Quantum anisotropic Heisenberg chains with superlattice structure: a DMRG study

TL;DR

This study uses DMRG to analyze spin superlattices made of XXZ chains with different anisotropies, revealing magnetization plateaus and confirming Tomonaga-Luttinger liquid behavior.

Contribution

It provides a detailed DMRG analysis of anisotropic Heisenberg superlattices, validating analytical predictions and bosonization results for magnetization and gap properties.

Findings

Identification of two magnetization plateaus, including a non-trivial one.

Good agreement between DMRG results and analytical predictions.

Confirmation of Tomonaga-Luttinger liquid description in gapless regions.

Abstract

Using the density matrix renormalization group technique, we study spin superlattices composed of a repeated pattern of two spin-1/2 XXZ chains with different anisotropy parameters. The magnetization curve can exhibit two plateaus, a non trivial plateau with the magnetization value given by the relative sizes of the sub-chains and another trivial plateau with zero magnetization. We find good agreement of the value and the width of the plateaus with the analytical results obtained previously. In the gapless regions away from the plateaus, we compare the finite-size spin gap with the predictions based on bosonization and find reasonable agreement. These results confirm the validity of the Tomonaga-Luttinger liquid superlattice description of these systems.