© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

physica status solidi (b)

Electrical conductivity in the strong‐coupling non‐half‐filled band Hubbard model

Dieter Ihle

Published Mar 1, 1978• 4 citations

Abstract

Abstract The chemical potential μ and the electrical dc conductivity σ in the one‐dimensional Hubbard model in the strong‐coupling region U≫t (U intra‐atomic Coulomb energy, –t nearest‐neighbour hopping integral) are calculated as functions of temperature and electron density n. In the non‐half‐filled band case n ≠ 1 the Bari‐Kaplan approximation lim (σ/t2) is shown to yield an un magnified image physical singularity in the dc conductivity at T = 0 which is connected with the discontinuity of the zero‐temperature chemical potential at n = 1. An improved calculation for n ≠ 1 going beyond the Bari‐Kaplan approximation (i.e. taking into account the band terms in μ and σ/t2) yields a finite zero‐temperature conductivity which is proportional to the first power in t. For small deviations from the half‐filled band case the conductivity as a function of increasing temperature subsequently shows a metal‐like behaviour, a semiconductor‐like behaviour, and a repeated decrease at high temperatures.

DOI: 10.1002/pssb.2220860133

Related papers

The electrical conductivity of an amorphous Hubbard model

K. L. Liu

We study the frequency-dependent electrical conductivity of a structurally disordered single-band Hubbard model near half-filling and in the strong-correlation limit. The electronic transfer integral is assumed to have a quasi-exponential form as used in the impurity-band problem of doped semiconductors. The short-time expansion of the current correlation function is calculated diagrammatically to the second order in the inverse temperature β and up to the seventh order in electronic hopping. Based on this expansion an approximate current correlation function is constructed. By means of the Kubo formula, the configurational average of the electrical conductivity is then calculated to order β2 for various atomic densities. The validity of the high-temperature expansion is examined. We also study the effect of spin polarization on the absorption line shape and the dc resistivity at different temperatures.

Canadian Journal of Physics•Jan 1, 1992•1 citation

Transport properties of the one-dimensional Hubbard model at finite temperature

Christoph Karrasch, Dante Marvin Kennes, Joel E. Moore

We study finite-temperature transport properties of the one-dimensional Hubbard model using the density matrix renormalization group. Our aim is twofold: First, we compute both the charge- and the spin-current correlation function of the integrable model at half filling. The former decays rapidly, implying that the corresponding Drude weight is either zero or very small. Second, we calculate the optical charge conductivity ${\ensuremath{\sigma}}_{r}eg(\ensuremath{\omega})$ in the presence of small integrability-breaking next-nearest-neighbor interactions (the extended Hubbard model). The dc conductivity is finite and diverges as the temperature is decreased below the gap. Our results thus suggest that the half-filled, gapped Hubbard model is a normal charge conductor at finite temperatures. As a test bed for our numerics, we compute ${\ensuremath{\sigma}}_{r}eg(\ensuremath{\omega})$ for the integrable XXZ spin chain in its gapped phase.

arXiv:1408.1891•Physical Review B•Oct 3, 2014•56 citations

Optical conductivity of the Hubbard model at finite temperature

José A. Riera, Elbio R. Dagotto

The optical conductivity, \ensuremath{\sigma}(\ensuremath{\omega}), of the two-dimensional one-band Hubbard model is calculated at finite temperature using exact diagonalization techniques on finite clusters. The in-plane dc resistivity, ${\mathrm{\ensuremath{\rho}}}_{\mathit{a}\mathit{b}}$, is also evalauted. We find that at large U/t and temperature T, ${\mathrm{\ensuremath{\rho}}}_{\mathit{a}\mathit{b}}$ is approximately linear with temperature. We also observed that \ensuremath{\sigma}(\ensuremath{\omega}) displays charge excitations, a midinfrared (MIR) band, and a Drude peak. The combination of the Drude peak and the MIR oscillator strengths leads to a conductivity that decays slower than 1/${\mathrm{\ensuremath{\omega}}}^{2}$ at energies smaller than the insulator gap near half filling.

arXiv:cond-mat/9401060•Physical review. B, Condensed matter•Jul 1, 1994•17 citations

Nearest‐Neighbour Poisson Approximation to a Functional Approach for the Hubbard Model

Ulrich Behn

Abstract In the framework of the Poisson approximation to a functional scheme for the Hubbard model the effect of the spatial correlation of the discrete stochastic potential Uvi(t) simulating the spin‐↓ subsystem is considered. For a half‐filled band in the paramagnetic case at zero temperature the density of states is calculated in a nearest‐neighbour approximation. For strong Coulomb repulsion the subbands occur sharper and the minimum in between is deeper compared with the single‐site approximation. The influence of the spatial correlation on the possible appearance of a gap within a dynamic approximation is discussed.

physica status solidi (b)•Mar 1, 1981•5 citations

Numerical Study of One‐Dimensional Strongly Correlated Systems

K. Kumari, Ishwar S Singh

Abstract The path‐integral formulation along with the quantum Monte Carlo method is used to study the physical properties of the one‐dimensional Hubbard model for various band fillings and values of interaction strength U. Results for singlet and triplet pairing correlations, local square magnetic moment, total energy, probability of double occupancy, and nearest‐neighbour charge‐density correlations are presented. These results are explored at β (inverse temperature) = 2.0, 1.0, and 0.5 for the linear chain N = 16. These results show that the effect of correlation on the physical quantities is small for low band‐filling and it becomes most evident for the half‐filled band at finite temperatures.

physica status solidi (b)•Aug 1, 1995•1 citation

Electrical Conductivity of the Two-Dimensional Half-Filled Hubbard Model

Feng Chen, He-Ping Ying, Tiefeng Xu +1 more

The electrical conductivity of the one-band Hubbard model on a two-dimensional square lattice at half-filling is studied through the grand canonical quantum Monte Carlo method. Our results support that there exists an insulator-to-metal transition for the half-filled Hubbard model at high temperature.

