Particle-hole symmetric localization in two dimensions

Motrunich, Olexei ; Damle, Kedar ; Huse, David A. (2002) Particle-hole symmetric localization in two dimensions Physical Review B: Condensed Matter and Materials Physics, 65 (6). Article ID 064206. ISSN 2469-9950

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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|lnE|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.

Item Type:Article
Source:Copyright of this article belongs to American Physical Society.
ID Code:103390
Deposited On:09 Mar 2018 11:29
Last Modified:09 Mar 2018 11:29

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