Crossover to Fermi-liquid behavior for weakly coupled Luttinger liquids in the anisotropic large-dimension limit

Article

关键词: SPIN-CHARGE SEPARATION;    HUBBARD-MODEL;    INTERACTING FERMIONS;    ORGANIC CONDUCTORS;    PARTICLE;    CHAINS;    SUPERCONDUCTIVITY;    TRANSITIONS;    COHERENCE;    EXPANSION;   

DOI  :  10.1103/PhysRevB.61.7909

来源: SCIE

【 摘 要 】

We study the problem of the crossover from one- to higher-dimensional metals by considering an array of Luttinger liquids tone-dimensional chains) coupled by a weak interchain hopping tl. We evaluate the exact asymptotic low-energy behavior of the self-energy in the anisotropic infinite-dimension limit. This limit extends the dynamical mean-field concept to the case of a chain embedded in a self-consistent medium. The system flows to a Fermi-liquid fixed point for energies below the dimensional crossover temperature, and the anomalous exponent ct renormalizes to zero, in the case of equal spin and charge velocities. In particular, the single-particle spectral function shows sharp quasiparticle peaks with nonvanishing weight along the whole Fermi surface, in contrast to the lowest-order result. Our result is obtained by carrying out a resummation of all diagrams of the expansion in t(perpendicular to) contributing to the anisotropic D-->infinity limit. This is done by serving, in an almost completely analytic way, an asymptotically exact recursive equation for the renormalized vertices, within a skeleton expansion. Our outcome shows that perturbation expansions in t(perpendicular to) restricted to lowest orders are unreliable below the crossover temperature. The extension to finite dimensions id discussed. This work extends our recent letter [Phys. Rev. Lett. 83, 128 (1999)], and includes all mathematical details.

【 授权许可】

Free