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One can easily verify that the overlap between the perfect VBS state and the state depicted in Fig. 5 is finite, while the overlap with the state in Fig. 5 vanishes. This is due to the fact that nearest-neighbor spins in a VBS state are contracted in singlets, and therefore an "occupied" site with pseudospin S̃ iz =±1/2 must have its nearest occupied neighbors with S̃ iz =±1/2, respectively. See, e.g., Ref..
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One can easily verify that the overlap between the perfect VBS state and the state depicted in Fig. 5 is finite, while the overlap with the state in Fig. 5 vanishes. This is due to the fact that nearest-neighbor spins in a VBS state are contracted in singlets, and therefore an "occupied" site with pseudospin S̃ iz =±1/2 must have its nearest occupied neighbors with S̃ iz =±1/2, respectively. See, e.g., Ref..
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