Finite-size effects for the gap in the excitation spectrum of the one-dimensional Hubbard model

Journal Article · Fri Jan 15 00:00:00 EST 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.013611· OSTI ID:21388774

Colome-Tatche, M ^[1]; Matveenko, S I ^[1]; Shlyapnikov, G V ^[1]

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1. Laboratoire de Physique Theorique et Modeles Statistiques, Universite Paris Sud, CNRS, F-91405 Orsay (France)

We study finite-size effects for the gap of the quasiparticle excitation spectrum in the weakly interacting regime one-dimensional Hubbard model with on-site attraction. Two types of corrections to the result of the thermodynamic limit are obtained. Aside from a power law (conformal) correction due to gapless excitations which behaves as 1/N{sub a}, where N{sub a} is the number of lattice sites, we obtain corrections related to the existence of gapped excitations. First of all, there is an exponential correction which in the weakly interacting regime (|U|<<t) behaves as approxexp(-N{sub a}DELTA{sub i}nfinity/4t) in the extreme limit of N{sub a}DELTA{sub i}nfinity/t>>1, where t is the hopping amplitude, U is the on-site energy, and DELTA{sub i}nfinity is the gap in the thermodynamic limit. Second, in a finite-size system a spin-flip producing unpaired fermions leads to the appearance of solitons with nonzero momenta, which provides an extra (nonexponential) contribution delta. For moderate but still large values of N{sub a}DELTA{sub i}nfinity/t, these corrections significantly increase and may become comparable with the 1/N{sub a} conformal correction. Moreover, in the case of weak interactions where DELTA{sub i}nfinity<<t, the exponential correction exceeds higher-order power law corrections in a wide range of parameters, namely for N{sub a} < or approx. (8t/DELTA{sub i}nfinity)ln(4t/|U|), and so does delta even in a wider range of N{sub a}. For a sufficiently small number of particles, which can be of the order of thousands in the weakly interacting regime, the gap is fully dominated by finite-size effects.

• OSTI ID: 21388774
• Journal Information: Physical Review. A, Vol. 81, Issue 1; Other Information: DOI: 10.1103/PhysRevA.81.013611; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
74 ATOMIC AND MOLECULAR PHYSICS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AMPLITUDES
CORRECTIONS
EXCITATION
FERMIONS
HUBBARD MODEL
ONE-DIMENSIONAL CALCULATIONS
SOLITONS
SPECTRA
SPIN FLIP
WEAK INTERACTIONS
BASIC INTERACTIONS
CRYSTAL MODELS
ENERGY-LEVEL TRANSITIONS
INTERACTIONS
MATHEMATICAL MODELS
QUASI PARTICLES