A complete characterization of the spectrum of the Kitaev model on spin ladders

TL;DR

This paper provides a complete analytical characterization of the spectrum of the Kitaev model on spin ladders, enabling detailed calculations of thermodynamic and quantum properties at any temperature.

Contribution

It presents the first closed-form solutions for all eigenvalues and eigenvectors of the Kitaev ladder model, facilitating comprehensive analysis of its physical properties.

Findings

Exact spectrum and eigenstates derived for the Kitaev ladder

Partition function and non-local operator averages computed explicitly

Framework suggested for extending results to more complex lattices

Abstract

We study the Kitaev model on a ladder network and find the complete spectrum of the Hamiltonian in closed form. Closed and manageable forms for all eigenvalues and eigenvectors, allow us to calculate the partition function and averages of non-local operators in addition to the reduced density matrices of different subsystems at arbitrary temperatures. It is also briefly discussed how these considerations can be generalized to more general lattices, including three-leg ladders and two dimensional square lattices.