Ground-State Phase Diagram of an Anisotropic S=1 Ferromagnetic-Antiferromagnetic Bond-Alternating Chain

TL;DR

This paper maps out the ground-state phase diagram of an anisotropic S=1 ferromagnetic-antiferromagnetic chain using numerical methods, revealing six phases including a symmetry-protected topological phase and comparing results with perturbation theory.

Contribution

It provides the first detailed numerical phase diagram of the anisotropic S=1 bond-alternating chain, identifying a wider region of the topological phase compared to related models.

Findings

Six distinct phases identified: XY1, large-D, intermediate-D, Haldane, singlet dimer, Ne9el.

The intermediate-D phase is a symmetry-protected topological phase.

The intermediate-D phase occupies a wider region than in the spin-2 chain case.

Abstract

By using mainly numerical methods, we investigate the ground-state phase diagram (GSPD) of an $S=1$ ferromagnetic-antiferromagnetic bond-alternating chain with the $XXZ$ and the on-site anisotropies. This system can be mapped onto an anisotropic spin-2 chain when the ferromagnetic interaction is much stronger than the antiferromagnetic interaction. Since there are many quantum parameters in this system, we numerically obtained the GSPD on the plane of the magnitude of the antiferromagnetic coupling versus its $XXZ$ anisotropy, by use of the exact diagonalization, the level spectroscopy as well as the phenomenological renormalization group. The obtained GSPD consists of six phases. They are the $XY$1, the large-$D$ (LD), the intermediate-$D$ (ID), the Haldane (H), the spin-1 singlet dimer (SD), and the N\'eel phases. Among them, the LD, the H, and the SD phases are the trivial phases, while the ID phase is the symmetry-protected topological phase. The former three are smoothly connected without any quantum phase transitions. It is also emphasized that the ID phase appears in a wider region compared with the case of the GSPD of the anisotropic spin-2 chain with the $XXZ$ and the on-site anisotropies. We also compare the obtained GSPD with the result of the perturbation theory.