### 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)xSU(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.

Original language | English |
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Pages (from-to) | 701-730 |

Number of pages | 30 |

Journal | Nuclear Physics B |

Volume | 538 |

Issue number | 3 |

Publication status | Published - Jan 18 1999 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*538*(3), 701-730.

**Scaling limit of the one-dimensional attractive Hubbard model : The non-half-filled band case.** / Woynarovich, F.; Forgács, P.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 538, no. 3, pp. 701-730.

}

TY - JOUR

T1 - Scaling limit of the one-dimensional attractive Hubbard model

T2 - The non-half-filled band case

AU - Woynarovich, F.

AU - Forgács, P.

PY - 1999/1/18

Y1 - 1999/1/18

N2 - 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

AB - 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

UR - http://www.scopus.com/inward/record.url?scp=0033579768&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033579768&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033579768

VL - 538

SP - 701

EP - 730

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -