Possible phases of two coupled n-component fermionic chains

TL;DR

This paper analyzes the phase diagram of two coupled n-component fermionic chains using renormalization group methods, identifying various gapless and gapped phases, and studying the effects of interactions and symmetries.

Contribution

It provides a comprehensive analytical study of possible phases in coupled fermionic chains, including fixed points, phase characterization, and the impact of symmetry and interactions.

Findings

Identified Luttinger-liquid and gapped phases for generic and special fillings.

Discovered that the SU(n) symmetric Hubbard ladder does not reach the Luttinger liquid fixed point.

Found that umklapp processes lead to insulating behavior in the system.

Abstract

A two-leg ladder with $n$-component fermionic fields in the chains has been considered using an analytic renormalization group method. The fixed points and possible phases have been determined for generic filling as well as for a half-filled system and for the case when one of the subbands is half filled. A weak-coupling Luttinger-liquid phase and several strong-coupling gapped phases have been found. In the Luttinger liquid phase, for the most general spin dependence of the couplings, all $2n$ modes have different velocities if the interband scattering processes are scaled out, while $n$ doubly degenerate modes appear if the interband scattering processes remain finite. The role of backward-scattering, charge-transfer and umklapp processes has been analysed using their bosonic form and the possible phases are characterized by the number of gapless modes. As a special case the SU($n$) symmetric Hubbard ladder has been investigated numerically. It was found that this model does not scale to the Luttinger liquid fixed point. Even for generic filling gaps open up in the spectrum of the spin or charge modes, and the system is always insulator in the presence of umklapp processes.