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" Neel order and stripe order; the last one corresponds to a non-trivial state with two coexisting mutually penetrating long-range orders. (C) 2012 Elsevier Ltd. All rights reserved.