Characterization of topological phases of dimerized Kitaev chain via edge correlation functions

Abstract

We study the interacting dimerized Kitaev chain at the symmetry point ∆ = t and the chemical potential µ = 0 under open boundary conditions, which can be exactly solved by applying two Jordan-wigner transformations and a spin rotation. By using exact analytic methods, we calculate two edge correlation functions of Majorana fermions and demonstrate that they can be used to distinguish different topological phases and characterize the topological phase transitions of the interacting system. According to the thermodynamic limit values of these two edge correlation functions, we give the phase diagram of the interacting system which includes three different topological phases: the trivial, the topological superconductor and the Su-Schrieffer-Heeger-like topological phase and we further distinguish the trivial phase by obtaining the local density distribution numerically.

Topological Phase Transition and Phase Diagrams in a Two‐Leg Kitaev Ladder System

“…Moreover, many aspects of the Kitaev model have been investigated systematically, for example, topological phases, order parameter, ground state entanglement and geometric entropy, the mapping in the optomechanical system, etc. On the other hand, significant research effort has also been dedicated to the exploration of the extended Kitaev model, such as the dimerized Kitaev chain with modulations in the chemical potential, non‐Hermitian Kitaev model, and higher‐spin Kitaev model …”

Exact solution to the Haldane-BCS-Hubbard model along the symmetric lines: Interaction-induced topological phase transition

“…First, the interactions may reduce the topological classification of free fermions in one dimension 7,8 and two dimensions 9 . Second, interactions may drive topological quantum phase transitions, which is demonstrated in exactly solvable models of interacting Kitaev chains [10][11][12] , the Haldane-Hubbard model 13 and the Z 2 Bose-Hubbard model 14 . Recently, Chen et.…”

End-to-end correlations in the Kitaev chain

“…The study of edge correlations in fermion chains has been addressed from different perspectives in various contributions, some of which cited here. References [8][9][10][11], for example, focus on the analytical aspects of the problem, while references [12][13][14][15][16] survey the relation with Majorana quasiparticles in number conserving systems. Here the analysis covers the whole range of parameters and is conceptually exact, albeit with a numerical component.…”