On the coexistence of different types of long-range order in the strongly frustrated two-dimensional Heisenberg model

In the spherically symmetric self-consistent approach to spin–spin Green’s functions, we consider a two-dimensional strongly frustrated J 1 − J 2 − J 3 quantum S = 1 / 2 antiferromagnet. In the classical limit S ≫ 1 , the phase diagram of the model demonstrates two triple points. We show that, in the quantum limit S = 1 / 2 for J 3 < 0 , a quadruple point of the quantum phase transition appears. At this point, the four coexisting phases are a disordered spin-liquid phase and three phases with different types of long-range order. Two of them are well-known “checkerboard” Néel order and stripe order; the last one corresponds to a non-trivial state with two coexisting mutually penetrating long-range orders.