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Duality relations and exotic orders in electronic ladder systems

We discuss duality relations in correlated electronic ladder systems to clarify mutual relations between various conventional and unconventional phases. For the generalized two-leg Hubbard ladder, we find two exact duality relations, and also one asymptotic relation which holds in the low-energy regime. These duality relations show that unconventional (exotic) density-wave orders such as staggered flux or circulating spin-current are directly mapped to conventional density-wave orders, which establishes the appearance of various exotic states with time-reversal and/or spin symmetry breaking. We also study duality relations in the SO(5) symmetry that was proposed to unify antiferromagnetism and d-wave superconductivity. We show that the same SO(5) symmetry also unifies circulating spin current order and s-wave superconductivity.