Chinese Physics Letters•Jan 1, 1994•1 citation

Abstract The chemical potential μ and the electrical dc conductivity σ in the one‐dimensional Hubbard model in the strong‐coupling region U≫t (U intra‐atomic Coulomb energy, –t nearest‐neighbour hopping integral) are calculated as functions of temperature and electron density n. In the non‐half‐filled band case n ≠ 1 the Bari‐Kaplan approximation lim (σ/t2) is shown to yield an un magnified image physical singularity in the dc conductivity at T = 0 which is connected with the discontinuity of the zero‐temperature chemical potential at n = 1. An improved calculation for n ≠ 1 going beyond the Bari‐Kaplan approximation (i.e. taking into account the band terms in μ and σ/t2) yields a finite zero‐temperature conductivity which is proportional to the first power in t. For small deviations from the half‐filled band case the conductivity as a function of increasing temperature subsequently shows a metal‐like behaviour, a semiconductor‐like behaviour, and a repeated decrease at high temperatures.

We study the frequency-dependent electrical conductivity of a structurally disordered single-band Hubbard model near half-filling and in the strong-correlation limit. The electronic transfer integral is assumed to have a quasi-exponential form as used in the impurity-band problem of doped semiconductors. The short-time expansion of the current correlation function is calculated diagrammatically to the second order in the inverse temperature β and up to the seventh order in electronic hopping. Based on this expansion an approximate current correlation function is constructed. By means of the Kubo formula, the configurational average of the electrical conductivity is then calculated to order β2 for various atomic densities. The validity of the high-temperature expansion is examined. We also study the effect of spin polarization on the absorption line shape and the dc resistivity at different temperatures.

We study finite-temperature transport properties of the one-dimensional Hubbard model using the density matrix renormalization group. Our aim is twofold: First, we compute both the charge- and the spin-current correlation function of the integrable model at half filling. The former decays rapidly, implying that the corresponding Drude weight is either zero or very small. Second, we calculate the optical charge conductivity ${\ensuremath{\sigma}}_{r}eg(\ensuremath{\omega})$ in the presence of small integrability-breaking next-nearest-neighbor interactions (the extended Hubbard model). The dc conductivity is finite and diverges as the temperature is decreased below the gap. Our results thus suggest that the half-filled, gapped Hubbard model is a normal charge conductor at finite temperatures. As a test bed for our numerics, we compute ${\ensuremath{\sigma}}_{r}eg(\ensuremath{\omega})$ for the integrable XXZ spin chain in its gapped phase.

The optical conductivity, \ensuremath{\sigma}(\ensuremath{\omega}), of the two-dimensional one-band Hubbard model is calculated at finite temperature using exact diagonalization techniques on finite clusters. The in-plane dc resistivity, ${\mathrm{\ensuremath{\rho}}}_{\mathit{a}\mathit{b}}$, is also evalauted. We find that at large U/t and temperature T, ${\mathrm{\ensuremath{\rho}}}_{\mathit{a}\mathit{b}}$ is approximately linear with temperature. We also observed that \ensuremath{\sigma}(\ensuremath{\omega}) displays charge excitations, a midinfrared (MIR) band, and a Drude peak. The combination of the Drude peak and the MIR oscillator strengths leads to a conductivity that decays slower than 1/${\mathrm{\ensuremath{\omega}}}^{2}$ at energies smaller than the insulator gap near half filling.

Abstract In the framework of the Poisson approximation to a functional scheme for the Hubbard model the effect of the spatial correlation of the discrete stochastic potential Uvi(t) simulating the spin‐↓ subsystem is considered. For a half‐filled band in the paramagnetic case at zero temperature the density of states is calculated in a nearest‐neighbour approximation. For strong Coulomb repulsion the subbands occur sharper and the minimum in between is deeper compared with the single‐site approximation. The influence of the spatial correlation on the possible appearance of a gap within a dynamic approximation is discussed.

Abstract The path‐integral formulation along with the quantum Monte Carlo method is used to study the physical properties of the one‐dimensional Hubbard model for various band fillings and values of interaction strength U. Results for singlet and triplet pairing correlations, local square magnetic moment, total energy, probability of double occupancy, and nearest‐neighbour charge‐density correlations are presented. These results are explored at β (inverse temperature) = 2.0, 1.0, and 0.5 for the linear chain N = 16. These results show that the effect of correlation on the physical quantities is small for low band‐filling and it becomes most evident for the half‐filled band at finite temperatures.