Majorana zero modes and long range edge correlation in interacting Kitaev chains: analytic solutions and density-matrix-renormalization-group study

TL;DR

This paper investigates the properties of one-dimensional Kitaev chains, both non-interacting and interacting, using exact solutions and DMRG, focusing on Majorana edge modes and long-range correlations in topological phases.

Contribution

It provides analytic solutions for non-interacting cases and applies DMRG to study interactions, introducing an edge correlation function to characterize topological order.

Findings

Edge correlation function effectively characterizes long-range order.

Phase diagram of interacting Kitaev chain mapped out.

Majorana zero modes identified in both non-interacting and interacting regimes.

Abstract

We study Kitaev model in one-dimension with open boundary condition by using exact analytic methods for non-interacting system at zero chemical potential as well as in the symmetric case of {\Delta} = t, and by using density-matrix-renormalizationgroup method for interacting system with nearest neighbor repulsion interaction. We suggest and examine an edge correlation function of Majorana fermions to characterize the long range order in the topological superconducting states and study the phase diagram of the interating Kitaev chain.