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It is widely accepted that the low-energy physics in edge-sharing cupratematerials has one-dimensional (1D) character. The relevant model to study suchsystems is believed to be the 1D extended Heisenberg model with ferromagneticnearest-neighbor (NN) interaction and antiferromagnetic next-nearest-neighborone. Thus far, however, theoretical studies of such materials have beenconfined to the case of isotropic interactions. In the present work, we comparethe spin susceptibility of the 1D extended Heisenberg model with anisotropy inthe NN channel, obtained by means of the Transfer Matrix Renormalization Groupmethod, with that of the edge-sharing chain cuprate Li$_2$CuO$_2$.

Analysis of the magnetic response of the edge-sharing chain cuprate Li$_2$CuO$_2$ within TMRG