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.
We calculate the full $I-V$ characteristics at vanishing temperature in the self-dual interacting resonant level model in two ways. The first uses careful time dependent DMRG with large number of states per block and a representation of the reservoir
s as leads subjected to a chemical potential. The other is based on integrability in the continuum limit, and generalizes early work of Fendley Ludwig Saleur on the boundary sine-Gordon model. The two approaches are in excellent agreement, and uncover among other things a power law decay of the current at large voltages when $U>0$.
