Basic theory To cite this article: R B Stinchcombe 1973 J. Phys. We denote such behavior a dynamical phase transition and explore its properties in the transverse-field Ising model. We study quantum phase transition in the fully frustrated Δ chain Ising model under transverse fields Γ at spins on tops of the triangles and λΓ at ones on bottoms of the triangles, by using perturbation expansions, the numerical diagonalization method and a mean-field approximation with the Jordan–Wigner transformation. II. I. 2. Beginning with an overview of quantum phase transitions, we introduce a number of model Hamiltonians. Related content Ising model in a transverse field. We review quantum phase transitions of spin systems in transverse magnetic fields taking the examples of the spin-1/2 Ising and XY models in a transverse field. We show the existence of a phase transition in the Ising model with transverse field for dimensionsv ≥ 2 provided the transverse term is sufficiently small. transition in the one-dimensional transverse-ﬁeld Ising model, which serves as a paradigm for one-dimensional quantum phase transitions . C: Solid State Phys. Ising model in a transverse field. From a generic introduction to in-depth discussions of the subtleties of the transverse field Ising and related models, it includes the essentials of quantum dynamics and quantum information. We provide exact solutions in one spatial dimension connecting them to conformal field theoretical studies. 6 2459 View the article online for updates and enhancements. The pairwise entanglement on a 2D lattice can be obtained by the reduced density matrix of this system with the concurrence as the measure of entanglement. The one-dimensional pure Ising model in a transverse field is the simplest solvable model that shows a quantum phase transition. You can find more about that e.g. Spectral functions and damping R B Stinchcombe-Thermal and magnetic properties of the transverse Ising model This is done by proving long-range order occurs using the reflection positivity of the Hamiltonian and localization of eigenvectors. The transverse field Ising and XY models (the simplest quantum spin models) provide the organising principle for the rich variety of interconnected subjects which are covered in this book. in the post Ground state degeneracy: Spin vs Fermionic language; in particular, the discussion below the answer lists some references where the derivation is carried out.. The 1D transverse field Ising model can be solved exactly by mapping it to free fermions. Specifically, we show that the equilibrium quantum phase transition and the dynamical phase transition in this model are intimately related. The quantum entanglement and quantum phase transition of the transverse-field Ising model on a square lattice were investigated by employing the quantum renormalization group method. The properties of this model are investigated in detail in Chap. It can be solved exactly, which permits us to establish the existence of dynamical phase transitions that are intimately related to the equilib-rium quantum phase transition in this model.