Laboratoire de Physique Théorique
Toulouse - UMR 5152

I will present our recent study of the critical properties of a Majorana chain in the presence of two competing interactions of the shortest possible range. The obtained phase diagram is very rich and contains nine different phases, including three floating, two Ising, and four gapped phases. In addition I will overview a wide variety of quantum phase transitions present in the system : the supersymmetric tri-critical Ising lines ; the Lifshitz critical line characterized by the dynamical critical exponent z=3 ; Kosterlitz-Thouless transitions, and an exotic first order transition between the floating and the gapped phases. I will discuss in detail the surprising feature of the obtained phase diagram - the emergence of the commensurate line at which the floating phases collapse into a direct transition. I will show numerical evidence that the resulting multi-critical point belongs to the universality class of the eight-vertex model.