Charge Density Waves and $x=1/8$ anomaly in   La$_{2-x-y}$(Nd,Eu)$_y$(Ba,Sr)$_x$CuO$_4$
  We adopt a $t_1-t_2-t_3-J-G$ model for explanation of $x=1/8$ anomaly in La$_{2-x}$Sr$_x$CuO$_4$ family compound. The calculated charge susceptibility shows a maximum near $(\pi,\pi)$ at intermediate temperatures and near $(\pi,\pi/2)$ as temperature approaches zero, in agreement with neutron scattering experiments. Coulomb repulsion $G$ between the first neighbors turns out to be the source of Charge Density Waves (CDW) in narrow band $t_1^{\mathit{eff}}, t_2^{\mathit{eff}}, t_3^{\mathit{eff}}<G$. For physically realistic hopping values we obtain the CDW amplitude $e_Q=x$. The in-phase domain structure as a candidate for "stripe" picture is proposed. 
I.A. Larionov and M.V. Eremin