the fully polarized one as a function of the on-site Coulomb repulsion. We present evidence that the transition is second order and determine the critical exponents numerically. In this parameter regime, the system can be described as a Luttinger liquid at weak coupling. We extract the Luttinger-liquid parameters and show how their behavior differs from that of the nearest-neighbor Hubbard model. The general weak-coupling phase diagram can be mapped onto that of the two-chain Hubbard model. We exhibit explicitly the adapted phase diagram and determine its validity by numerically calculating spin and charge gaps using the density-matrix renormalization group.

arXiv:cond-mat/9712310•Physical review. B, Condensed matter•Aug 1, 1998•117 citations
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.
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 and confirm anomalous flux quantization in the SC statenear 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.
Using the numerical diagonalization method, we investigate the ferromagnetism and the superconductivity in the multi-orbital Hubbard model in one-dimension. To examine the superconductivity, we calculate the critical exponent Kρ based on the Luttinger liquid theory and the anomalous flux quantization in the superconducting region. Analyzing the value of Kρ, we obtain the phase diagram on the U′ - J parameter plane including the superconducting phase and the fully polarized ferromagnetic phase.
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.
Quasiparticle bands of the two-dimensional Hubbard model are calculated using the Roth two-pole approximation to the one-particle Green's function. Excellent agreement is obtained with recent Monte Carlo calculations, including an anomalous volume of the Fermi surface near half-filling, which can possibly be explained in terms of a breakdown of Fermi liquid theory. The calculated bands are very flat around the (\ensuremath{\pi},0) points of the Brillouin zone in agreement with photoemission measurements of cuprate superconductors. With doping there is a shift in spectral weight from the upper band to the lower band. The Roth method is extended to deal with superconductivity within a four-pole approximation allowing electron-hole mixing. It is shown that triplet p-wave pairing never occurs. A self-consistent solution with singlet ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$-wave pairing is found and optimal doping occurs when the van Hove singularity, corresponding to the flat band part, lies at the Fermi level. Nearest-neighbor antiferromagnetic correlations play an important role in flattening the bands near the Fermi level and in favoring superconductivity. However, the mechanism for superconductivity is a local one, in contrast to spin-fluctuation exchange models. For reasonable values of the hopping parameter the transition temperature Tc{\mathit{T}}_{\mathit{c}}Tc​ is in the range 10--100 K. The optimum doping ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$ lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and 2${\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$/kTc{\mathit{kT}}_{\mathit{c}}kTc​\ensuremath{\simeq}4.
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).
We study the phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping using exact diagonalization, the density-matrix renormalization group, the Edwards variational ansatz, and an adaptation of weak-coupling calculations on the two-chain Hubbard model. We find that a substantial region of the strong-coupling phase diagram is ferromagnetic, and that three physically different limiting cases are connected in one ferromagnetic phase. At a point in the phase diagram at which there are two Fermi points at weak coupling, we study carefully the phase transition from the paramagnetic state to the fully polarized one as a function of the on-site Coulomb repulsion. We present evidence that the transition is second order and determine the critical exponents numerically. In this parameter regime, the system can be described as a Luttinger liquid at weak coupling. We extract the Luttinger-liquid parameters and show how their behavior differs from that of the nearest-neighbor Hubbard model. The general weak-coupling phase diagram can be mapped onto that of the two-chain Hubbard model. We exhibit explicitly the adapted phase diagram and determine its validity by numerically calculating spin and charge gaps using the density-matrix renormalization group.