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It is known that these string order parameters are not sufficient to characterize uniquely the RS and the DC phases, because both phases have even topological quantum number (i.e., Oodd =0 but Oeven ≠0) (Ref.). However, since the possibility of the DC phase is ruled out by our results in Figs. 1 2, the only possible phase with even topological quantum number is just the RS phase. One then can use string order parameters to locate the regions of the Haldane and the RS phases.
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It is known that these string order parameters are not sufficient to characterize uniquely the RS and the DC phases, because both phases have even topological quantum number (i.e., Oodd =0 but Oeven ≠0) (Ref.). However, since the possibility of the DC phase is ruled out by our results in Figs. 1 2, the only possible phase with even topological quantum number is just the RS phase. One then can use string order parameters to locate the regions of the Haldane and the RS phases.
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