Eur. Phys. J. B (2015) 88: 259
https://doi.org/10.1140/epjb/e2015-60142-2

Regular Article

Phase diagram of J₁-J₂ transverse field Ising model on the checkerboard lattice: a plaquette-operator approach

¹ Department of Physics, Sharif University of Technology, 11155-9161 Tehran, Iran
² Center of excellence in Complex Systems and Condensed Matter (CSCM), Sharif University of Technology, 1458889694 Tehran, Iran
³ Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany

^a e-mail: marziehsadrzadeh@physics.sharif.edu

Received: 24 February 2015
Received in final form: 12 August 2015
Published online: 14 October 2015

Abstract

We study the effect of quantum fluctuations by means of a transverse magnetic field (Γ) on the antiferromagnetic J₁-J₂ 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 J₂ > J₁. The bosonic excitation gap vanishes at the critical points to the Néel (J₂ < J₁) and collinear (J₂ > J₁) ordered phases, which defines the critical phase boundaries. At the homogeneous coupling (J₂ = J₁) and its close neighborhood, the (canted) RPS state, established from an-harmonic fluctuations, lasts for low fields, Γ/J₁ ≲ 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.