Local and nonlocal order parameters in the Kitaev chain

TL;DR

This paper investigates the phase diagram of the interacting dimerized Kitaev chain using string order parameters, revealing both local and nonlocal phases and identifying the universality class at criticality.

Contribution

It introduces a method to calculate string order parameters in the Kitaev chain with interactions and dimerization, connecting them to local order parameters via duality transformations.

Findings

Identification of phases with local and nonlocal order parameters.

Confirmation of 2D Ising universality class at criticality.

Exact solvability at a symmetric point.

Abstract

We have calculated order parameters for the phases of the Kitaev chain with interaction and dimerization at a special symmetric point applying the Jordan-Wigner and other duality transformations. We use string order parameters (SOPs) defined via the correlation functions of the Majorana string operators. The SOPs are mapped onto the local order parameters of some dual Hamiltonians and easily calculated. We have shown that the phase diagram of the interacting dimerized chain comprises the phases with the conventional local order as well as the phases with nonlocal SOPs. From the results for the critical indices we infer the 2D Ising universality class of criticality at the particular symmetry point where the model is exactly solvable.