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

Sadrzadeh, M ; Sharif University of Technology | 2015

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  1. Type of Document: Article
  2. DOI: 10.1140/epjb/e2015-60142-2
  3. Publisher: springer berlin , 2015
  4. Abstract:
  5. 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
  6. Keywords:
  7. Bosons ; Excited states ; Hamiltonians ; Ising model ; Phase diagrams ; Phase transitions ; Quantum electronics ; Spin fluctuations ; Continuous transitions ; Effective Hamiltonian ; Plaquette interactions ; Quantum phase transitions ; Solid State and Materials ; Translational symmetry ; Transverse magnetic field ; Transverse-field Ising model ; Quantum theory
  8. Source: European Physical Journal B ; Volume 88, Issue 10 , October , 2015 ; 14346028 (ISSN)
  9. URL: http://link.springer.com/article/10.1140%2Fepjb%2Fe2015-60142-2