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A topological insulator and its spin analogue as a gapped spin liquid havecharacteristic low energy excitations (edge states) within the gap when thesystems have boundaries. This is the bulk-edge correspondence, which impliesthat the edge states themselves characterize the gapped bulk spin liquid. Basedon the general principle, we analyzed the vector chirality phase of thespin-1/2 ladder with ring exchange by using the edge states and theentanglement entropy.

Edge states of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchange