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

Physical review. B, Condensed matter

Optical conductivity of the Hubbard model

J. J. Vicente Alvarez, C. A. Balseiro, Hermenegildo Alejandro Ceccatto

Published Jul 15, 1997• 3 citations
Publisher

Abstract

We study the response to a static electric field (charge stiffness) and the frequency-dependent conductivity of the Hubbard model in a resonant-valence-bond-type paramagnetic phase. This phase is described by means of a charge and spin rotational-invariant approach, based on a mixed fermion-boson representation of the original strongly correlated electrons. We found that the Mott transition at half filling is well described by the charge stiffness behavior, and that the values for this quantity off half filling agree reasonably well with numerical results. Furthermore, for the frequency-dependent conductivity we trace back to the origin of the band that appears inside the Hubbard gap to magnetic pair breaking. This points to a magnetic origin of the midinfrared band in high-${T}_{c}$ compounds.

DOI
10.1103/physrevb.56.1141

Related papers

Dynamic conductivity of strongly correlated electrons: The Hubbard model on a cubic lattice

L. Tan, J. Callaway

The frequency-dependent (optical) conductivity of the Hubbard model on a three-dimensional cubic lattice is studied through calculations on a small cluster. The interaction strength is varied between the weak- and strong-coupling limits. Results are reported for the half-filled band, and for small hole dopings away from half filling. The formation of a Hubbard gap is observed. Results are related to aspects of the current discussion of the metal-insulator transition in bulk systems.

Physical review. B, Condensed matter•Sep 1, 1992•12 citations

Synergetic effect of spin-orbit coupling and Zeeman splitting on the optical conductivity in the one-dimensional Hubbard model

Adrien Bolens, Hosho Katsura, Masao Ogata +1 more

We study how the synergetic effect of spin-orbit coupling (SOC) and Zeeman splitting (ZS) affects the optical conductivity in the one-dimensional Hubbard model using the Kubo formula. We focus on two phenomena: (1) the electric dipole spin resonance (EDSR) in the metallic regime and (2) the optical conductivity in the Mott-insulating phase above the optical gap. In both cases, we calculate qualitatively the effects of SOC and ZS and how they depend on the relative angle between the SOC vector and the magnetic field direction. First, we investigate the spin resonance without electron correlation (the Hubbard parameter $U=0$). Although, neither SOC nor ZS causes any resonance by itself in the optical conductivity, the EDSR becomes possible when both of them exist. The resulting contribution to the optical conductivity is analyzed analytically. The effect of $U$ on the spin resonance is also studied with a numerical method. It is found that at half filling, the resonance is first enhanced for small $U$ and then suppressed when the optical gap is large enough. In the strong coupling limit $U\ensuremath{\rightarrow}\ensuremath{\infty}$ at half filling, we also refer to the resonance between the lower and upper Hubbard bands appearing at $\ensuremath{\omega}\ensuremath{\sim}U$, above the optical gap. A large magnetic field tends to suppress the signal while it is recovered thanks to SOC depending on the relative angle of the magnetic field.

arXiv:1704.03153•Physical review. B./Physical review. B•Jun 8, 2017•4 citations

From Slater to Mott–Heisenberg physics: the antiferromagnetic phase of the Hubbard model

Thomas Pruschke, Robert Zitzler

We study the optical conductivity of the one-band Hubbard model in the Néel state at half filling at T = 0 using the dynamical mean-field theory. For small values of the Coulomb parameter clear signatures of a Slater insulator expected from a weak-coupling theory are found, while the strongly correlated system can be well described in terms of a Mott–Heisenberg picture. However, in contrast to the paramagnet, we do not find any evidence for a transition between these two limiting cases but rather a smooth crossover as a function of the Coulomb interaction.

arXiv:cond-mat/0309192•Journal of Physics Condensed Matter•Nov 7, 2003•34 citations

Cluster dynamical mean field theory study of antiferromagnetic transition in the square-lattice Hubbard model: Optical conductivity and electronic structure

