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We consider quantum spin systems with dimerization, which at strong coupling have singlet ground states. To account for strong correlations, the S = 1 elementary excitations are described as dilute Bose gas with infinite on-site repulsion. This approach is applied to the two-layer Heisenberg antiferromagnet at T = 0 with general couplings. Our analytic results for the triplet gap, the excitation spectrum and the location of the quantum critical point are in excellent agreement with numerical results, obtained by dimer series expansions.

We analyze the phase diagram of the frustrated Heisenberg antiferromagnet, the J1 − J2 model, in two dimensions. Two quantum phase transitions in the model are already known: the second order transition from the Néel state to the spin liquid state at (J2/J1)c2 = 0.38, and the first order transition from the spin liquid state to the collinear state at (J2/J1)c4 = 0.60. We have found evidence for two new second order phase transitions: the transition from the spin columnar dimerized state to the state with plaquette type modulation at (J2/J1)c3 = 0.50±0.02, and the transition from the simple Néel state to the Néel state with spin columnar dimerization at (J2/J1)c1 = 0.34 ± 0.04. We also present an independent calculation of (J2/J1)c2 = 0.38 using a new approach. PACS: 75.10.Jm, 75.30.Kz, 75.40.Gb, 75.30.Ds The nature of the quantum disordered phases of lowdimensional quantum antiferromagnets is a topic of fundamental importance for the physics of quantum magnetism [1]. Such phases can result from mobile holes in an antiferromagnetic background as in the t − J or Hubbard model at finite doping. Alternatively, competition of purely magnetic interactions can also lead to destruction of long-range order. A typical example of the second kind is the J 1 − J 2 model which exhibits a quantum disordered (spin-liquid) phase due to second-neighbor frustrating interactions. Even though it has been intensively studied during the last ten years, the J 1 −J 2 model apparently still holds many secrets. This model is also an ideal testing ground for the theory of quantum phase transitions because it has very complex dynamics and contains a variety of transitions. Exact diagonalization studies [2] have shown that the excitation spectrum of the model is quite complex and that finite-size effects are large [3]. Spin-wave like expansions around the simple Néel state (which occurs for small frustration) naturally cannot give any information about the ground state at stronger frustration, and consequently non-perturbative methods are needed to analyze the latter regime.An important insight into the disordered regime was achieved by field-theory methods [4,5] and dimer series expansions [6,5,7]. The above works have established the range of the disordered regime, 0.38 < g < 0.60 (g = J 2 /J 1 ), and have also shown that the ground state in this regime is dominated by short-range singlet (dimer) formation in a given pattern (see Fig.1). The stability of such a configuration implies that the lattice symmetry is spontaneously broken and the ground state is fourfold degenerate. This picture is somewhat similar to the one dimensional situation, where the Lieb-SchultzMattis theorem guarantees that a gapped phase always breaks the translational symmetry and is doubly degenerate, whereas gapless excitations correspond to a unique ground state [8].Two very recent calculations [9,10] performed by Green function Monte Carlo methods have raised new questions on the structure of the intermediate phase. The authors of Ref.[9] claim stability of the...

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