Spin-chirality duality in a spin ladder with four-spin cyclic exchange

Effect of four-spin cyclic exchange on magnetism is studied in the two-leg S=1/2 ladder. We develop an exact spin-chirality duality transformation, under which the system is self-dual when the four-spin exchange J_4 is half of the two-spin exchange. Using the density-matrix renormalization-group method and the duality relation, we find that the four-spin exchange makes the vector chirality correlation dominant. A "chirality short-range resonating-valence-bond" phase is identified for the first time at large J_4.