Toshihiro Sato, Hirokazu Tsunetsugu

We numerically study optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ near the ``antiferromagnetic'' phase transition in the square-lattice Hubbard model at half filling. We use a cluster dynamical mean field theory and calculate conductivity including vertex corrections and, to this end, we have reformulated the vertex corrections in the antiferromagnetic phase. We find that the vertex corrections change various important details in temperature and $\ensuremath{\omega}$ dependencies of conductivity in the square lattice, and this contrasts sharply the case of the Mott transition in the frustrated triangular lattice. Generally, the vertex corrections enhance variations in the $\ensuremath{\omega}$ dependence, and sharpen the Drude peak and a high-$\ensuremath{\omega}$ incoherent peak in the paramagnetic phase. They also enhance the dip in $\ensuremath{\sigma}(\ensuremath{\omega})$ at $\ensuremath{\omega}=0$ in the antiferromagnetic phase. Therefore, the dc conductivity is enhanced in the paramagnetic phase and suppressed in the antiferromagnetic phase, but this change occurs slightly below the transition temperature. We also find a temperature region above the transition temperature in which the dc conductivity shows an insulating behavior but $\ensuremath{\sigma}(\ensuremath{\omega})$ retains the Drude peak, and this region is stabilized by the vertex corrections. We also investigate which fluctuations are important in the vertex corrections and analyze momentum dependence of the vertex function in detail.

Physical review. B./Physical review. B•Aug 8, 2016•18 citations

Slave-boson analysis of the two-dimensional Hubbard model

David Riegler, Michael Klett, Titus Neupert +2 more

We present a comprehensive study of the two-dimensional one-band Hubbard model applying the spin-rotation-invariant slave-boson method. We utilize a spiral magnetic mean field and fluctuations around a paramagnetic mean field to determine the magnetic phase diagram and find the two approaches to be in good agreement. Apart from the commensurate phases characterized by ordering wave vectors $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$, $(0,\ensuremath{\pi})$, and (0,0) we find incommensurate phases where the ordering wave vectors $\mathbf{Q}=(Q,Q)$ and $(Q,\ensuremath{\pi})$ vary continuously with filling, interaction strength, or temperature. The mean-field quantities magnetization and effective mass are found to change discontinuously at the phase boundaries separating the $(Q,Q)$ and $(Q,\ensuremath{\pi})$ phases, indicating a first-order transition. The band structure and Fermi surface is shown in selected cases. The dynamic spin and charge susceptibilities as well as the structure factors are calculated and discussed, including the emergence of collective modes of the zero sound and Mott insulator type. The dynamical conductivity is calculated in dependence of doping, interaction strength, and temperature. Finally, a temperature-interaction strength phase diagram is established.

arXiv:1912.07631•Physical review. B./Physical review. B•Jun 15, 2020•25 citations

Slave-Boson analysis of the 2D Hubbard model

David Riegler, Michael Klett, Titus Neupert +2 more

We present a comprehensive study of the 2D one-band Hubbard model applying the spin rotation invariant slave-boson method. We utilize a spiral magnetic mean field and fluctuations around a paramagnetic mean field to determine the magnetic phase diagram and find the two approaches to be in good agreement. Apart from the commensurate phases characterized by ordering wave vectors Q=(π,π),(0,π), and (0,0) we find incommensurate phases where the ordering wave vectors Q=(Q,Q), and (Q,π) vary continuously with filling, interaction strength or temperature. The mean field quantities magnetization and effective mass are found to change discontinuously at the phase boundaries separating the (Q,Q) and (Q,π) phases, indicating a first order transition. The band structure and Fermi surface is shown in selected cases. The dynamic spin and charge susceptibilities as well as the structure factors are calculated and discussed, including the emergence of collective modes of the zero sound and Mott insulator type. The dynamical conductivity is calculated in dependence of doping, interaction strength and temperature. Finally, a temperature-interaction strength phase diagram is established.

