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One-Particle an Two-Particle Instability of Coupled Luttinger Liquids

Daniel Boies·C. Bourbonnais·A. -M. S. Tremblay
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Abstract

It is shown that the Luttinger liquid is unstable to arbitrarily small transverse hopping. It becomes either a Fermi liquid or exhibits long-range order at zero temperature. The crossover temperatures below which either transverse coherent band motion or long-range order start to develop can be finite even when spin and charge velocities differ. Explicit scaling relations for the one-particle and two-particle crossover temperatures are derived in terms of transverse hopping amplitude, spin and charge velocities as well as anomalous exponents. The special case of infinite-range transverse hopping can be treated exactly and yields a Fermi liquid down to zero temperature, unless the anomalous exponent $θ$ is larger than unity.

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Daniel Boies, C. Bourbonnais, A. -M. S. Tremblay. 1994-08-17. One-Particle an Two-Particle Instability of Coupled Luttinger Liquids. https://doi.org/10.1103/physrevlett.74.968

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