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Particle-hole symmetric localization in two dimensions

Motrunich, Olexei and Damle, Kedar and Huse, David A. (2002) Particle-hole symmetric localization in two dimensions. Physical Review B, 65 (6). Art. No. 064206. ISSN 0163-1829. doi:10.1103/PhysRevB.65.064206.

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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|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.

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Motrunich, Olexei0000-0001-8031-0022
Additional Information:© 2002 The American Physical Society Received 5 August 2001; published 23 January 2002 We would like to thank N. Read for a useful discussion. The work at Princeton was supported by NSF grant No. DMR-9802468, and at Harvard by NSF Grant No. DMR-9981283.
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Issue or Number:6
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ID Code:7121
Deposited By: Archive Administrator
Deposited On:10 Jan 2007
Last Modified:08 Nov 2021 20:39

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