Spin-Spin Correlations in the Kitaev Model at Finite Temperatures: Approximate and Exact Results via Green's Function Equation of Motion

TL;DR

This paper investigates the finite temperature spin-spin correlations in the Kitaev model using a Green's function approach that preserves SU(2) symmetry, providing approximate and exact results relevant for understanding Majorana fermions and topological quantum computing.

Contribution

It introduces a Green's function method that maintains SU(2) symmetry to analyze the Kitaev model's finite temperature properties, offering both approximate and exact results.

Findings

Temperature dependence of correlations closely matches exact zero-temperature results.

The method provides several exact results for spin Green's functions.

The approach enhances understanding of Majorana fermions in the Kitaev model.

Abstract

The Kitaev model, defined on a honeycomb lattice, features an exactly solvable ground state with fractionalized Majorana fermion excitations, which can potentially form non-Abelian anyons crucial for fault-tolerant topological quantum computing. Although Majorana fermions are essential for obtaining the exact ground state, their physical interpretation in terms of spin operators remains unclear. In this study, we employ a Green's function approach that maintains SU(2) symmetry to address this issue and explore the model's finite temperature properties. Our results demonstrate that the computed temperature dependence of the correlation functions closely approximates the exact values at zero temperature, confirming the accuracy of our method. We also present several exact results concerning the spin Green's function and spin-spin correlation functions that are specific to the Kitaev model.