Bilayer antiferromagnet with four-spin interaction

We investigate a spin-1/2 Heisenberg antiferromagnet with four-spin interaction on bilayer square and honeycomb lattices. In addition to the standard Neel and quantum disordered phases, these models can be expected to have a valence-bond-solid (VBS) phase [1]. Our aim is to locate the VBS phase and to investigate, in particular, a transition from quantum disorder to VBS. This is potentially a deconfined quantum critical point [1]. We use a recently introduced ground state projection Monte Carlo method which allows us to study these models without negative-sign problems [2].\hfill\break [1] A. Vishwanath et al, Phys. Rev. B {\bf 69}, 224416 (2004). \hfill\break [2] A. W. Sandvik, Phys. Rev. Lett. {\bf 95}, 207203 (2005).