Quantum phase transitions in a spin-1 antiferromagnetic chain with long-range interactions and modulated single-ion anisotropy

TL;DR

This study explores how long-range interactions and modulated anisotropy influence quantum phase transitions in a spin-1 antiferromagnetic chain, revealing changes in phase boundaries and transition orders using advanced numerical techniques.

Contribution

It introduces a detailed analysis of the combined effects of long-range interactions and anisotropy on phase diagrams and transition types in spin chains using density-matrix renormalization group methods.

Findings

Long-range interactions alter phase boundaries quantitatively.

Certain conditions induce a first-order transition between Néel and large-D phases.

Fidelity susceptibility effectively detects quantum critical points.

Abstract

We study the phase diagram of spin-1 antiferromagnetic chain with isotropic antiferromagnetic interactions decaying with a power-law $\propto r^{-\alpha}$ ($\alpha\ge 1$) accompanied by modulated single-ion anisotropy. Employing the techniques of the density-matrix renormalization group, effects of long-range interactions and single-ion anisotropy on a variety of correlations are investigated. In order to check the consistency, the fidelity susceptibilities are evaluated across quantum phase transitions. The quantum critical points are faithfully detected and orders of phase transitions are determined. The correlation-length critical exponent is extracted from scaling functions of the fidelity susceptibility. The presence of long-range interactions leads to quantitative change of the phase boundaries and reduces the order of phase transition under certain conditions. A direct first-order transition between the periodic N\'eel phase and the large-$D$ phase occurs for slowly decaying antiferromagnetic interactions.