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arXiv · 1004.1532

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

P. Markos·L. Schweitzer
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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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P. Markos, L. Schweitzer. 2010-04-09. Logarithmic scaling of Lyapunov exponents in disordered chiral two-dimensional lattices. https://doi.org/10.1103/physrevb.81.205432

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