@article{ISI:000086597400067,
 abstract = {We study the spectrum of fermions hopping on a chain with a weak
incommensuration close to dimerization; both q, the deviation of the
wave number from pi, and delta, the strength of the incommensuration,
are small. For free fermions, we use a continuum Dirac theory to show
that there are an infinite number of bands which meet at zero energy as
q approaches zero. In the limit that the ratio q/delta-->0, the number
of states lying inside the q = 0 gap is nonzero and equal to 2
delta/pi(2). Thus the limit q-->0 differs from q=0; this can be seen
clearly in the behavior of the specific heat at low temperature. For
interacting fermions or the XXZ spin-1/2 chain close to dimerization, we
use bosonization and a renormalization group analysis to argue that
similar results hold; as q-->0, there is a nontrivial density of states
near zero energy. However, the limit q-->0 and q=0 give the same results
near commensurate wave numbers which are different from pi; for both
free and interacting fermions, we find that a nonzero value of q is
necessary to close the gap. Our results for free fermions are applied to
the Azbel-Hofstadter problem of electrons hopping on a two-dimensional
lattice in the presence of a magnetic field. Finally, we discuss the
complete energy spectrum of free fermions with incommensurate hopping by
going up to higher orders in delta.},
 author = {Sen, D and Lal, S},
 doi = {10.1103/PhysRevB.61.9001},
 eissn = {2469-9969},
 issn = {2469-9950},
 journal = {PHYSICAL REVIEW B},
 month = {APR 1},
 number = {13},
 pages = {9001-9013},
 researcherid-numbers = {Lal, Siddhartha/A-1414-2013},
 times-cited = {7},
 title = {One-dimensional fermions with incommensuration},
 unique-id = {ISI:000086597400067},
 volume = {61},
 year = {2000}
}