D. Sen and S. Lal 2000 Europhys. Lett. 52 337 doi:10.1209/epl/i2000-00444-0
D. Sen and S. Lal
Show affiliationsWe 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 q/δ → 0. Thus the limit q → 0 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.
75.10.Jm Quantized spin models
71.10.Fd Lattice fermion models (Hubbard model, etc.)
71.10.Pm Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.)
Issue 3 (1 November 2000)
Received 28 June 1999, accepted for publication 12 September 2000, in final form 12 September 2000
D. Sen and S. Lal 2000 Europhys. Lett. 52 337
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