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.

References in corpus (5)

• Anderson Transitions
• On the minimal conductivity of graphene
• Conductivity of disordered graphene at half filling
• Universality of the metal-insulator transition in three-dimensional disordered systems
• Exponents of the localization length in the 2D Anderson model with off-diagonal disorder

Cited by in corpus (5)

• Localization of Dirac Fermions in Finite-Temperature Gauge Theory
• Metal-insulator transition in a 2D system of chiral unitary class
• Disordered two-dimensional electron systems with chiral symmetry
• Generalized multifractality in 2D disordered systems of chiral symmetry classes
• Scaling at chiral quantum critical points in two dimensions