A unifying approach to unconventional orders in frustrated spin systems

A unifying approach to competing quantum orders in frustrated two-leg spin ladders (1D) and square-lattice antiferromagnets (2D) is presented. Hidden relationship and quantum phase transitions among the competing orders are discussed. Our approach reveals that these systems have a relatively simple phase structure in spite of its complicated interactions. In particular, there is an intriguing U(1) symmetry (which exists only approximately in 2D) which mixes up antiferromagnetic order parameter with that of the p-type nematic. On top of it, we found an emergent U(1)-symmetry. On the basis of the field-theoretical- and variational analysis, we give a qualitative picture for the global structure of the phase diagram. Interesting connection to other models (e.g. bosonic t-J model) and its application to the 2D problem are also discussed