A study of topological characterization and symmetries for a quantum simulated Kitaev chain

Abstract: An attempt is made to quantum simulate the topological classification, such as winding number, geometric phase and symmetry properties for a quantum simulated Kitaev chain. We find, {\alpha} (ratio between the spin-orbit coupling and magnetic field) and the range of momentum space of consideration, which plays a crucial role for the topological classification. We show explicitly that the topological quantum phase transition does not occurs at k = 0 limit for the quantum simulated Kitaev chain. We observe that the quasi-particle mass of the Majorana mode plays the significant role in topological quantum phase transition. We also show that the symmetry properties of simulated Kitaev chain is the same with original Kitaev chain. The exact solution of simulated Kitaev chain is given. This work provides a new perspective on new emerging quantum simulator and also for the topological state of matter.