Mean-field RVB ground states of lattice models of CuNCN

Recently we proposed to describe the fascinating physics of copper carbodiimide, CuNCN, with help of the anisotropic trangular antiferromagnetic Heisenberg model with the parameters J_a and J_ab extending along the a, and a ± b lattice directions and a new frustrated Heisenberg antiferromagnetic model with exchange parameters J_c, J_a, and J_ac, extending along the c, a, and a ± c (c-a-ca model) directions assuming the resonating valence bond (RVB) type of the corresponding phases. Here we discuss possible RVB ground states of these models in the mean-field approximation and show that in either case it is a two-dimensional RVB state. The difference between the models is that in the ground state of the triangular model the quasiparticle spectrum features a finite (although exponentially small) energy gap for arbitrary weak Jab whereas that of the c-a-ca model shows two pseudo gaps and a linear dependence of the quasiparticle density of states in the low-energy range.