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arXiv:1005.2015 · Journal of the Physical Society of Japan

Nonequilibrium Current in the One Dimensional Hubbard Model at Half-Filling

Shunsuke Kirino, Kazuo Ueda

Published Sep 10, 2010• 20 citations
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Abstract

Nonlinear transport in the one dimensional Hubbard model at half-filling under a finite bias voltage is investigated by the adaptive time-dependent density matrix renormalization group method. For repulsive on-site interaction, dielectric breakdown of the Mott insulating ground state to a current-carrying nonequilibrium steady state is clearly observed when the voltage exceeds the charge gap. It is found that by increasing the voltage further the current-voltage characteristics are scaled only by the charge gap and the scaling curve exhibits almost linear dependence on the voltage whose slope is suppressed by the electron correlation. In the case of attractive interaction the linear conductance is the perfect one $2e^2/h$ which agrees with the prediction by the Luttinger liquid theory.

DOI
10.1143/jpsj.79.093710

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Nonlinear transport in the one dimensional Hubbard model at half-filling under a finite bias voltage is investigated by the adaptive time-dependent density matrix renormalization group method. For repulsive on-site interaction, dielectric breakdown of the Mott insulating ground state to a current-carrying nonequilibrium steady state is clearly observed when the voltage exceeds the charge gap. It is found that by increasing the voltage further the current-voltage characteristics are scaled only by the charge gap and the scaling curve exhibits almost linear dependence on the voltage whose slope is suppressed by the electron correlation. In the case of attractive interaction the linear conductance is the perfect one 2e2/h2e^2/h2e2/h which agrees with the prediction by the Luttinger liquid theory.
Nonequilibrium transport in the one dimensional Hubbard model at half-filling is studied by the time-dependent density matrix renormalization group method. It is clearly demonstrated that dielectric breakdown of the Mott insulating phase to a nonequilibrium steady state occurs when an external voltage is larger than the charge gap. From the numerically obtained current-voltage characteristics we find that the current is suppressed by the correlation effect when compared with that of a band insulator and that the current is scaled only by the charge gap for small voltages compared to the band width.
We calculate the nonequilibrium electronic transport properties of a one-dimensional interacting chain at half filling, coupled to noninteracting leads. The interacting chain is initially in a Mott insulator state that is driven out of equilibrium by applying a strong bias voltage between the leads. For bias voltages above a certain threshold we observe the breakdown of the Mott insulator state and the establishment of a steady-state electronic current through the system. Based on extensive time-dependent density-matrix renormalization-group simulations, we show that this steady-state current always has the same functional dependence on voltage, independent of the microscopic details of the model and we relate the value of the threshold to the Lieb-Wu gap. We frame our results in terms of the Landau-Zener dielectric breakdown picture. Finally, we also discuss the real-time evolution of the current, and characterize the current-carrying state resulting from the breakdown of the Mott insulator by computing the double occupancy, the spin structure factor, and the entanglement entropy.
We study the one-dimensional Anderson-Hubbard model using the density-matrix renormalization-group method. The influence of disorder on the Tomonaga- Luttinger liquid behavior is quantitatively discussed. Based on the finite-size scaling analysis of density-density correlation functions, we find the following results: (i) the charge exponent is significantly reduced by disorder at low filling and near half filling, (ii) the localization length decays as $\ensuremath{\xi}\ensuremath{\sim}{\ensuremath{\Delta}}^{\ensuremath{-}2}$, where $\ensuremath{\Delta}$ is the disorder strength, independently of the on-site Coulomb interaction as well as band filling, and (iii) the localization length is strongly suppressed by the on-site Coulomb interaction near half filling in association with the formation of the Mott plateaus.
We study a one-dimensional SU(N) Hubbard model with an attractive on-site interaction and N>2N>2N>2 at half-filling on the bipartite lattice using density-matrix renormalization-group method and a perturbation theory. We find that the ground state of the SU(N) Hubbard model is a charge density wave state with two-fold degeneracy. All the excitations are found to be gapful, resulting in an insulating ground state, on contrary to that in the SU(2) case. Moreover, the charge gap is equal to the Cooperon gap, which behaves as −2Nt2/(N−1)U-2Nt^2/(N-1)U−2Nt2/(N−1)U in the strong coupling regime. However, the spin gap ΔsΔ_{s}Δs​ and the quasiparticle gap Δ1Δ_{1}Δ1​ as well open exponentially in the weak coupling region, while in the strong coupling region, they linearly depend on UUU such that Δs∼−U(N−1)Δ_{s}\sim -U(N-1)Δs​∼−U(N−1) and Δ1∼−U(N−1)/2Δ_{1}\sim -U(N-1)/2Δ1​∼−U(N−1)/2.
We investigate low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction U<0U<0U<0 using the density-matrix renormalization-group method as well as perturbation theory. We find that the ground state is a charge-density-wave state with long-range order. The ground state is completely incompressible since all the excitations are gapful. The charge gap, which is the same as the four-particle excitation gap, is a nonmonotonic function of UUU, while the spin gap and others increase with increasing $\ensuremath{\mid}U\ensuremath{\mid}$ and have linear asymptotic behaviors.
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.