2001/07/28 by Olexei I. Motrunich, Olexei Motrunich, Kedar Damle +1 · 5 citations
Mathematics · Physics and Astronomy · #Condensed matter physics #Density of states #Exponent #Gravitational singularity #Mathematical physics #Mathematics #Physics #Power law #Quantum many-body systems #Quantum mechanics #Renormalization group #Theoretical and Computational Physics #Topological Materials and Phenomena #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.65.064206
published as Phys. Rev. B 65, 064206 (2002) · 18 pages (two-column PRB format), 10 eps figures included
arxiv created 2001/07/28 · openalex publication_date 2002/01/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We revisit two-dimensional particle-hole symmetric sublattice localization problem, focusing on the origin of the observed singularities in the density of states \ensuremathρ(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 \ensuremathρ(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 \ensuremathρ(E)\ensuremath∼E^\ensuremath-1e^\ensuremath-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.