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A unifying approach to competing quantum orders in generalized two-leg spinladders is presented. Hidden relationship and quantum phase transitions amongthe competing orders are thoroughly discussed by means of a low-energy fieldtheory starting from an SU(4) quantum multicritical point. Our approach revealsthat the system has a relatively simple phase structure in spite of itscomplicated interactions. On top of the U(1)-symmetry which is known fromprevious studies to mixes up antiferromagnetic order parameter with that of thep-type nematic, we find an emergent U(1)-symmetry which mixes order parametersdual to the above. On the basis of the field-theoretical- and variationalanalysis, we give a qualitative picture for the global structure of the phasediagram. Interesting connection to other models (e.g. bosonic t-J model) isalso discussed.Comment: 33 pages incl. 8 figures, accepted for publication in Phys.Rev.

Competing orders and hidden duality symmetries in two-leg spin ladder systems