How to distinguish the Haldane/Large-D state and the intermediate-D state in an S=2 quantum spin chain with the XXZ and on-site anisotropies

TL;DR

This study uses numerical methods to clarify the phase diagram of an S=2 quantum spin chain, focusing on distinguishing the Haldane, large-D, and intermediate-D states, and confirms the existence of the intermediate-D phase.

Contribution

The paper provides a detailed numerical analysis and a physical explanation for distinguishing three gapped phases in an S=2 spin chain, clarifying the existence of the intermediate-D phase.

Findings

Identification of the XY, Haldane, intermediate-D, large-D, and Ne9el phases in the phase diagram.

Development of a level spectroscopy method to distinguish three gapped states.

Confirmation of the intermediate-D phase existence in the phase diagram.

Abstract

We numerically investigate the ground-state phase diagram of an S=2 quantum spin chain with the $XXZ$ and on-site anisotropies described by ${\mathcal H}=\sum_j (S_j^x S_{j+1}^x+S_j^y S_{j+1}^y+\Delta S_j^z S_{j+1}^z) + D \sum_j (S_j^z)^2$, where $\Delta$ denotes the XXZ anisotropy parameter of the nearest-neighbor interactions and $D$ the on-site anisotropy parameter. We restrict ourselves to the $\Delta>0$ and $D>0$ case for simplicity. Our main purpose is to obtain the definite conclusion whether there exists or not the intermediate-$D$ (ID) phase, which was proposed by Oshikawa in 1992 and has been believed to be absent since the DMRG studies in the latter half of 1990's. In the phase diagram with $\Delta>0$ and $D>0$ there appear the XY state, the Haldane state, the ID state, the large-$D$ (LD) state and the N\'eel state. In the analysis of the numerical data it is important to distinguish three gapped states; the Haldane state, the ID state and the LD state. We give a physical and intuitive explanation for our level spectroscopy method how to distinguish these three phases.