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

References in corpus (2)

• Ward identities and Chiral anomaly in the Luttinger liquid
• Existence of Solutions to the Bethe Ansatz Equations for the 1D Hubbard Model: Finite Lattice and Thermodynamic Limit

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• Renormalization Group and Asymptotic Spin--Charge separation for Chiral Luttinger liquids
• Universal Luttinger Liquid Relations in the 1D Hubbard Model
• Borel summability of ${\varphi }_4^4$ planar theory via multiscale analysis