Aperiodic quantum XXZ chains: Renormalization-group results

TL;DR

This paper investigates the low-energy properties of aperiodic quantum XXZ spin chains using a renormalization-group approach, revealing how aperiodicity influences thermodynamics and ground-state correlations across different anisotropy regimes.

Contribution

It provides a comprehensive analysis of aperiodic XXZ chains, extending renormalization-group methods to classify effects of various aperiodic sequences on low-energy physics.

Findings

Thermodynamic properties follow XX chain scaling in the easy-plane regime.

Ground-state structures differ from the random-singlet phase.

Aperiodicity effects depend on the specific sequence and anisotropy.

Abstract

We report a comprehensive investigation of the low-energy properties of antiferromagnetic quantum XXZ spin chains with aperiodic couplings. We use an adaptation of the Ma-Dasgupta-Hu renormalization-group method to obtain analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations of chains with couplings following several two-letter aperiodic sequences, including the quasiperiodic Fibonacci and other precious-mean sequences, as well as sequences inducing strong geometrical fluctuations. For a given aperiodic sequence, we argue that in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly-known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. We also discuss the nature of the ground-state structures, and their comparison with the random-singlet phase, characteristic of random-bond chains.