Constructive Renormalization for Interacting Fermions

R. Shankar

Valeri N. Kotov, Bruno Uchoa, Oleg P. Sushkov

Adrian A. Drǎgulescu, Adrian Neagu

Domenico Giuliano, Andrea Kazemi Nava

We construct a generalized Fermionic Renormalization Group approach to describe junctions of strongly interacting spinful one-dimensional quantum wires. Our approach is based on a combined use of bosonization and fermionization techniques to build nonlocal transformations between dual fermion operators. It allows for trading strongly interacting (in the original coordinates) fermionic Hamiltonian for weakly interacting (in the dual coordinates) ones. Using such an approach, on one hand we are able to pertinently complement the results about the phase diagram of the junction obtained within bosonization approach, on the other hand, we map out the full crossover of the conductance tensors between any two fixed points in the phase diagram connected by a renormalization group trajectory.

Julian Lichtenstein, David Sánchez de la Peña, D. Rohe +3 more

A.N. Vall, S. É. Korenblit, V. M. Leviant +2 more

Exact solutions of two-particle eigenvalue problems for nonrelativistic four-fermion interaction are obtained. Appearance of Goldstone mode is found. The connection between a renormalization procedure and construction of self-adjoint extensions is revealed.