Phase diagram of J 1 -J 2 transverse field Ising model on the checkerboard lattice: a plaquette-operator approach

We study the effect of quantum fluctuations by means of a transverse magnetic field (Γ) on the antiferromagnetic J 1 -J 2 Ising model on the checkerboard lattice, the two dimensional version of the pyrochlore lattice. The zero-temperature phase diagram of the model has been obtained by employing a plaquette operator approach (POA). The plaquette operator formalism bosonizes the model, in which a single boson is associated to each eigenstate of a plaquette and the inter-plaquette interactions define an effective Hamiltonian. The excitations of a plaquette would represent an-harmonic fluctuations of the model, which lead not only to lower the excitation energy compared with a single-spin flip but also to lift the extensive degeneracy in favor of a resonating plaquette solid (RPS) state, which breaks lattice translational symmetry, in addition to a unique collinear phase for J 2 > J 1 . The bosonic excitation gap vanishes at the critical points to the Néel (J 2 > J 1 ) and collinear (J 2 > J 1 ) ordered phases, which defines the critical phase boundaries. At the homogeneous coupling (J 2 =J 1 ) and its close neighborhood, the (canted) RPS state, established from an-harmonic fluctuations, lasts for low fields, Γ/J 1 ≲ 0.3, which is followed by a transition to the quantum paramagnet (polarized) phase at high fields. The transition from RPS state to the Néel phase is either a deconfined quantum phase transition or a first order one, however a continuous transition occurs between RPS and collinear phases. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015