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Journal of Physics Conference Series

Anomalous non-equilibrium electron transport in one-dimensional quantum nano wire at half-filling: time dependent density renormalization group study

Masahiko Okumura, Hiroaki Onishi, S Yamada, Masahiko Machida

Published Nov 1, 2010• 0 citations
Publisher

Abstract

We study non-equilibrium properties of one-dimensional Hubbard model by the density-matrix renormalization-group method. First, we demonstrate stability of "doublon", which characterized by double occupation on a site due to the integrability of the model. Next, we present a kind of anomalous transport caused by the doublons created under strong non-equilibrium conditions in an optical lattice system regarded as an ideal testbed to investigate fundamental properties of the Hubbard model. Finally, we give a result on development of the pair correlation function in a strong non-equilibrium condition. This can be understood as a development of coherence among many excited doublons.

DOI
10.1088/1742-6596/248/1/012031

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We study non-equilibrium properties of one-dimensional Hubbard model by the density-matrix renormalization-group method. First, we demonstrate stability of "doublon", which characterized by double occupation on a site due to the integrability of the model. Next, we present a kind of anomalous transport caused by the doublons created under strong non-equilibrium conditions in an optical lattice system regarded as an ideal testbed to investigate fundamental properties of the Hubbard model. Finally, we give a result on development of the pair correlation function in a strong non-equilibrium condition. This can be understood as a development of coherence among many excited doublons.
The fate of a local two-hole doublon excitation in the one-dimensional Fermi-Hubbard model is systematically studied for strong Hubbard interaction UUU in the entire filling range using the density-matrix renormalization group (DMRG) and the Bethe ansatz. For strong UUU, two holes at the same site form a compound object whose decay is impeded by the lack of phase space. Still, a partial decay is possible on an extremely short time scale where phase-space arguments do not yet apply. We argue that the initial decay and the resulting intermediate state are relevant for experiments performed with ultracold atoms loaded into an optical lattice as well as for (time-resolved) CVV Auger-electron spectroscopy. The detailed discussion comprises the mixed ballistic-diffusive real-time propagation of the doublon through the lattice, its partial decay on the short time scale as a function of filling and interaction strength, as well as the analysis of the decay products, which are metastable on the intermediate time scale that is numerically accessible and which show up in the two-hole excitation (Auger) spectrum. The ambivalent role of singly occupied sites is key to understanding the doublon physics; for high fillings, ground-state configurations with single occupancies are recognized to strongly relax the kinematic constraints and to open up decay channels. For fillings close to half-filling, however, their presence actually blocks the doublon decay. Finally, the analysis of the continua in the two-hole spectrum excludes a picture where the doublon decays into unbound electron holes for generic fillings, different from the limiting case of the completely filled band. We demonstrate that the decay products as well as the doublon propagation should rather be understood in terms of Bethe ansatz eigenstates.
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.
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 real-time evolution of a charge-excited state in a one-dimensional ege_{\rm g}eg​-orbital degenerate Hubbard model, by a time-dependent density-matrix renormalization group method. Considering a chain along the zzz direction, electrons hop between adjacent 3z2−r23z^2-r^23z2−r2 orbitals, while x2−y2x^2-y^2x2−y2 orbitals are localized. For the charge-excited state, a holon-doublon pair is introduced into the ground state at quarter filling. At initial time, there is no electron in a holon site, while a pair of electrons occupies 3z2−r23z^2-r^23z2−r2 orbital in a doublon site. As the time evolves, the holon motion is governed by the nearest-neighbor hopping, but the electron pair can transfer between 3z2−r23z^2-r^23z2−r2 orbital and x2−y2x^2-y^2x2−y2 orbital through the pair hopping in addition to the nearest-neighbor hopping. Thus holon and doublon propagate at different speed due to the pair hopping that is characteristic of multi-orbital systems.
We investigate the spin or charge transport in a one-dimensional strongly correlated system by using the adaptive time-dependent density-matrix renormalization-group method. The model we consider is a non-half-filled Hubbard chain with a bond of controllable spin-dependent electron hoppings, which is found to cause a blockade of spin current with little influence on charge current. We have considered (1) the spread of a wave packet of both spin and charge and (2) the spin and charge currents induced by a spin-dependent voltage bias. It is found that the spin-charge separation plays a crucial role in the spin-current blockade, which may be utilized to observe the spin-charge separation directly.
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.