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• W1498924013 abstract "Particle-hole symmetric localization problems are studied in low dimensions with the emphasis on understanding the origin of the observed singularities in the low-energy density of states. Pure imaginary random hopping and bipartite random hopping problems are considered. In quasi-1D geometry, such systems generically exhibit localized behavior, and are also found to have power-law density of states with nonuniversal dynamical exponents. Griffiths-like mechanism is identified that generates the singularly many low-energy states. Distinct localized phases are separated by delocalized critical points, and at these points the density of states has strong Dyson singularity near the band center. Similar mechanism is argued to be operative in all particle-hole symmetric localized phases in any dimension. Higher-dimensional systems can also exhibit true metallic or critical delocalized phases, and one such system—the 2D bipartite random hopping problem—is studied in great detail. General such system is known to exhibit critical behavior and a density of states that diverges stronger than any integrable power-law. Crucial to understanding the origin of this behavior is a particular model—the random vector potential model—which is critical and has a power-law density of states with a continuously varying dynamical exponent. This model is shown to undergo a dynamical transition from a weak-disorder regime to a strongdisorder regime, with the dynamical exponent changing its behavior, and in the strong-disorder regime the low-energy states are identified with local extrema of the defining two-dimensional Gaussian surface. This dynamical transition is a counterpart of the static transition known to occur in this system, thus completing the available physical picture of the random vector potential model. In the general case, this “surface fluctuation” mechanism, combined with a well-known RG treatment of a vortex glass problem, leads to a proposal of the asymptotic behavior of the density of states ρ(E) ∼ E−1e−| lnE|2/3 different from previous predictions. Analytical and numerical arguments are given in support of this picture." @default.
• W1498924013 created "2016-06-24" @default.
• W1498924013 creator A5040183342 @default.
• W1498924013 date "2001-01-01" @default.
• W1498924013 modified "2023-10-18" @default.
• W1498924013 title "Particle-Hole Symmetric Localization Problems in One and Two Dimensions" @default.
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