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We investigate weakly coupled quarter-filled ladders with model parametersrelevant for NaV_2O_5 using density-matrix renormalization group calculationson an extended Hubbard model coupled to the lattice. NaV2O5 exhibitssuper-antiferroelectric charge order with a zigzag pattern on each ladder. Weshow that this order, with a periodicity of four ladders, causes a spindimerization along the ladder and a corresponding spin gap of the samemagnitude as that observed experimentally. The spin gap is destroyed again atlarge charge order due to a restructuring of the spins. An analysis of aneffective spin model predicts a re-creation of the gap by inter-ladder singletswhen the charge order increases further.Comment: 4+ pages; revised version; accepted by PR

Creation and Destruction of a Spin Gap in Weakly Coupled Quarter-Filled Ladders