Magnetic phase diagram of spin-1/2 two-leg ladder with four-spin ring exchanges

We study a spin-1/2 two-leg Heisenberg ladder with four-spin ring exchanges under a magnetic field. We introduce an exact duality transformation, which is an extension of the spin-chirality duality developed previously and yields a new self-dual surface in the parameter space. We then determine the magnetic phase diagram using the numerical approaches of the density-matrix renormalization-group and exact diagonalization methods. We demonstrate the appearance of a magnetization plateau and a Tomonaga-Luttinger liquid with a dominant vector-chirality quasi-long-range order for a wide parameter regime of strong ring exchange. A "nematic" phase, in which magnons form bound pairs and magnonpairing correlation functions dominate, is also identified.