Edge states of a spin-1/2 two-leg ladder with four-spin ring exchange

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-1/2 ladder with ring exchange by using the edge states and the entanglement entropy.