Scaling limit of the one-dimensional attractive Hubbard model: the non-half-filled band case |
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| Institution: | 1. Research Institute for Solid State Physics and Optics of''the Hungarian Academy of Sciences, 1525 Budapest 114, Pf 49, Hungary;2. Laboratoire de Mathématique et Physique Théorique, CNRS UPRES-A 6083, Départernent de Physique, Faculté des Sciences, Université de Tours, Parc de Grandmont, F-37200 Tours, France;1. NorthShore University HealthSystem, Department of Radiation Medicine, 2650 Ridge Ave., Evanston, IL 60201, USA;2. Oakton Community College, Des Plaines, IL, USA;3. School of Biological & Chemical Sciences, Queen Mary University of London, London, UK;4. Swiss Tropical and Public Health Institute, Parasite Chemotherapy, Basel, Switzerland;5. University of Basel, Basel, Switzerland;6. Drugs for Neglected Diseases initiative (DNDi), Geneva, Switzerland;1. Laboratoire de Physique Théorique, CNRS UMR 5152, Université Paul Sabatier, F-31062 Toulouse, France;2. Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, Université de Cergy-Pontoise, Site de Saint-Martin, F-95300 Cergy-Pontoise Cedex, France;3. Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwake-Cho, Kyoto 606-8502, Japan |
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| Abstract: | The scaling limit of the less than half-filled attractive Hubbard chain is studied. This is a continuum limit in which the particle number per lattice site, n, is kept finite (0 < n < 1) while adjusting the interaction and bandwidth in such a way that there is a finite mass gap. We construct this limit both for the spectrum and the secular equations describing the excitations. We find that similarly to the half-filled case, the limiting model has a massive and a massless sector. The structure of the massive sector is closely analogous to that of the half-filled band and consequently to the chiral invariant SU(2) Gross-Neveu (CGN) model. The structure of the massless sector differs from that of the half-filled band case: the excitations are of particle and hole type, however they are not uniquely defined. The energy and the momentum of this sector exhibits a tower structure corresponding to a conformal field theory with c = 1 and SU(2) × SU(2) symmetry. The energy-momentum spectrum and the zero temperature free energy of the states with finite density coincides with that of the half-filled case supporting the identification of the limiting model with the SU(2) symmetric CGN theory. |
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