• From Ising Model to Kitaev Chain: An Introduction to Topological Phase Transitions

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/reso/026/11/1539-1558

    • Keywords

       

      Ising model, Kitaev chain, topo-logical phase transition, Majorana zero modes, Suzuki–Trotter, inverse Jordan–Wigner, Bogoli-ubon, p-wave superconductor, quantum computation

    • Abstract

       

      In this general article, we map the one-dimensional trans-verse 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.

    • Author Affiliations

       

      Kartik Chhajed1

      1. Department of Physical Science IISER Mohali, Punjab, India.
    • Dates

       

© 2021-2022 Indian Academy of Sciences, Bengaluru.