The density-matrix renormalization-group method is applied to the one-dimensional Kondo-lattice model with the Coulomb interaction between the conduction electrons. The spin and charge gaps are calculated as a function of the exchange constant $J$ and the Coulomb interaction ${U}_{c}$ . It is shown that both the spin and charge gaps increase with increasing $J$ and ${U}_{c}$ . The spin gap vanishes in the limit of $J\ensuremath{\rightarrow}0$ for any ${U}_{c}$ with an exponential form, ${\ensuremath{\Delta}}_{s}\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}\frac{1}{\ensuremath{\alpha}({U}_{c})J\ensuremath{\rho}}]$. The exponent, $\ensuremath{\alpha}({U}_{c})$, is determined as a function of ${U}_{c}$ . The charge gap is generally much larger than the spin gap. In the limit of $J\ensuremath{\rightarrow}0$, the charge gap vanishes as ${\ensuremath{\Delta}}_{c}=\frac{1}{2}J$ for ${U}_{c}=0$ but for a finite ${U}_{c}$ it tends to a finite value, which is the charge gap of the Hubbard model.The density-matrix renormalization-group method is applied to the one-dimensional Kondo-lattice model with the Coulomb interaction between the conduction electrons. The spin and charge gaps are calculated as a function of the exchange constant $J$ and the Coulomb interaction ${U}_{c}$. It is shown that both the spin and charge gaps increase with increasing $J$ and ${U}_{c}$. The spin gap vanishes in the limit of $J\ensuremath{\rightarrow}0$ for any ${U}_{c}$ with an exponential form, ${\ensuremath{\Delta}}_{s}\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}\frac{1}{\ensuremath{\alpha}({U}_{c})J\ensuremath{\rho}}]$. The exponent, $\ensuremath{\alpha}({U}_{c})$, is determined as a function of ${U}_{c}$. The charge gap is generally much larger than the spin gap. In the limit of $J\ensuremath{\rightarrow}0$, the charge gap vanishes as ${\ensuremath{\Delta}}_{c}=\frac{1}{2}J$ for ${U}_{c}=0$ but for a finite ${U}_{c}$ it tends to a finite value, which is the charge gap of the Hubbard model.

arXiv:cond-mat/9608117Physical review. B, Condensed matterApr 1, 199667 citations

Low Temperature Spin Diffusion in the One-Dimensional Quantum O(3) Nonlinear σ Model

Subir Sachdev A, Kedar Damle

An effective, low temperature, classical model for spin transport in the one-dimensional, gapped, quantum $\mathrm{O}(3)$ nonlinear $\ensuremath{\sigma}$ model is developed. Its correlators are obtained by a mapping to a model solved earlier by Jepsen. We obtain universal functions for the ballistic-to-diffusive crossover and the value of the spin diffusion constant, and these are claimed to be exact at low temperatures. Implications for experiments on one-dimensional insulators with a spin gap are noted.An effective, low temperature, classical model for spin transport in the one-dimensional, gapped, quantum $\mathrm{O}(3)$ nonlinear $\ensuremath{\sigma}$ model is developed. Its correlators are obtained by a mapping to a model solved earlier by Jepsen. We obtain universal functions for the ballistic-to-diffusive crossover and the value of the spin diffusion constant, and these are claimed to be exact at low temperatures. Implications for experiments on one-dimensional insulators with a spin gap are noted.

arXiv:cond-mat/9610115Physical Review LettersFeb 3, 1997124 citations

Spin dynamics for the t-J model

Zhongbing Huang, Shiping Feng

arXiv:cond-mat/9805308Physics Letters AMay 1, 19985 citations

Effects of spin fluctuations in the t−J model

T. Obermeier, Thomas Pruschke, J. Keller

arXiv:cond-mat/9607037Physica B Condensed MatterFeb 1, 19971 citation

Renormalization Group Analysis of the Spin-Gap Phase in the One-Dimensional t - J Model

Masaaki Nakamura, K. Nomura, Atsuhiro Kitazawa

We study the spin-gap phase in the one-dimensional $t$ - $J$ model, assuming that it is caused by the backward scattering process. Based on the renormalization group analysis and symmetry, we can determine the transition point between the Tomonaga-Luttinger liquid and the spin-gap phases, by the level crossing of the singlet and the triplet excitations. In contrast to the previous works, the obtained spin-gap region is unexpectedly large. We also determine that the universality class of the transition belongs to the $k\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ SU(2) Wess-Zumino-Witten model.We study the spin-gap phase in the one-dimensional $t$- $J$ model, assuming that it is caused by the backward scattering process. Based on the renormalization group analysis and symmetry, we can determine the transition point between the Tomonaga-Luttinger liquid and the spin-gap phases, by the level crossing of the singlet and the triplet excitations. In contrast to the previous works, the obtained spin-gap region is unexpectedly large. We also determine that the universality class of the transition belongs to the $k\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ SU(2) Wess-Zumino-Witten model.

arXiv:cond-mat/9708204Physical Review LettersOct 27, 199748 citations

J

and the Coulomb interaction

{U}_{c}

. It is shown that both the spin and charge gaps increase with increasing

J

and

{U}_{c}

. The spin gap vanishes in the limit of $J\ensuremath{\rightarrow}0$ for any

{U}_{c}

with an exponential form, ${\ensuremath{\Delta}}_{s}\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}\frac{1}{\ensuremath{\alpha}({U}_{c})J\ensuremath{\rho}}]$. The exponent, $\ensuremath{\alpha}({U}_{c})$, is determined as a function of

{U}_{c}

. The charge gap is generally much larger than the spin gap. In the limit of $J\ensuremath{\rightarrow}0$, the charge gap vanishes as ${\ensuremath{\Delta}}_{c}=\frac{1}{2}J$ for

{U}_{c}=0

but for a finite

{U}_{c}

it tends to a finite value, which is the charge gap of the Hubbard model.

An effective, low temperature, classical model for spin transport in the one-dimensional, gapped, quantum

\mathrm{O}(3)

nonlinear $\ensuremath{\sigma}$ model is developed. Its correlators are obtained by a mapping to a model solved earlier by Jepsen. We obtain universal functions for the ballistic-to-diffusive crossover and the value of the spin diffusion constant, and these are claimed to be exact at low temperatures. Implications for experiments on one-dimensional insulators with a spin gap are noted.

We study the spin-gap phase in the one-dimensional

t

J

model, assuming that it is caused by the backward scattering process. Based on the renormalization group analysis and symmetry, we can determine the transition point between the Tomonaga-Luttinger liquid and the spin-gap phases, by the level crossing of the singlet and the triplet excitations. In contrast to the previous works, the obtained spin-gap region is unexpectedly large. We also determine that the universality class of the transition belongs to the

k\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1

SU(2) Wess-Zumino-Witten model.