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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-siteanisotropies, in addition to the popular $D_2 \sum_j (S_j^z)^2$ term, weconsider the $D_4 \sum_j (S_j^z)^4$ term. Mainly we use the exactdiagonalization and the level spectroscopy analysis. We show that the Haldanestate, large-$D$ state and the Dimer2 state belong to the same trivial phase,by finding the existence of adiabatic paths directly connecting these stateswithout the quantum phase transition. Similarly, we show that theintermediate-$D$ state and the Dimer1 state belong to the same symmetryprotected topological phase.

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