Spin and hole excitation spectra and spectral weights are calculated for the half-filled Hubbard model, as functions of $t∕U$ . We find that the high energy spin spectra are sensitive to charge fluctuations. The energy difference $\ensuremath{\Delta}(\ensuremath{\pi},0)\ensuremath{-}\ensuremath{\Delta}(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)$ in the single-magnon dispersion relation, which is negative for the Heisenberg model, changes sign at a fairly small $t∕U\ensuremath{\approx}0.053(5)$. The hole bandwidth is proportional to $J$ , and considerably larger than in the $t\text{\ensuremath{-}}J$ models. It has a minimum at $(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)$ and a very weak dispersion along the antiferromagnetic zone boundary. A good fit to the measured spin spectra in ${\mathrm{La}}_{2}\mathrm{Cu}{\mathrm{O}}_{4}$ at $T=10\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is obtained with the parameter values $U=3.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ , $t=0.35\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ .Spin and hole excitation spectra and spectral weights are calculated for the half-filled Hubbard model, as functions of $t∕U$. We find that the high energy spin spectra are sensitive to charge fluctuations. The energy difference $\ensuremath{\Delta}(\ensuremath{\pi},0)\ensuremath{-}\ensuremath{\Delta}(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)$ in the single-magnon dispersion relation, which is negative for the Heisenberg model, changes sign at a fairly small $t∕U\ensuremath{\approx}0.053(5)$. The hole bandwidth is proportional to $J$, and considerably larger than in the $t\text{\ensuremath{-}}J$ models. It has a minimum at $(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)$ and a very weak dispersion along the antiferromagnetic zone boundary. A good fit to the measured spin spectra in ${\mathrm{La}}_{2}\mathrm{Cu}{\mathrm{O}}_{4}$ at $T=10\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is obtained with the parameter values $U=3.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, $t=0.35\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$.

arXiv:cond-mat/0501029Physical Review BJul 18, 20057 citations

Temperature dependence of charge transport in the half-filled one-dimensional Hubbard model

J. M. P. Carmelo, Pedro D Sacramento

The use of hydrodynamic transport theory seems to indicate that the charge diffusion constant $D$ of the one-dimensional (1D) half-filled Hubbard model, whose Drude weight vanishes, diverges for temperature $T>0$ , which would imply anomalous superdiffusive charge transport. Here the leading term of that constant is derived for low finite temperatures ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ where ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}$ is the Mott-Hubbard gap. It only diverges in the $T\ensuremath{\rightarrow}0$ limit, being finite and decreasing upon increasing $T$ within the ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ regime. Our exact results both provide valuable physical information on a complex quantum problem and bring about the interesting unsolved issue of how charge transport evolves from normal diffusive for ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ to anomalous superdiffusive in the ${k}_{B}T\ensuremath{\rightarrow}\ensuremath{\infty}$ limit.The use of hydrodynamic transport theory seems to indicate that the charge diffusion constant $D$ of the one-dimensional (1D) half-filled Hubbard model, whose Drude weight vanishes, diverges for temperature $T>0$, which would imply anomalous superdiffusive charge transport. Here the leading term of that constant is derived for low finite temperatures ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ where ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}$ is the Mott-Hubbard gap. It only diverges in the $T\ensuremath{\rightarrow}0$ limit, being finite and decreasing upon increasing $T$ within the ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ regime. Our exact results both provide valuable physical information on a complex quantum problem and bring about the interesting unsolved issue of how charge transport evolves from normal diffusive for ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ to anomalous superdiffusive in the ${k}_{B}T\ensuremath{\rightarrow}\ensuremath{\infty}$ limit.

arXiv:2411.10783Physical review. B./Physical review. BNov 15, 202410 citations

Ground state properties of half-filled Hubbard model

Canio Noce, Mario Cuoco

Physics Letters AJul 1, 19971 citation

Charge and spin transport in the one-dimensional Hubbard model

Shi-Jian Gu, Nuno M. R. Peres, J. M. P. Carmelo

In this paper we study the charge and spin currents transported by the elementary excitations of the one-dimensional Hubbard model. The corresponding current spectra are obtained by both analytic methods and numerical solution of the Bethe-ansatz equations. For the case of half-filling, we find that the spin-triplet excitations carry spin but no charge, while charge $η$ -spin triplet excitations carry charge but no spin, and both spin-singlet and charge $η$ -spin-singlet excitations carry neither spin nor charge currents.In this paper we study the charge and spin currents transported by the elementary excitations of the one-dimensional Hubbard model. The corresponding current spectra are obtained by both analytic methods and numerical solution of the Bethe-ansatz equations. For the case of half-filling, we find that the spin-triplet excitations carry spin but no charge, while charge $η$-spin triplet excitations carry charge but no spin, and both spin-singlet and charge $η$-spin-singlet excitations carry neither spin nor charge currents.

arXiv:0710.4444Journal of Physics Condensed MatterNov 19, 200712 citations

On the ground state of the half-filled Hubbard model

B. Mehlig, Peter Fulde

The European Physical Journal BSep 1, 19944 citations

Spin and hole excitation spectra and spectral weights are calculated for the half-filled Hubbard model, as functions of

t∕U

. We find that the high energy spin spectra are sensitive to charge fluctuations. The energy difference $\ensuremath{\Delta}(\ensuremath{\pi},0)\ensuremath{-}\ensuremath{\Delta}(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)$ in the single-magnon dispersion relation, which is negative for the Heisenberg model, changes sign at a fairly small $t∕U\ensuremath{\approx}0.053(5)$. The hole bandwidth is proportional to

J

, and considerably larger than in the $t\text{\ensuremath{-}}J$ models. It has a minimum at $(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)$ and a very weak dispersion along the antiferromagnetic zone boundary. A good fit to the measured spin spectra in

{\mathrm{La}}_{2}\mathrm{Cu}{\mathrm{O}}_{4}

T=10\phantom{\rule{0.3em}{0ex}}\mathrm{K}

is obtained with the parameter values

U=3.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}

t=0.35\phantom{\rule{0.3em}{0ex}}\mathrm{eV}

The use of hydrodynamic transport theory seems to indicate that the charge diffusion constant

D

of the one-dimensional (1D) half-filled Hubbard model, whose Drude weight vanishes, diverges for temperature

T>0

, which would imply anomalous superdiffusive charge transport. Here the leading term of that constant is derived for low finite temperatures ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ where ${\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}$ is the Mott-Hubbard gap. It only diverges in the $T\ensuremath{\rightarrow}0$ limit, being finite and decreasing upon increasing

T

within the ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ regime. Our exact results both provide valuable physical information on a complex quantum problem and bring about the interesting unsolved issue of how charge transport evolves from normal diffusive for ${k}_{B}T/{\mathrm{\ensuremath{\Delta}}}_{\ensuremath{\eta}}\ensuremath{\ll}1$ to anomalous superdiffusive in the ${k}_{B}T\ensuremath{\rightarrow}\ensuremath{\infty}$ limit.

η

-spin triplet excitations carry charge but no spin, and both spin-singlet and charge

η

-spin-singlet excitations carry neither spin nor charge currents.