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Quantum phase diagram of the two-dimensional transverse-field Ising model: Unconstrained tree tensor network and mapping analysis

Sadrzadeh, M ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1103/PhysRevB.99.144414
  3. Publisher: American Physical Society , 2019
  4. Abstract:
  5. We investigate the ground-state phase diagram of the frustrated transverse-field Ising (TFI) model on the checkerboard lattice (CL), which consists of Néel, collinear, quantum paramagnet, and plaquette-valence bond solid (-VBS) phases. We implement a numerical simulation that is based on the recently developed unconstrained tree tensor network ansatz, which systematically improves the accuracy over the conventional methods as it exploits the internal gauge selections. At the highly frustrated region (J2=J1), we observe a second-order phase transition from the plaquette-VBS state to the paramagnet phase at the critical magnetic-field Γc=0.28 with the associated critical exponents ν=1 and γ≃0.4, which are obtained within the finite-size scaling analysis on different lattice sizes N=4×4,6×6,8×8. The stability of the plaquette-VBS phase at low magnetic fields is examined by a spin-spin correlation function, which verifies the presence of plaquette-VBS at J2=J1 and rules out the existence of a Néel phase. In addition, our numerical results suggest that the transition from the Néel (for J2
  6. Keywords:
  7. Forestry ; Ground state ; Ising model ; Lattice theory ; Magnetic fields ; Mapping ; Numerical methods ; Paramagnetism ; Phase diagrams ; Tensors ; Checkerboard lattices ; Critical magnetic field ; Finite-size scaling analysis ; Ground state phase diagram ; Quantum phase diagrams ; Second-order phase transition ; Spin-spin correlation functions ; Transverse-field Ising model ; Quantum theory
  8. Source: Physical Review B ; Volume 99, Issue 14 , 2019 ; 24699950 (ISSN)
  9. URL: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.99.144414