Duality approach to one-dimensional degenerate electronic systems

TL;DR

This paper explores a duality-based classification of zero-temperature spin-gapped phases in one-dimensional multicomponent electronic systems, revealing symmetry-dependent dualities and analyzing phase transitions.

Contribution

It introduces a novel duality framework for classifying phases based on symmetry algebra, applied to two-leg electronic ladders.

Findings

Duality symmetries form a finite classification scheme.

Classification depends solely on symmetry algebra.

Application to two-leg ladders illustrates the approach.

Abstract

We investigate the possible classification of zero-temperature spin-gapped phases of multicomponent electronic systems in one spatial dimension. At the heart of our analysis is the existence of non-perturbative duality symmetries which emerge within a low-energy description. These dualities fall into a finite number of classes that can be listed and depend only on the algebraic properties of the symmetries of the system: its physical symmetry group and the maximal continuous symmetry group of the interaction. We further characterize possible competing orders associated to the dualities and discuss the nature of the quantum phase transitions between them. Finally, as an illustration, the duality approach is applied to the description of the phases of two-leg electronic ladders for incommensurate filling.