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Ground State Phase Diagram of Two-dimensional Frustrated Ising Model in Transverse Field

Sadrzadeh, Marzieh | 2017

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 49449 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Langari, Abdollah
  7. Abstract:
  8. In this thesis, we study the effect of quantum fluctuations by means of a transverse magnetic field () on the ground state of frustrated antiferromagnetic Ising models on the checkerboard and square lattices with nearest neigbor couplings J1 and next-to-nearest neighbor couplings J2. At zero field, such models have exponentially large degenerate classical ground states at J2 ... J1 for the checkerboard lattice and at J2 = 0:5J1 for the square lattice. Quantum fluctuations can have a major role to lift the degeneracies toward a unique quantum ground states. We consider two types of quantum fluctuations, harmonic ones by using linear spin wave theory (LSWT) with single-spin flip excitations above a long-range magnetically ordered background and anharmonic fluctuations, by employing a cluster-operator approach (COA) with multi-spin cluster type fluctuations above a non-magnetic cluster ordered background. Our findings reveal that the harmonic fluctuations of LSWT fail to lift the extensive degeneracy as well as signaling a violation of the Hellmann-Feynman theorem in some regions of instability on the quantum phase diagram. However, the anharmonic quantum fluctuations of COA (plaquette-type in checkerboard lattice and string-type in square lattice) are able to lift the degeneracy of the highly frustrated points toward a valence bond solid (VBS) state (plaquette-VBS for checkerboard and string-VBS for square lattice). The VBS phases are obtained from an effective theory consistent with the Hellmann-Feynman theorem as well. Our results are further confirmed by implementing exact diagonalization on small lattices. The emergent non-magnetic VBS phases are gapped and breaks lattice spatial symmetry with only two-fold degeneracy, which bears a continuous quantum phase transition to the quantum paramagnet phase of high fields. The critical behavior of such transitions are characterized by calculating the universal critical exponents. Finally, we introduce a transformation, which maps the low-energy behvior of the checkerboard lattice to the square lattice
  9. Keywords:
  10. Quantum Phase Transition ; Quantum Fluctuations ; Ising model ; Frustrated Magnets ; Collective Excitations ; Quantum Spin Liquid

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