Classification and Stability of Phases of the Multicomponent One-Dimensional Electron Gas

TL;DR

This paper classifies the ground-state phases of complex one-dimensional electronic systems using a fixed-point approach, emphasizing stability analysis, symmetry breaking, and excitations, with applications to multichain Hubbard models and related systems.

Contribution

It introduces a fixed-point strategy for phase classification, including a new generalization of Luttinger's theorem, and demonstrates the instability of many exotic phases due to the spin-gap proximity effect.

Findings

Many exotic phases are unstable due to the spin-gap proximity effect.

A new generalized Luttinger's theorem shows a gapless even-charge mode in incommensurate systems.

The analysis provides a systematic way to classify phases based on stability and symmetry.

Abstract

The classification of the ground-state phases of complex one-dimensional electronic systems is considered in the context of a fixed-point strategy. Examples are multichain Hubbard models, the Kondo-Heisenberg model, and the one-dimensional electron gas in an active environment. It is shown that, in order to characterize the low-energy physics, it is necessary to analyze the perturbative stability of the possible fixed points, to identify all discrete broken symmetries, and to specify the quantum numbers and elementary wave vectors of the gapless excitations. Many previously-proposed exotic phases of multichain Hubbard models are shown to be unstable because of the ``spin-gap proximity effect.'' A useful tool in this analysis is a new generalization of Luttinger's theorem, which shows that there is a gapless even-charge mode in any incommensurate N-component system.