Finitesize effects for the gap in the excitation spectrum of the onedimensional Hubbard model
Abstract
We study finitesize effects for the gap of the quasiparticle excitation spectrum in the weakly interacting regime onedimensional Hubbard model with onsite 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_{a}, where N_{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 ~exp(N_{a}Δ_{∞}/4t) in the extreme limit of N_{a}Δ_{∞}/t≫1, where t is the hopping amplitude, U is the onsite energy, and Δ_{∞} is the gap in the thermodynamic limit. Second, in a finitesize system a spinflip producing unpaired fermions leads to the appearance of solitons with nonzero momenta, which provides an extra (nonexponential) contribution δ. For moderate but still large values of N_{a}Δ_{∞}/t, these corrections significantly increase and may become comparable with the 1/N_{a} conformal correction. Moreover, in the case of weak interactions where Δ_{∞}≪t, the exponential correction exceeds higherorder power law corrections in a wide range of parameters, namely for N_{a}≲(8t/Δ_{∞})ln(4t/U), and so does δ even in a wider range of N_{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 finitesize effects.
 Publication:

Physical Review A
 Pub Date:
 January 2010
 DOI:
 10.1103/PhysRevA.81.013611
 Bibcode:
 2010PhRvA..81a3611C
 Keywords:

 03.75.Ss;
 71.10.Pm;
 03.75.Mn;
 Degenerate Fermi gases;
 Fermions in reduced dimensions;
 Multicomponent condensates;
 spinor condensates