The spin-1/2 J1-J2 antiferromagnet is a prototypical model for frustrated magnetism and one possible candidate for a realization of a spin liquid phase. The generalization of this system on the anisotropic square lattice is given by the J1-J2-J In the search of exotic quantum states and quantum phase transitions, frustrated antiferromagnetic systems have increasingly become the center of attention [1,2]. The competing interactions between spins potentially lead to a large entropy even at low temperatures, which together with quantum fluctuations may give rise to quantum phases with unconventional or topological order parameters [3][4][5]. In particular, the so-called spin liquid state without long range order of a conventional (local) order parameter has been much discussed in the literature ever since Anderson related this phase to hightemperature superconductivity [6]. A solid proof for a system which shows a spin liquid ground state has long been elusive, due to inherent numerical and analytical problems in frustrated systems. Nonetheless, some good evidence for possible spin liquid states has recently been presented for the Hubbard model on the honeycomb [7] and the anisotropic triangular lattice [8], as well as for for the Heisenberg model on a Kagome lattice [1, 9-11], and on the J 1 -J 2 frustrated square lattice [12][13][14].In particular, the J 1 -J 2 Heisenberg model has been treated with a vast array of theoretical methods , which is also the model originally considered by Anderson [6]. Early numerical works have shown an intermediate phase between ordinary Néel order for J 2 0.4J 1 and collinear Néel order for J 2 0.6J 1 [15], but the underlying correlations in this phase remain hotly debated. Most works have predicted a plaquette or columnar dimer order as the most likely scenario [16][17][18][19][20][21][22][23][24][25][26], but more recent numerical works have again proposed a spin liquid [12][13][14]. Unfortunately, the issue may never be conclusively solved using numerical methods, since convergence with finite size and/or temperature of data from density matrix renormalization group (DMRG) or tensor matrix methods is very slow. In particular, it was shown recently for the related two-dimensional (2D) J-Q model that the finite size scaling on moderate lengths would lead to the prediction of a spin liquid, even though the system orders in the thermodynamic limit [44]. In general, the slow convergence is related to the observation that spin liquid states are often very close in energy to competing states with dimer order [10,11].In light of the disappointing numerical situation, analytical methods become very important, but the problem is difficult since series expansions [16,36], chain meanfield theories [45], spin wave theories [23] or coupled cluster methods [25,40,41] have to incorporate frustrating