Nontrivial Quantized Berry Phases for Itinerant Spin Liquids

Abstract

Quantized Berry phases used as local order parameters in t – J models are studied. A texture pattern of the local order parameters is topologically stable due to the quantization of non-Abelian Berry phases defined by low-energy states below a spin gap, which exists in the large J / t case with a few electrons. We have confirmed that the itinerant singlets in the wide class of t – J models carry the nontrivial Berry phase π. In the large J / t case for the one-dimensional t – J model, the Berry phases are uniformly π when the number of electrons is N = 4 n + 2 ( n =0,1,2,...).