Abstract
Chapter 10 mentions the XY model in a transverse field and the Kitaev model as related models to the transverse Ising model. The XY model in a transverse field is another simplest model, except the transverse Ising model, that exhibits a zero-temperature quantum phase transition. It also gives the pseudo-spin representation of the BCS Hamiltonian of the superconductivity. The spin-1/2 transverse XY chain can be diagonalised by using the Jordan-Wigner transformation, as the transverse Ising chain is. The Kitaev model, on the other hand, can be transformed into a free fermion model coupled with a field, which commutes with the Hamiltonian, by the Jordan-Wigner transformation, though it is defined in two dimension. Several properties of the ground state and the dynamical behaviour following a slow quench of a parameter are mentioned.
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Suzuki, S., Inoue, Ji., Chakrabarti, B.K. (2013). Related Models. In: Quantum Ising Phases and Transitions in Transverse Ising Models. Lecture Notes in Physics, vol 862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33039-1_10
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DOI: https://doi.org/10.1007/978-3-642-33039-1_10
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