Fermi surface renormalization and quantum confinement in the two-coupled chains model

TL;DR

This paper investigates how the Fermi surface and quantum confinement are renormalized in a two coupled chains model of spinless fermions, revealing a transition from Luttinger liquid to a gapped state at strong coupling.

Contribution

It provides a self-consistent RG analysis including Fermi surface renormalization, highlighting the transition to a charge-gapped regime at strong coupling.

Findings

Quantum confinement occurs only at strong coupling.

Fermi liquid regime is stabilized by umklapp interactions at weak coupling.

Quasiparticle amplitude vanishes at intermediate coupling.

Abstract

We address the problem of the Fermi surface renormalization and the quantum confinement regime (QCR) in the two coupled chains model(TCCM) of spinless fermions. We perform a self-consistent calculation of the renormalization group(RG) flows of the renormalized TCCM couplings and quasiparticle weight. On top of that we take explicitly into account the renormalization of the Fermi surface. The flow of the difference of the renormalized Fermi wave vectors associated with the bonding and antibonding bands has a dramatic effect on the single particle spectrum. Although the quasiparticle amplitude is nullified already at intermediate coupling the QCR is only observed at strong coupling. The state associated with this regime has a charge gap and it is not a Luttinger liquid. In contrast, the Fermi liquid regime is stabilized by the umklapp "$g_2$--like" interactions at very weak coupling regime.