•Jan 1, 2019•0 citations
We study the response to a static electric field (charge stiffness) and the frequency-dependent conductivity of the Hubbard model in a resonant-valence-bond-type paramagnetic phase. This phase is described by means of a charge and spin rotational-invariant approach, based on a mixed fermion-boson representation of the original strongly correlated electrons. We found that the Mott transition at half filling is well described by the charge stiffness behavior, and that the values for this quantity off half filling agree reasonably well with numerical results. Furthermore, for the frequency-dependent conductivity we trace back to the origin of the band that appears inside the Hubbard gap to magnetic pair breaking. This points to a magnetic origin of the midinfrared band in high-Tc{T}_{c}Tc​ compounds.
We study how the synergetic effect of spin-orbit coupling (SOC) and Zeeman splitting (ZS) affects the optical conductivity in the one-dimensional Hubbard model using the Kubo formula. We focus on two phenomena: (1) the electric dipole spin resonance (EDSR) in the metallic regime and (2) the optical conductivity in the Mott-insulating phase above the optical gap. In both cases, we calculate qualitatively the effects of SOC and ZS and how they depend on the relative angle between the SOC vector and the magnetic field direction. First, we investigate the spin resonance without electron correlation (the Hubbard parameter U=0U=0U=0). Although, neither SOC nor ZS causes any resonance by itself in the optical conductivity, the EDSR becomes possible when both of them exist. The resulting contribution to the optical conductivity is analyzed analytically. The effect of UUU on the spin resonance is also studied with a numerical method. It is found that at half filling, the resonance is first enhanced for small UUU and then suppressed when the optical gap is large enough. In the strong coupling limit $U\ensuremath{\rightarrow}\ensuremath{\infty}$ at half filling, we also refer to the resonance between the lower and upper Hubbard bands appearing at $\ensuremath{\omega}\ensuremath{\sim}U$, above the optical gap. A large magnetic field tends to suppress the signal while it is recovered thanks to SOC depending on the relative angle of the magnetic field.
We study the optical conductivity of the one-band Hubbard model in the Néel state at half filling at T = 0 using the dynamical mean-field theory. For small values of the Coulomb parameter clear signatures of a Slater insulator expected from a weak-coupling theory are found, while the strongly correlated system can be well described in terms of a Mott–Heisenberg picture. However, in contrast to the paramagnet, we do not find any evidence for a transition between these two limiting cases but rather a smooth crossover as a function of the Coulomb interaction.
We numerically study optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ near the ``antiferromagnetic'' phase transition in the square-lattice Hubbard model at half filling. We use a cluster dynamical mean field theory and calculate conductivity including vertex corrections and, to this end, we have reformulated the vertex corrections in the antiferromagnetic phase. We find that the vertex corrections change various important details in temperature and $\ensuremath{\omega}$ dependencies of conductivity in the square lattice, and this contrasts sharply the case of the Mott transition in the frustrated triangular lattice. Generally, the vertex corrections enhance variations in the $\ensuremath{\omega}$ dependence, and sharpen the Drude peak and a high-$\ensuremath{\omega}$ incoherent peak in the paramagnetic phase. They also enhance the dip in $\ensuremath{\sigma}(\ensuremath{\omega})$ at $\ensuremath{\omega}=0$ in the antiferromagnetic phase. Therefore, the dc conductivity is enhanced in the paramagnetic phase and suppressed in the antiferromagnetic phase, but this change occurs slightly below the transition temperature. We also find a temperature region above the transition temperature in which the dc conductivity shows an insulating behavior but $\ensuremath{\sigma}(\ensuremath{\omega})$ retains the Drude peak, and this region is stabilized by the vertex corrections. We also investigate which fluctuations are important in the vertex corrections and analyze momentum dependence of the vertex function in detail.
We present a comprehensive study of the two-dimensional one-band Hubbard model applying the spin-rotation-invariant slave-boson method. We utilize a spiral magnetic mean field and fluctuations around a paramagnetic mean field to determine the magnetic phase diagram and find the two approaches to be in good agreement. Apart from the commensurate phases characterized by ordering wave vectors $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$, $(0,\ensuremath{\pi})$, and (0,0) we find incommensurate phases where the ordering wave vectors Q=(Q,Q)\mathbf{Q}=(Q,Q)Q=(Q,Q) and $(Q,\ensuremath{\pi})$ vary continuously with filling, interaction strength, or temperature. The mean-field quantities magnetization and effective mass are found to change discontinuously at the phase boundaries separating the (Q,Q)(Q,Q)(Q,Q) and $(Q,\ensuremath{\pi})$ phases, indicating a first-order transition. The band structure and Fermi surface is shown in selected cases. The dynamic spin and charge susceptibilities as well as the structure factors are calculated and discussed, including the emergence of collective modes of the zero sound and Mott insulator type. The dynamical conductivity is calculated in dependence of doping, interaction strength, and temperature. Finally, a temperature-interaction strength phase diagram is established.
We present a comprehensive study of the 2D one-band Hubbard model applying the spin rotation invariant slave-boson method. We utilize a spiral magnetic mean field and fluctuations around a paramagnetic mean field to determine the magnetic phase diagram and find the two approaches to be in good agreement. Apart from the commensurate phases characterized by ordering wave vectors Q=(π,π),(0,π), and (0,0) we find incommensurate phases where the ordering wave vectors Q=(Q,Q), and (Q,π) vary continuously with filling, interaction strength or temperature. The mean field quantities magnetization and effective mass are found to change discontinuously at the phase boundaries separating the (Q,Q) and (Q,π) phases, indicating a first order transition. The band structure and Fermi surface is shown in selected cases. The dynamic spin and charge susceptibilities as well as the structure factors are calculated and discussed, including the emergence of collective modes of the zero sound and Mott insulator type. The dynamical conductivity is calculated in dependence of doping, interaction strength and temperature. Finally, a temperature-interaction strength phase diagram is established.