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

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

1994-08-17

arxiv.org/abs/cond-mat/9408047v1

Phys. Rev. Lett. 74, 968-971 (1995) (4 pages)

Physics

Condensed Matter

J1K 2R1 REVTEX 3.0, one figure available on request, Report # CRPS-94-10

Scientific paper

10.1103/PhysRevLett.74.968

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 $\theta $ is larger than unity.

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