2002/07/31 by C. Mudry, Christopher Mudry, Shinsei Ryu +3 · 64 citations
Mathematics · Physics and Astronomy · #Bipartite graph #Cold Atom Physics and Bose-Einstein Condensates #Combinatorics #Mathematics #Quantum chaos and dynamical systems #Quantum many-body systems #cond-mat
paper · pdf · doi:10.1103/physrevb.67.064202
published in Physical review. B, Condensed matter 67(6) (American Physical Society) · 30 pages, final version published in PRB
openalex publication_date 2003/02/28 · arxiv created 2003/03/05 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Gade [Nucl. Phys. B 398, 499 (1993)] has shown that the density of states for a particle hopping on a two-dimensional bipartite lattice in the presence of weak disorder and in the absence of time-reversal symmetry (chiral unitary universality class) is anomalous in the vicinity of the band center \ensuremathε=0 whenever the disorder preserves the sublattice symmetry. More precisely, using a nonlinear \ensuremathσ model that encodes the sublattice (chiral) symmetry and the absence of time-reversal symmetry she argues that the disorder average density of states diverges as |\ensuremathε|^\ensuremath-1exp(\ensuremath-c|ln\ensuremathε|^\ensuremathκ) with c some nonuniversal positive constant and \ensuremathκ=1/2 a universal exponent. Her analysis has been extended to the case when time-reversal symmetry is present (chiral orthogonal universality class) for which the same exponent \ensuremathκ=1/2 was predicted. Motrunich et al. [Phys. Rev. B 65, 064206 (2002)] have argued that the exponent \ensuremathκ=1/2 does not apply to the density of states in the chiral orthogonal universality class. They predict that \ensuremathκ=2/3 instead. We confirm the analysis of Motrunich et al. within a field theory for two flavors of Dirac fermions subjected to two types of weak uncorrelated random potentials: a purely imaginary vector potential and a complex valued mass potential. This model is the naive continuum limit of a model describing a particle hopping on a square lattice in the background of a \ensuremathπ-flux phase and subjected to weak disorder that preserves the sublattice symmetry and time-reversal invariance. By commonly held universality arguments, this model is believed to belong to the chiral orthogonal universality class. Our calculation relies in an essential way on the existence of infinitely many local composite operators with negative anomalous scaling dimensions.