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arXiv:1604.00452 · Journal of the Physical Society of Japan

Ground-State Phase Diagram of the Bond-Alternating S = 2 Quantum Spin Chain with the XXZ and On-Site Anisotropies — Symmetry Protected Topological Phase versus Trivial Phase —

Kiyomi Okamoto, Takashi Tonegawa, Tôru Sakai

Published May 23, 2016• 8 citations
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Abstract

We investigate the ground-state phase diagram of the bond-alternating $S=2$ quantum spin chain with the $XXZ$ and on-site anisotropies. For the on-site anisotropies, in addition to the popular $D_2 \sum_j (S_j^z)^2$ term, we consider the $D_4 \sum_j (S_j^z)^4$ term. Mainly we use the exact diagonalization and the level spectroscopy analysis. We show that the Haldane state, large-$D$ state and the Dimer2 state belong to the same trivial phase, by finding the existence of adiabatic paths directly connecting these states without the quantum phase transition. Similarly, we show that the intermediate-$D$ state and the Dimer1 state belong to the same symmetry protected topological phase.

DOI
10.7566/jpsj.85.063704

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We investigate the edge modes at T=0 in the intermediate-D (ID) phase and the large-D (LD) phase of the S=2 quantum spin chain with the XXZ anisotropy and the generalized on-site anisotropies by use of the DMRG. There exists a gapless edge mode in the ID phase, while no gapless edge mode in the LD phase. These results are consistent with the physical pictures of these phases. We also show the ground-state phase diagrams obtained by use of the exact diagonalization and the level spectroscopy analysis.
We numerically investigate the ground-state phase diagram of an S = 2 quantum spin chain with the XXZ and on-site anisotropies described by = Σ j ( S j x S j + 1 x + S j y S j + 1 y + Δ S j z S j+1 z ) + D Σ j ( S j z ) 2 , where Δ denotes the XXZ anisotropy parameter of the nearest-neighbor interactions and D the on-site anisotropy parameter. We restrict ourselves to the Δ > 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 Δ > 0 and D > 0 there appear the XY state, the Haldane state, the ID state, the large- D (LD) state and the Néel 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.
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