Fermi surface renormalization and confinement in two coupled metallic chains

TL;DR

This paper investigates how interactions affect the Fermi surface in coupled chains of spinless fermions, revealing that while strong backscattering can lead to confinement, more precise calculations show only weak confinement effects.

Contribution

The study introduces a non-perturbative functional renormalization group method that accounts for vertex corrections and wave-function renormalizations in coupled fermionic chains.

Findings

Interchain backscattering reduces Fermi momentum separation.

A simple approximation predicts a confinement transition.

More accurate calculations show only weak confinement effects.

Abstract

Using a non-perturbative functional renormalization group approach involving both fermionic and bosonic fields we calculate the interaction-induced change of the Fermi surface of spinless fermions moving on two chains connected by weak interchain hopping t_{bot}. We show that interchain backscattering can strongly reduce the distance Delta between the Fermi momenta associated with the bonding and the antibonding band, corresponding to a large reduction of the effective interchain hopping t_{bot}^{*} A self-consistent one-loop approximation neglecting marginal vertex corrections and wave-function renormalizations predicts a confinement transition for sufficiently large interchain backscattering, where the renormalized t_{bot}^{*} vanishes. However, a more accurate calculation taking vertex corrections and wave-function renormalizations into account predicts only weak confinement in the sense that 0< | t_{bot}^{*} | << | t_{bot} |. Our method can be applied to other strong-coupling problems where the dominant scattering channel is known.