From Ising model to Kitaev Chain -- An introduction to topological phase transitions
In this general article, we map the one-dimensional transverse field quantum Ising model of ferromagnetism to Kitaev's one-dimensional p-wave superconductor, which has its application in fault-tolerant topological quantum computing. Kitaev Chain is an example of a new class of quantum critical phenomena, the topological phase transition. Mapping Pauli's spin operators of transverse field quantum Ising chain to spinless fermionic creation and annihilation operators by Inverse Jordan-Wigner transformation leads to a Hamiltonian form closely related Kitaev Chain.