We study frustrated ferromagnetic spin-1 chains, where the ferromagnetic nearest-neighbor coupling competes with the antiferromagnetic next-nearest-neighbor coupling. We use the density-matrix renormalization group to obtain the ground states. Through the analysis of spin-spin correlations we identify the double Haldane phase as well as the ferromagnetic phase. It is shown that the ferromagnetic coupling leads to incommensurate correlations in the double Haldane phase. Such short-range correlations transform continuously into the ferromagnetic instability at the transition to the ferromagnetic phase. We also compare the results with the spin-1/2 and classical spin systems and discuss the string orders in the system.
Bibliographical noteFunding Information:
This work was supported by the National Research Foundation of Korea through Grant No. 2008-0061893 (G.S.J.), Grant No. 2013R1A1A2007959 (H.J.L. and G.S.J.), and Grant No. 2016R1D1A1A09917318 (M.Y.C.).
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