Low-energy properties of aperiodic quantum spin chains

TL;DR

This paper studies how aperiodic coupling patterns affect the low-energy and thermodynamic properties of antiferromagnetic quantum XXZ spin chains, using a renormalization-group approach and analyzing specific sequences like Fibonacci and Rudin-Shapiro.

Contribution

It adapts the Ma-Dasgupta-Hu renormalization-group method to aperiodic XXZ chains and classifies the effects of aperiodicity on their low-energy behavior, especially in the easy-plane anisotropy regime.

Findings

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

Ground-state correlations are influenced by the aperiodic sequences.

Fibonacci and Rudin-Shapiro sequences produce similar geometrical fluctuations to randomness.

Abstract

We investigate the low-energy properties of antiferromagnetic quantum XXZ spin chains with couplings following two-letter aperiodic sequences, by an adaptation of the Ma-Dasgupta-Hu renormalization-group method. 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. As representative illustrations, we present analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations for couplings following the Fibonacci quasiperiodic structure and a binary Rudin-Shapiro sequence, whose geometrical fluctuations are similar to those induced by randomness.