Logarithmic scaling of Lyapunov exponents in disordered chiral two-dimensional lattices

Abstract

We analyze the scaling behavior of the two smallest Lyapunov exponents for electrons propagating on two-dimensional lattices with energies within a very narrow interval around the chiral critical point at E=0 in the presence of a perpendicular random magnetic flux. By a numerical analysis of the energy and size dependence we confirm that the two smallest Lyapunov exponents are functions of a single parameter. The latter is given by ln L/ln xi(E), which is the ratio of the logarithm of the system width L to the logarithm of the correlation length xi(E). Close to the chiral critical point and energy |E| << E_0, we find a logarithmically divergent energy dependence lnxi(E)proporitonal to |\ln(E_0/|E|)|^{1/2}, where E_0 is a characteristic energy scale. Our data are in agreement with the theoretical prediction of M. Fabrizio and C. Castelliani [Nucl.\Phys.B 583, 542 (2000)] and resolve an inconsistency of previous numerical work.

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Cited by in corpus (8)

• Metal-insulator transition in 2D random fermion systems of chiral symmetry classes
• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Metal-insulator transition in a 2D system of chiral unitary class
• Generalized multifractality in 2D disordered systems of chiral symmetry classes
• Disordered two-dimensional electron systems with chiral symmetry
• Scaling at chiral quantum critical points in two dimensions
• Partial preservation of chiral symmetry and colossal magnetoresistance in adatom doped graphene
• Scaling behavior of disordered lattice fermions in two dimensions