Transverse Ising Chain (Pure System)

Abstract

AbstractThe one-dimensional pure Ising model in a transverse field is the simplest solvable model that shows a quantum phase transition. The properties of this model are investigated in detail in Chap. 2. First, the quantum critical point is identified by employing duality argument. The Hamiltonian of the transverse Ising chain is then diagonalised and its ground-state properties are investigated by using the Jordan-Wigner transformation, which maps the system to a free fermion system. Next, approximate methods such as the exact diagonalisation method with finite size scaling, which can be also applied to interacting fermion systems, and the real-space renormalisation group method are introduced. The finite temperature property and an experimental study of the transverse Ising chain are mentioned in the last part of this chapter. Details of the Jordan-Wiger transformation, diagonalisation of a general Hamiltonian quadratic in fermion operators, and the calculation of correlation functions of the transverse Ising chain are included in appendices.KeywordsCorrelation LengthEntanglement EntropyQuantum Phase TransitionTransverse FieldFinite Size ScalingThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.