Abstract
A topological insulator and its spin analog as a gapped spin liquid have characteristic low-energy excitations (edge states) within the gap when the systems have boundaries. This is the bulk-edge correspondence, which implies that the edge states themselves characterize the gapped bulk spin liquid. Based on the general principle, we analyzed the vector chirality and rung-singlet phases of the spin-$\frac{1}{2}$ ladder with ring exchange by using the edge states and the entanglement entropy.
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