From ising model to kitaev chain: An introduction to topological phase transitions.

Abstract

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 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.