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Paper   IPM / Physic / 15035
School of Physics
  Title:   Exactly solvable spin chain models corresponding to BDI class of topological superconductors
1.  S.A. Jafari
2.  F. Shahbazi
  Status:   Published
  Journal: Scientific Reports
  Vol.:  6
  Year:  2016
  Pages:   32720
  Supported by:  IPM
We present an exactly solvable extension of the quantum XY chain with longer range multi-spin interactions. Topological phase transitions of the model are classified in terms of the number of Majorana zero modes, nM which are in turn related to an integer winding number, nW. The present class of exactly solvable models belong to the BDI class in the Altland-Zirnbauer classification of topological superconductors. We show that time reversal (TR) symmetry of the spin variables translates into a sliding particle-hole (PH) transformation in the language of Jordan-Wigner (JW) fermions - a PH transformation followed by a π shift in the wave vector (πPH). Presence of πPH symmetry restricts the nW (nM) of TR symmetric extensions of XY to odd (even) integers. The πPH operator may serve in further detailed classification of topological superconductors in higher dimensions as well.

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