Ground state phase diagram of the Hamiltonian (2) in the plane of coupling ratios defined in Eqs. (5a) and (5b). The phase boundaries are based on scans versus g for for several values of h, as exemplified by Figs. 4,6 and 7. The resulting transition points are indicated with + and ×symbols and the curves are smooth interpolations and extrapolations of these points. The solid curves denote first-order transitions, and the dotted curve segment denotes a continuous (or possibly very weakly first-order) DQC transition. The three first-order phase boundaries meet at a triple point denoted by the yellow star, and there is possibly a tricritical point on the AFM–cVBS curve, with location approximately at the blue circle.