Critical behavior of ac conductivity near the Anderson transition

Abstract

We investigate the dynamic scaling behavior of ac conductivity s(v) in three-dimensional ~3D! unitary and symplectic systems in addition to orthogonal one by means of large-scale simulations. It is demonstrated that the ac conductivity near the Anderson transition behave as s(v)}v d (d.1/3) for all of the above systems. Numerical calculations are performed by an efficient algorithm based on the forced oscillator method ~FOM!, which enables us to accurately treat large-scale quantum systems with less computational effort. The values of the exponents d are determined by the finite-time scaling method for the FOM.@S0163-1829~99!11943-X# I. INTRODUCTION The scaling arguments of localization 1,2 have stimulated many works on both static and dynamic behavior of disordered electron systems, especially on the Anderson transition. The existence of this transition essentially depends only on the dimensionality and the symmetries of the systems. Three-dimensional ~3D! systems generally show the Anderson transition as a function of the strength of disorder and the Fermi energy, and their critical behavior are classified into three universality classes according to the basic symmetry of the Hamiltonian. The systems being invariant under spin rotation in addition to time-reversal symmetry constitute the orthogonal class, while the systems being invariant under time reversal but having no spin-rotation symmetry belong to the symplectic class. The rest forms the unitary class characterized by the absence of time-reversal symmetry. 3 Many numerical works have contributed to reveal both the static and dynamic behavior of the transition through the