Topological Identification of location of spin–singlet pairs and edge states

Abstract

Quantized Berry phases proposed as a new tool for exploring gapped quantum liquids at zero temperature which do not exhibit symmetry breaking are applied to identify location of spin-singlet pairs in the open boundary conditions. In the S = 1/2 Heisenberg chain with bond alternation, a relation between the Berry phases and the edge state is studied. The results agree with the picture of the nonlocal singlet of free spins at the open boundaries with the exponentially small effective coupling. Discrepancy between the Berry phases of the periodic and open boundary conditions indicates relocation of the local singlets.