Strong disorder renormalization group study of aperiodic quantum Ising chains

TL;DR

This paper uses a strong-disorder renormalization group approach to analyze the quantum phase transition in aperiodic Ising chains, deriving critical exponents and ground state structures, with results confirmed by numerical methods.

Contribution

It provides analytical and asymptotically exact critical exponents for aperiodic quantum Ising chains, extending understanding beyond the Onsager universality class.

Findings

Derived critical exponents for aperiodic chains

Identified ground state structures near criticality

Confirmed results with numerical finite-size scaling

Abstract

We employ an adaptation of a strong-disorder renormalization-group technique in order to analyze the ferro-paramagnetic quantum phase transition of Ising chains with aperiodic but deterministic couplings under the action of a transverse field. In the presence of marginal or relevant geometric fluctuations induced by aperiodicity, for which the critical behavior is expected to depart from the Onsager universality class, we derive analytical and asymptotically exact expressions for various critical exponents (including the correlation-length and the magnetization exponents, which are not easily obtainable by other methods), and shed light onto the nature of the ground state structures in the neighborhood of the critical point. The main results obtained by this approach are confirmed by finite-size scaling analyses of numerical calculations based on the free-fermion method.