Phase diagram of J1-J2 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 (Gamma) 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 Neel (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, Gamma/J(1) less than or similar to 0.3, which is followed by a transition to the quantum paramagnet (polarized) phase at high fields. The transition from RPS state to the Neel phase is either a deconfined quantum phase transition or a first order one, however a continuous transition occurs between RPS and collinear phases.