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 J1−J2−J3J1−J2−J3 quantum S=1/2S=1/2 antiferromagnet. In the classical limit S≫1S≫1, the phase diagram of the model demonstrates two triple points. We show that, in the quantum limit S=1/2S=1/2 for J3<0J3<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.

► We consider a 2D J1−J2−J3J1−J2−J3S=1/2S=1/2 Heisenberg antiferromagnet at T=0T=0. ► The spherically symmetric Green’s functions approach is used. ► We examine phase transitions between ordered states and the spin liquid. ► The obtained phase diagram agrees with the available numerical data. ► A new phase with coexisting long-range orders is manifested.