Particle-hole symmetric localization in two dimensions
Abstract
We revisit two-dimensional particle-hole symmetric sublattice localization problem, focusing on the origin of the observed singularities in the density of states ρ(E) at the band center E=0. The most general system of this kind [R. Gade, Nucl. Phys. B 398, 499 (1993)] exhibits critical behavior and has ρ(E) that diverges stronger than any integrable power law, while the special random vector potential model of Ludwig et al. [Phys. Rev. B 50, 7526 (1994)] has instead a power-law density of states with a continuously varying dynamical exponent. We show that the latter model undergoes a dynamical transition with increasing disorder-this transition is a counterpart of the static transition known to occur in this system; in the strong-disorder regime, we identify the low-energy states of this model with the local extrema of the defining two-dimensional Gaussian random surface. Furthermore, combining this ``surface fluctuation'' mechanism with a renormalization group treatment of a related vortex glass problem leads us to argue that the asymptotic low-E behavior of the density of states in the general case is ρ(E)~E-1e-c\|ln E\|2/3, different from earlier prediction of Gade. We also study the localized phases of such particle-hole symmetric systems and identify a Griffiths ``string'' mechanism that generates singular power-law contributions to the low-energy density of states in this case.
- Publication:
-
Physical Review B
- Pub Date:
- February 2002
- DOI:
- 10.1103/PhysRevB.65.064206
- arXiv:
- arXiv:cond-mat/0107582
- Bibcode:
- 2002PhRvB..65f4206M
- Keywords:
-
- 72.90.+y;
- 74.40.+k;
- Other topics in electronic transport in condensed matter;
- Fluctuations;
- Condensed Matter - Disordered Systems and Neural Networks
- E-Print:
- 18 pages (two-column PRB format), 10 eps figures included