Non-periodic Ising quantum chains and conformal invariance

TL;DR

This paper examines non-periodic Ising quantum chains with substitution rule modulations, showing that only specific cases preserve conformal invariance at criticality, while others do not.

Contribution

It provides a detailed analysis of substitution rule modulated chains, clarifying when conformal invariance is maintained or broken at critical points.

Findings

Certain substitution rules preserve conformal invariance.

Most non-periodic sequences do not lead to conformal invariance.

Critical behavior depends on the structure of the modulation sequence.

Abstract

A while ago, Luck (J. Stat. Phys. 72 (1993) 417) investigated the critical behaviour of one-dimensional Ising quantum chains with couplings constants modulated according to general non-periodic sequences. In this short note, we take a closer look at the case where the sequences are obtained from (two-letter) substitution rules and at the consequences of Luck's results at criticality. They imply that only for a certain class of substitution rules the long-distance behaviour is still described by the c=1/2 conformal field theory of a free Majorana fermion as for the periodic Ising quantum chain, whereas the general case does not lead to a conformally invariant scaling limit.