Aperiodic and correlated disorder in XY-chains: exact results

TL;DR

This paper provides exact results for the thermodynamic properties of XY quantum chains with aperiodic and correlated disorder, classifying the relevance of different substitution rules and calculating critical exponents for marginal cases.

Contribution

It generalizes an exact renormalization group method to XY chains with arbitrary substitution rule disorder, offering a detailed classification and exact critical exponents for marginal aperiodicity.

Findings

Relevance criteria for aperiodic modulations in XY chains

Classification of sequences as irrelevant, marginal, or relevant

Exact calculation of critical exponents for marginal aperiodic sequences

Abstract

We study thermodynamic properties, specific heat and susceptibility, of XY quantum chains with coupling constants following arbitrary substitution rules. Generalizing an exact renormalization group transformation, originally formulated for Ising quantum chains, we obtain exact relevance criteria of Harris-Luck type for this class of models. For two-letter substitution rules, a detailed classification is given of sequences leading to irrelevant, marginal or relevant aperiodic modulations. We find that the relevance of the same aperiodic sequence of couplings in general will be different for XY and Ising quantum chains. By our method, continuously varying critical exponents may be calculated exactly for arbitrary (two-letter) substitution rules with marginal aperiodicity. A number of examples are given, including the period-doubling, three-folding and precious mean chains. We also discuss extensions of the renormalization approach to a special class of long-range correlated random chains, generated by random substitutions.