Tunneling between coupled Luttinger liquids

Abstract

We consider the problem of tunneling between spinless 1D Luttinger liquid chains. We show how to map the problem onto the 4-state chiral clock model together with a free boson for the total charge mode. We use a variety of results, some of them exact, from the integrable chiral Potts model and the study of commensurate/incommensurate transitions to deduce the physics of coupled Luttinger liquids. For those intrachain interaction strengths for which interchain tunneling is relevant, we find that it can lead to the formation of symmetric and antisymmetric bands with split Fermi surfaces, depending on the relative strengths of interchain tunneling and interchain interactions. With split Fermi surfaces, the tunneling is coherent. It is not possible to have two gapless Fermi surfaces with the same Fermi momentum when interchain tunneling is relevant. However, interchain interactions can drive the formation of a gap, in which case interchain transport will be incoherent. We comment on the possible relevance of our results to c-axis transport in high-T_c superconductors.

11 pages, 2 figures. v2: fixed typos

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• Crossover from Luttinger- to Fermi-liquid behavior in strongly anisotropic systems in large dimensions
• Classification and Stability of Phases of the Multicomponent One-Dimensional Electron Gas
• Quantum Hall Bilayers and the Chiral Sine-Gordon Equation
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• On the phase diagram of the discrete $Z_6$ spin models

Cited by in corpus (1)

• A Coulomb gas approach to the anisotropic one-dimensional Kondo lattice model at arbitrary filling