Eb. Kolomeisky, INTERACTION, DISORDER, AND COMMENSURABILITY IN ONE AND NEARLY ONE-DIMENSION, Physical review. B, Condensed matter, 48(8), 1993, pp. 4998-5003
The interplay between Anderson localization and Mott localization is c
onsidered in the vicinity of one dimension for a collection of interac
ting spinless fermions or repulsive bosons. We demonstrate that in the
absence of commensurability effects an Anderson localization transiti
on does take place for d less-than-or-equal-to 1. It is characterized
by a critical dynamical exponent z having value z=2-d for d-->1-0, in
disagreement with the previous claims that z always equals d. We find
that there is only a localized phase for d > 1 and expect that this si
milarity between free fermions and interacting quantum particles will
be valid up to two dimensions. We also consider the competition betwee
n the effects of commensurability, disorder, and interaction in exactl
y one dimension. The outcome strongly depends on the order of umklapp
scattering responsible for the formation of the Mott insulator in the
pure case. If it is DELTAk = 2k(F) scattering and the disorder is suff
iciently weak, the Mott phase survives and the Anderson phase interven
es almost everywhere between the Mott insulator and the conductor, exc
ept at one special symmetry-enhanced point corresponding to the fixed
commensurate filling: here, as in the pure case, the Mott transition b
elongs to the Kosterlitz-Thouless universality class. For sufficiently
strong disorder, or for any disorder and higher-order scattering, the
path from the Mott insulator phase (if it survives) to the conductor
always crosses the Anderson phase.