Localization in a system of N coupled chains

Prigodin, V. N.; Firsov, Yu. A.; Weller, Wolfgang

doi:10.1016/0038-1098(86)90706-4

Cited by 35 publications

(30 citation statements)

References 7 publications

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“…This, again, could only take place in the case of strong interactions or presence of a spin or charge gap, a problem that also is present in later work by Brazovskiȋ and Yakovenko [231]. Interestingly, however, in such a gapped regime, Prigodin and Firsov obtain a maximum of the superconducting T c as a function of t ⊥ for t ⊥ ∼ ∆, where ∆ is the 1D spin or charge gap [222]. T c at maximum is significantly higher than in the 3D limit t ⊥ → t .…”

Section: Crossover To Higher Dimensionsmentioning

confidence: 87%

“…Its efficiency may therefore be severly reduced if there are only collective excitations. While z(k = t ⊥ /v F ) = 0 in general, we still expect that a reduced quasi-particle residue z(t ⊥ ) ≪ 1 will delay the establishment of 3D coherence in the single-electron dynamics [21,22,222]. Charge-spin separation could also confine particles on their chains because a holon and spinon must tunnel together -yet in general they are separated [223].…”

Section: Crossover To Higher Dimensionsmentioning

confidence: 99%

“…A description of the system for finite t ⊥ is, however, a difficult task. We only briefly review the major achievements and refer the reader to more extended treatments [21,22,222] for further details.…”

Section: Crossover To Higher Dimensionsmentioning

confidence: 99%

“…Early work starts from the exact solution of the 1D models and adds t ⊥ as a perturbation [222,224,231]. In this way, one generates an effective transfer of a pair of particles.…”

Section: Crossover To Higher Dimensionsmentioning

confidence: 99%

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One-dimensional Fermi liquids

1995

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We review the progress in the theory of one-dimensional (1D) Fermi liquids which has occurred over the past decade. The usual Fermi liquid theory based on a quasi-particle picture, breaks down in one dimension because of the Peierls divergence in the particlehole bubble producing anomalous dimensions of operators, and because of charge-spin separation. Both are related to the importance of scattering processes transferring finite momentum. A description of the low-energy properties of gapless one-dimensional quantum systems can be based on the exactly solvable Luttinger model which incorporates these features, and whose correlation functions can be calculated. Special properties of the eigenvalue spectrum, parameterized by one renormalized velocity and one effective coupling constant per degree of freedom fully describe the physics of this model. Other gapless 1D models share these properties in a low-energy subspace. The concept of a "Luttinger liquid" implies that their low-energy properties are described by an effective Luttinger model, and constitutes the universality class of these quantum systems. Once the mapping on the Luttinger model is achieved, one has an asymptotically exact solution of the 1D many-body problem. Lattice models identified as Luttinger liquids include the 1D Hubbard model off half-filling, and variants such as the t − J-or the extended Hubbard model. Also 1D electron-phonon systems or metals with impurities can be Luttinger liquids, as well as the edge states in the quantum Hall effect.We discuss in detail various solutions of the Luttinger model which emphasize different aspects of the physics of 1D Fermi liquids. Correlation functions are calculated in detail using bosonization, and the relation of this method to other approaches is discussed. The correlation functions decay as non-universal power-laws, and scaling relations between their exponents are parameterized by the effective coupling constant. Charge-spin separation only shows up in dynamical correlations. The Luttinger liquid concept is developed from perturbations of the Luttinger model. Mainly specializing to the 1D Hubbard model, we review a variety of mappings for complicated models of interacting electrons onto Luttinger models, and thereby obtain their correlation functions. We also discuss the generic behaviour of systems not falling into the Luttinger liquid universality class because of gaps in their low-energy spectrum. The Mott transition provides an example for the transition from Luttinger to non-Luttinger behaviour, and recent results on this problem are summarized. Coupling chains by interactions or tunneling allows transverse coherence to establish in the single-or two-particle dynamics, and drives the systems away from a Luttinger liquid. We discuss the influence of charge-spin separation and of the anomalous dimensions on the transverse dynamics of the electrons. The edge states in the quani tum Hall effect provide a realization of a modified, chiral Luttinger liquid whose detailed properties differ...

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Section: Crossover To Higher Dimensionsmentioning

confidence: 87%

Section: Crossover To Higher Dimensionsmentioning

confidence: 99%

Section: Crossover To Higher Dimensionsmentioning

confidence: 99%

“…Early work starts from the exact solution of the 1D models and adds t ⊥ as a perturbation [222,224,231]. In this way, one generates an effective transfer of a pair of particles.…”

Section: Crossover To Higher Dimensionsmentioning

confidence: 99%

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One-dimensional Fermi liquids

1995

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“…[32,36]). The appearance of d-wave superconductivity in ladder systems is well understood within a strong coupling scenario, where a spin gap leads to interchain Cooper pairing.…”

Section: B Discussionmentioning

confidence: 99%

Renormalization-group calculations withk‖-dependent couplings in a ladder

2005

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We calculate the phase diagram of a ladder system, with a Hubbard interaction and an interchain coupling t ⊥ . We use a Renormalization Group method, in a one loop expansion, introducing an original method to include k dependence of couplings. We also classify the order parameters corresponding to ladder instabilities. We obtain different results, depending on whether we include k dependence or not. When we do so, we observe a region with large antiferromagnetic fluctuations, in the vicinity of small t ⊥ , followed by a superconducting region with a simultaneous divergence of the Spin Density Waves channel. We also investigate the effect of a non local backward interchain scattering : we observe, on one hand, the suppression of singlet superconductivity and of Spin Density Waves, and, on the other hand, the increase of Charge Density Waves and, for some values of t ⊥ , of triplet superconductivity. Our results eventually show that k is an influential variable in the Renormalization Group flow, for this kind of systems.

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Normal state properties of BEDT compounds

Joo

Meddeb

Charfi‐Kaddour

et al. 2004

Physica Status Solidi (b)

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PACS 74.20.Mn, 74.25Fy, 74.70.Kn The κ-(BEDT-TTF) 2 X organic superconductors are described by a two parameter 2D surface model, in which bandwidth and departure from perfect nesting can be varied. We have studied the spin fluctuation effect on the normal state properties in a Fermi liquid approach using the RPA approximation. The calculated NMR relaxation rate exhibits a peak in 1/(T 1 T), which strongly decreases when the departure from the perfect nesting of the Fermi surface and the bandwidth decrease. Our calculations show also that the spin fluctuations induce an unusual resistivity temperature dependence. These results are in a good agreement with experimental data done in κ-(BEDT-TTF) 2 X, at least qualitatively.

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Localization in a system of N coupled chains

Cited by 35 publications

References 7 publications

One-dimensional Fermi liquids

One-dimensional Fermi liquids

Renormalization-group calculations withk‖-dependent couplings in a ladder

Normal state properties of BEDT compounds

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