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Based on density functional calculations, we present a detailed theoreticalstudy of the electronic structure and the magnetic properties of the quasi-onedimensional chain cuprate Li_2ZrCuO_4 (Li_2CuZrO_4). For the relevant ratio ofthe next-nearest neighbor exchange J_2 to the nearest neighbor exchange J_1 wefind alpha = -J_2/J_1 = 0.22\pm0.02 which is very close to the critical pointat 1/4. Owing this vicinity to a ferromagnetic-helical critical point, we studyin detail the influence of structural peculiarities such as the reported Lidisorder and the non-planar chain geometry on the magnetic interactionscombining the results of LDA based tight-binding models with LDA+U derivedexchange parameters. Our investigation is complemented by an exactdiagonalization study of a multi-band Hubbard model for finite clusterspredicting a strong temperature dependence of the optical conductivity forLi_2ZrCuO_4.

Electronic structure and magnetic properties of Li_2ZrCuO_4 - a spin 1/2 Heisenberg system in vicinity to a quantum critical point