7 February 2023 Tue 4 pm

We consider a strongly interacting one-dimensional (1D) system with N channels. We study the conditions necessary for the coexistence of various perturbations. The most general interaction (beyond forward-scattering quadratic terms in the Lagrangian) is restricted by the neutrality requirement, meaning that each term in the Hamiltonian conserves the number of particles. To become relevant and open a gap the perturbation has to represent a new field, and new fields have to preserve the form of Lagrangian. There is another constraint (formulated by Haldane) on the type of perturbations allowed to coexist. The conductance (in e 2 /h units) of the remaining free fields can be presented as the difference between the initial conductance of all N channels and the conductance eliminated by K compatible relevant perturbations which freeze K corresponding fields. The variety of possible combinations of the relevant perturbations provides the variety of possible fractional conductances.

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