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Rigorous Proof of Luttinger Liquid Behavior in the 1d Hubbard Model

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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 based 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

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, I-00133, Rome, Italy

    Vieri Mastropietro

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  1. Vieri Mastropietro
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Correspondence to Vieri Mastropietro.

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Mastropietro, V. Rigorous Proof of Luttinger Liquid Behavior in the 1d Hubbard Model. J Stat Phys 121, 373–432 (2005). https://doi.org/10.1007/s10955-005-7007-0

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  • DOI: https://doi.org/10.1007/s10955-005-7007-0

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