Renormalization Group Technique for Quasi-one-dimensional Interacting Fermion Systems at Finite Temperature

TL;DR

This paper reviews the renormalization group method applied to quasi-one-dimensional interacting fermion systems at finite temperature, emphasizing scaling theory, interchain coupling effects, and the emergence of the Kohn-Luttinger mechanism.

Contribution

It extends the renormalization group analysis to include interchain coupling and finite temperature effects in quasi-one-dimensional fermion systems, highlighting crossover phenomena and multiple energy scales.

Findings

Analysis of the crossover phenomenology in quasi-1D systems

Clarification of two-loop level peculiarities in RG method

Discussion of Kohn-Luttinger mechanism in superconducting and density-wave channels

Abstract

We review some aspects of the renormalization group method for interacting fermions. Special emphasis is placed on the application of scaling theory to quasi-one-dimensional systems at non zero temperature. We begin by introducing the scaling ansatz for purely one-dimensional fermion systems and its extension when interchain coupling and dimensionality crossovers are present at finite temperature. Next, we review the application of the renormalization group technique to the one-dimensional electron gas model and clarify some peculiarities of the method at the two-loop level. The influence of interchain coupling is then included and results for the crossover phenomenology and the multiplicity of characteristic energy scales are summarized. The emergence of the Kohn-Luttinger mechanism in quasi-one-dimensional electronic structures is discussed fo both superconducting and density-wave channels.