Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations

TL;DR

This paper investigates the out-of-equilibrium dynamics of the isotropic Kitaev spin-1/2 model on the Bethe lattice by solving Heisenberg equations for specific spin operators, providing insights into its temporal evolution.

Contribution

It introduces a direct Heisenberg equation approach to study the Kitaev model's dynamics on the Bethe lattice, bypassing the spin-fermion mapping limitations.

Findings

Calculated time-dependent expectation values for specific initial states.

Demonstrated the feasibility of the Heisenberg equations approach for this model.

Provided insights into the model's dynamical behavior far from equilibrium.

Abstract

The Kitaev model on the honeycomb lattice, while being integrable via the spin-fermion mapping, has generally resisted an analytical treatment of the far-from-equilibrium dynamics due to the extensive number of relevant configurations of conserved charges. Here we study a close proxy of this model, the isotropic Kitaev spin-$1/2$ model on the Bethe lattice. Instead of relying on the spin-fermion mapping, we take a straightforward approach of solving Heisenberg equations for a tailored subset of spin operators. The simplest operator in this subset corresponds to the energy contribution of a single bond direction. As an example, we calculate the time-dependent expectation value of this observable for a factorized translation-invariant (or staggered-translation-invariant) initial state with arbitrary initial (staggered) polarization.