Edge states of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchange
  A topological insulator and its spin analogue 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 phase of the spin-1/2 ladder with ring exchange by using the edge states and the entanglement entropy. 
Mitsuhiro Arikawa, Shou Tanaya, Isao Maruyama, Yasuhiro Hatsugai