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Quantized Berry phases as local order parameters in t-J models are studied. Atexture pattern of the local order parameters is topologically stable due tothe quantization of non-Abelian Berry phases defined by low-energy states belowa spin gap, which exists in the large J/t case with a few electrons. We haveconfirmed that itinerant singlets in the wide class of t-J models carry thenontrivial Berry phase pi. In the large J/t case for the one-dimensional t-Jmodel, Berry phases are uniformly pi when the number of electrons is N =4n +2,($n=0,1,2,...$).

Nontrivial quantized Berry phases for itinerant spin liquids