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arXiv:cond-mat/0407701 · New Journal of Physics

Quantum Monte Carlo simulation for the spin-drag conductance of the Hubbard model

Kim Louis, Claudius Gros

Published Dec 7, 2004• 6 citations
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Abstract

In the situation of two electrostatically coupled conductors, a current in one conductor may induce a current in the other one. We will study this phenomenon, called Coulomb drag, in the Hubbard chain where the two 'conductors' are given by fermions with different spin orientations. With the aid of a Monte Carlo approach, which we presented in a recent paper, we calculate the trans-conductance in different variants of the Hubbard chain (with/without impurity and additional (long-ranged) interactions) for different fillings.

DOI
10.1088/1367-2630/6/1/187

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In the situation of two electrostatically coupled conductors, a current in one conductor may induce a current in the other one. We will study this phenomenon, called Coulomb drag, in the Hubbard chain where the two 'conductors' are given by fermions with different spin orientations. With the aid of a Monte Carlo approach, which we presented in a recent paper, we calculate the trans-conductance in different variants of the Hubbard chain (with/without impurity and additional (long-ranged) interactions) for different fillings.
Charge carriers moving in a quantum wire may induce, via the Coulomb interaction and momentum conservation, a drag current in another quantum wire located nearby. In addition, tunnelling of carriers between the two parallel wires is considered. For spinless carriers the problem can be mapped onto the one-dimensional Hubbard model. The exact solution of the Hubbard chain and conformal field theory are used to calculate the critical exponents for the temperature dependence of the drag current between the two wires. The exponents are non-universal and depend on the interaction strength, the band filling and the tunnelling amplitude. For a repulsive interaction the drag current is opposite to the driving current, while for an attractive interaction they are parallel.
We have analyzed Coulomb drag between currents of interacting electrons in two parallel one-dimensional conductors of finite length LLL attached to external reservoirs. For strong coupling, the relative fluctuations of electron density in the conductors acquire energy gap MMM. At energies larger than $\ensuremath{\Gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{const}\ifmmode\times\else\texttimes\fi{}{v}_{\ensuremath{-}}\mathrm{exp}(\ensuremath{-}LM/{v}_{\ensuremath{-}})/L+{\ensuremath{\Gamma}}_{+}$, where ${\ensuremath{\Gamma}}_{+}$ is the impurity scattering rate, and, for $L>{v}_{\ensuremath{-}}/M$, where ${v}_{\ensuremath{-}}$ is the fluctuation velocity, the gap leads to an ``ideal'' drag with almost equal currents in the conductors. At low energies the drag is suppressed by coherent instanton tunneling, and the zero-temperature transconductance vanishes, indicating the Fermi-liquid behavior.
The spin Coulomb drag is the decay of the spin current in a metal as a consequence of the Coulomb interaction between up- and down-spin carriers. This interaction reduces the spin current but does not change the spin-polarization. We calculate the critical exponents of the resistivity for up- and down-spin electrons and the transresistivity for the spin-polarized Hubbard chain with nonmagnetic impurities within the Kubo formalism using the Bethe ansatz solution and conformal invariance. Due to the Luttinger liquid properties the temperature dependence of the transport correlation functions follow power laws of TTT with nonuniversal exponents.
The spin Coulomb drag is the decay of the spin current in a metal as a consequence of the Coulomb interaction between up- and down-spin carriers. This interaction reduces the spin current but does not change the spin-polarization. We calculate the critical exponents of the resistivity for up- and down-spin electrons and the transresistivity for the spin-polarized Hubbard chain with nonmagnetic impurities within the Kubo formalism using the Bethe ansatz solution and conformal invariance. Due to the Luttinger liquid properties the temperature dependence of the transport correlation functions follow power laws of TTT with nonuniversal exponents.
We calculate the critical exponent of the temperature dependence of the drag current between two parallel quantum wires. The two wires have carriers with equal mass but they may have different electron density. The electrons interact via a $\ensuremath{\delta}$-function spin-exchange potential, which is attractive or repulsive depending on whether the interacting particles are in a spin-singlet or spin-triplet state. This interaction leads to the formation of spin-singlet or spin-triplet bound states of the Cooper type (preformed hard core bosons that do not condensate). Depending on the parameters, the drag current can be parallel or opposite to the driving current. The critical exponent of the drag current is calculated using the Bethe Ansatz solution of the model and conformal field theory.