Phase Diagram of a Spin Ladder with Cyclic Four Spin Exchange

We present the phase diagram of the $S=1/2$ Heisenberg model on the two leg ladder with cyclic four spin exchange, determined by a combination of Exact Diagonalization and Density Matrix Renormalization Group techniques. We find six different phases and regimes: the rung singlet phase, a ferromagnetic phase, two symmetry broken phases with staggered dimers and staggered scalar chiralities, and a gapped region with dominant vector chirality or collinear spin correlations. We localize the phase transitions and investigate their nature.