Frustrated cuprate route from antiferromagnetic to ferromagnetic spin-1/2 Heisenberg chains:: Li2ZrCuO4 as a missing link near the quantum critical point

From thermodynamics, local spin density approximation+Hubbard U studies and exact diagonalizations of a five-band Hubbard model on CuO2 stripes we find that Li2ZrCuO4 (Li2CuZrO4 in traditional notation) is close to a ferromagnetic critical point. Analyzing its susceptibility chi(T) and specific heat c(p)(T,H) within a Heisenberg model, we show that the ratio of the 2nd to the 1st neighbor exchange integrals alpha=-J(2)/J(1)similar to 0.3 is close to the critical value alpha(c)=1/4. Comparing with related chain cuprates we explain the rather strong field dependence of c(p), the monotonic downshift of the peak of chi(T), and its increase for alpha ->alpha(c)+0.