Corrections to Single Parameter Scaling at the Anderson Transition

Abstract

The Anderson transition [1], which is a continuous quantum phase transition induced by disorder, can be described by the single parameter scaling [2, 3]. One of the conclusion of the scaling theory is that the Anderson transition is universal, i.e., it does not depend on the details of the models but depends only on the basic symmetry of the system. The field theoretic approach made clear that the transitions are classified into three universality classes, namely, orthogonal, unitary and symplectic classes [4]. However, analytic approaches fail to estimate quantitatively the critical exponents. Numerical investigation, therefore, has been playing an important role to discuss quantitatively the critical behaviour of the Anderson transition [5–7].