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.Comment: 33 pages incl. 8 figures, accepted for publication in Phys.Rev.