Crossover from Luttinger- to Fermi-liquid behavior in strongly anisotropic systems in large dimensions

TL;DR

This paper investigates how weak interchain coupling in an array of Luttinger liquids leads to a crossover from non-Fermi-liquid to Fermi-liquid behavior, emphasizing the importance of self-consistent expansion in large dimensions.

Contribution

It introduces a self-consistent perturbative approach to describe the crossover from Luttinger-liquid to Fermi-liquid behavior in anisotropic systems in large dimensions.

Findings

Anomalous exponent scales to zero below the crossover temperature.

Coherent quasiparticles with finite weight emerge along the Fermi surface.

Self-consistent expansion restores Fermi-liquid behavior.

Abstract

We consider the low-energy region of an array of Luttinger liquids coupled by a weak interchain hopping. The leading logarithmic divergences can be re-summed to all orders within a self-consistent perturbative expansion in the hopping, in the large-dimension limit. The anomalous exponent scales to zero below the one-particle crossover temperature. As a consequence, coherent quasiparticles with finite weight appear along the whole Fermi surface. Extending the expansion self-consistently to all orders turns out to be crucial in order to restore the correct Fermi-liquid behavior.