FM 2005-8

Author: Vieri Mastropietro

Title: Rigorous proof of Luttinger liquid behavior in the 1d Hubbard model
Abstract: We give the first rigorous (non perturbative) proof of Luttinger liquid behavior in the one dimensional Hubbard model, for small repulsive interaction and values of the density different from half filling. The analysis is based on the combination of multiscale analysis with Ward identities bases on a hidden and approximate local chiral gauge invariance. No use is done of exact solutions or special integrability properties of the Hubbard model, and the results can be in fact easily generalized to include non local interactions, magnetic fields or interaction with external potentials.

Keywords: Interacting fermions, spin, Ward identities, Renormalization Group

Vieri Mastropietro
Dipartimento di Matematica
Università di Roma Due
Via della Ricerca scientifica, Roma, Italia