We have undertaken a study of the propagation of carriers in one-dimensional (1D) aperiodic systems within the tight-binding scheme under the action of electric fields. We have concentrated on the Fibonacci (F) and Thue-Morse (TM) lattices, which are of great practical importance since these structures can be fabricated thanks to recent technological advances. We show that superdi6usion takes place for both lattices in the field-free case. The mean-square displacement (MSD) follows the law (n ) oc t with n = 1.55 for the F lattice and n = 1.65 for the TM lattice. When the field is included, the particle localizes, i.e. , the MSD is bound, even for weak field intensities.

A central tenet in the theory of quantum phase transitions (QPTs) is that a nonanalyticity in a ground-state energy implies a QPT. Here we report on a finding that challenges this assertion. As a case study we take a phase diagram of a one-dimensional band insulator with spin-orbit coupled electrons, supporting trivial, and topological gapped phases separated by intersecting critical surfaces. The intersections define multicritical lines across which the ground-state energy becomes nonanalytical, concurrent with a closing of the band gap, but with no phase transition taking place.

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We study the single-band Hubbard model, extended by an intersite interaction R . The method used is the high-temperature series expansion. Series to the sixth order are obtained for the grand canonical potential 0, staggered magnetic susceptibility OAF, charge-ordered susceptibility yzo, and compressibility K. These series are derived with general values of R" and the intrasite interaction U, for half-filling (n = 1) on a simple cubic lattice. We find that the antiferromagnetic phase is stabilized by repulsive W, in the limit of strong intrasite repulsion. The effect of nonzero hopping t on the charge-ordered and condensed phases is also examined. We find that the critical temperature for transition to a condensed phase is reduced, while the charge-ordered phase is destabilized by t for small, positive, or negative U, and stabilized for large, negative U.