Ansatz for Majorana modes for a quantum walk in a finite wire
Ho Tat Lam, Yue Yu, Kwok Yip Szeto · Physical Review A · 2016
The topological phases in a one-dimensional quantum walk can be classified by the coin parameters. By solving for the general exact solutions of bound states in a one-dimensional quantum walk with boundaries specified by different coin parameters, we show that these bound states are Majorana modes with quasienergy $E=0,\ensuremath{\pi}$. These modes are qualitatively different for different boundary conditions used. For systems with two boundaries, such as finite wires, we find the same exact solution as the single boundary system if the boundary condition is antisymmetric. For a two-boundary system with symmetric boundary conditions in a finite wire, the interaction energy between two Majorana bound states can be computed as a function of the length of the wire and the coin parameter in the wire. Suggestions of observing these modes are provided.