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

Regular Article

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.

Keywords

Solid State and Materials 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of PhysicsSharif University of TechnologyTehranIran
  2. 2.Center of excellence in Complex Systems and Condensed Matter (CSCM)Sharif University of TechnologyTehranIran
  3. 3.Max-Planck-Institut für Physik komplexer SystemeDresdenGermany

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