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arXiv · 2110.13123

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

Oleksandr Gamayun·Oleg Lychkovskiy
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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.

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Oleksandr Gamayun, Oleg Lychkovskiy. 2021-10-25. Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations. https://doi.org/10.21468/scipostphys.12.5.175

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