22 April 2025 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 neutrality requirement restricts the most general interaction (beyond forward-scattering quadratic terms in the Lagrangian), 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 must preserve the form of Lagrangian. There is another constraint (formulated by Haldane) on the type of perturbations that are allowed to coexist. The conductance (in e2/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. Two possible approaches exist to calculate a conductance: a scattering matrix and the Kubo formula. We present the proof of the conductance independence of the interactions in the wire in the presence of relevant perturbations (crucial for applying the Kubo formula). The variety of possible combinations of the relevant perturbations provides the variety of possible fractional conductances

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