Strong-disorder renormalization group study of aperiodic quantum Ising chains

Abstract

We employ an adaptation of a strong-disorder renormalization group technique in order toanalyze the ferro–paramagnetic quantum phase transition of Ising chains with aperiodicbut deterministic couplings under the action of a transverse field. In the presence ofmarginal or relevant geometric fluctuations induced by aperiodicity, for which the criticalbehavior is expected to depart from the Onsager universality class, we derive analytical andasymptotically exact expressions for various critical exponents (including the correlationlength and the magnetization exponents, which are not easily obtainable by othermethods), and shed light onto the nature of the ground-state structures in theneighborhood of the critical point. The main results obtained by this approach areconfirmed by finite-size scaling analyses of numerical calculations based on the free-fermionmethod.