Competing Orders and Hidden Duality Symmetries in Two-leg Spin Ladder Systems

A unifying approach to competing quantum orders in generalized two-leg spin ladders is presented. Hidden relationship and quantum phase transitions among the competing orders are thoroughly discussed by means of a low-energy field theory starting from an SU(4) quantum multicritical point. Our approach reveals that the system has a relatively simple phase structure in spite of its complicated interactions. On top of the U(1)-symmetry which is known from previous studies to mixes up antiferromagnetic order parameter with that of the p-type nematic, we find an emergent U(1)-symmetry which mixes order parameters dual to the above. 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) is also discussed.