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| Paper IPM / Physic / 15035 |
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| Abstract: | |||||
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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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