One-dimensional fermions with incommensuration close to dimerization
Centre for Theoretical Studies, Indian Institute of Science -
Bangalore 560012, India
Accepted: 12 September 2000
We study a model of fermions hopping on a chain with a weak incommensuration close to dimerization; both q, the deviation of the wave number from π, and δ, the strength of the incommensuration, are assumed to be small. For free fermions, we show that there are an infinite number of energy bands which meet at zero energy as q approaches zero. The number of states lying inside the q=0 gap remains nonzero as . Thus the limit differs from q=0, as can be seen clearly in the low-temperature specific heat. For interacting fermions or the XXZ spin-(1/2) chain, we use bosonization to argue that similar results hold. Finally, our results can be applied to the Azbel-Hofstadter problem of particles hopping on a two-dimensional lattice in the presence of a magnetic field.
PACS: 71.10.Fd – Lattice fermion models (Hubbard model, etc.) / 71.10.Pm – Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.) / 75.10.Jm – Quantized spin models
© EDP Sciences, 2000