Detection of topological symmetry in the one-dimensional Affleck-Kennedy-Lieb-Tasaki model of integer spin with ultracold spinor atoms in optical lattices

A scheme is proposed for detection of the topology in the one-dimensional Affleck-Kennedy-Lieb-Tasaki model, based on ultracold spinor atomic gas in an optical lattice. For this purpose, a global operation O(θ) is introduced with respect to the breaking of spinrotational symmetry. Consequently, the topology can be manifested unambiguously by identifying the special values of θ where the expectation value of the global operator with degenerate ground states is vanishing. Furthermore, experimentally θ can be detected readily by the interference of ultracold atomic gases. This scheme can be implemented readily in experiment since it does not need the addressing of individual atoms or the probing of a boundary.