Renormalization-group analysis of the one-dimensional extended Hubbard model with a single impurity

Andergassen, Sabine; Enss, Tilman; Meden, V.; Metzner, Walter; Schollwöck, Ulrich; Schönhammer, K.

doi:10.1103/physrevb.73.045125

Cited by 46 publications

(75 citation statements)

References 45 publications

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“…In the presence of a sizable backscattering component (g 1,⊥ > 0) the asymptotic low-energy regime is usually reached via a complex crossover behavior [6,7,8]. We expect the same to hold for the more realistic setups studied here, which would render the behavior of G(T ) even more complex (and less "universal") than described in the present work.…”

Section: Introductionsupporting

confidence: 56%

“…General aspects of the fRG can be found in [23], [24], and [25], while its application to inhomogeneous LLs is described in [8], [11] and [16]. By comparison to results for small systems obtained by density-matrix renormalization group and to exact results from bosonization and Bethe ansatz for the asymptotic behavior, it was shown that the fRG in the truncation scheme used here captures the relevant physics not only in the asymptotic low-energy regime but also on finite energy scales [11,16].…”

Section: The Functional Renormalization Groupmentioning

confidence: 99%

“…The implementation of finite temperatures requires at each step of the flow the replacement of the flow parameter Λ by the nearest Matsubara frequency [8].…”

Section: The Functional Renormalization Groupmentioning

confidence: 99%

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Coupling-geometry-induced temperature scales in the conductance of Luttinger liquid wires

Wächter

Meden

Schönhammer

2009

J. Phys.: Condens. Matter

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Abstract. We study electronic transport through a one-dimensional, finite-length quantum wire of correlated electrons (Luttinger liquid) coupled at arbitrary position via tunnel barriers to two semi-infinite, one-dimensional as well as stripe-like (twodimensional) leads, thereby bringing theory closer towards systems resembling setups realized in experiments. In particular, we compute the temperature dependence of the linear conductance G of a system without bulk impurities. The appearance of new temperature scales introduced by the lengths of overhanging parts of the leads and the wire implies a G(T ) which is much more complex than the power-law behavior described so far for end-coupled wires. Depending on the precise setup the wide temperature regime of power-law scaling found in the end-coupled case is broken up in up to five fairly narrow regimes interrupted by extended crossover regions. Our results can be used to optimize the experimental setups designed for a verification of Luttinger liquid power-law scaling.

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Section: Introductionsupporting

confidence: 56%

Section: The Functional Renormalization Groupmentioning

confidence: 99%

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Coupling-geometry-induced temperature scales in the conductance of Luttinger liquid wires

Wächter

Meden

Schönhammer

2009

J. Phys.: Condens. Matter

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“…This can be understood as follows. The crossover scale ∆ is strongly affected by the size of the open boundary analog of a g 1,⊥ two-particle scattering process [17,36,40] which cannot be written quadratically in the bosonic densities. Its initial value (with respect to an RG flow) in the extended Hubbard model is given by g 1,⊥ = U + 2V cos(2k F ) with k F = nπ/2.…”

Section: Spectral Properties Of the Extended Hubbard Modelmentioning

confidence: 99%

Local spectral properties of Luttinger liquids: scaling versus nonuniversal energy scales

Schuricht¹,

Andergassen²,

Meden³

2012

J. Phys.: Condens. Matter

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Abstract. Motivated by recent scanning tunneling and photoemission spectroscopy measurements on self-organized gold chains on a germanium surface we reinvestigate the local single-particle spectral properties of Luttinger liquids. In the first part we use the bosonization approach to exactly compute the local spectral function of a simplified field theoretical low-energy model and take a closer look at scaling properties as a function of the ratio of energy and temperature. Translational invariant Luttinger liquids as well as those with an open boundary (cut chain geometry) are considered. We explicitly show that the scaling functions of both setups have the same analytic form. The scaling behavior suggests a variety of consistency checks which can be performed on measured data to experimentally verify Luttinger liquid behavior. In a second part we approximately compute the local spectral function of a microscopic lattice model-the extended Hubbard model-close to an open boundary using the functional renormalization group. We show that as a function of energy and temperature it follows the field theoretical prediction in the low-energy regime and point out the importance of nonuniversal energy scales inherent to any microscopic model. The spatial dependence of this spectral function is characterized by oscillatory behavior and an envelope function which follows a power law both in accordance with the field theoretical continuum model. Interestingly, for the lattice model we find a phase shift which is proportional to the two-particle interaction and not accounted for in the standard bosonization approach to Luttinger liquids with an open boundary. We briefly comment on the effects of several one-dimensional branches cutting the Fermi energy and Rashba spin-orbit interaction.

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“…For the extended Hubbard model and vanishing SOI, this has been done in Ref. 16 using fRG. As the parameterization of the two-particle vertex used there relies on spin conservation, it cannot easily be extended to the present situation with SOI.…”

Section: 16mentioning

confidence: 99%

Spin-polarized currents through interacting quantum wires with nonmagnetic leads

Birkholz

Meden

2009

Phys. Rev. B

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We study the performance of a quantum wire spin filter that is based on the Rashba spin-orbit interaction in the presence of the electron-electron interaction. The finite length wire is attached to two semi-infinite nonmagnetic leads. Analyzing the spin polarization of the linear conductance at zero temperature, we show that spin-filtering is possible by adequate tuning of the system parameters first considering noninteracting electrons. Next, the functional renormalization group method is used to capture correlation effects induced by the Coulomb interaction. For short wires we show that the energy regime in which spin polarization is found is strongly affected by the Coulomb interaction. For long wires we find the power-law suppression of the total conductance on low energy scales typical for inhomogeneous Luttinger liquids while the degree of spin polarization stays constant.

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Renormalization-group analysis of the one-dimensional extended Hubbard model with a single impurity

Cited by 46 publications

References 45 publications

Coupling-geometry-induced temperature scales in the conductance of Luttinger liquid wires

Coupling-geometry-induced temperature scales in the conductance of Luttinger liquid wires

Local spectral properties of Luttinger liquids: scaling versus nonuniversal energy scales

Spin-polarized currents through interacting quantum wires with nonmagnetic leads

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