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

• URL: http://arxiv.org/abs/2110.13123v4
• Date: Mon, 4 Apr 2022 13:17:17 GMT
• Title: Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations
• Authors: Oleksandr Gamayun and Oleg Lychkovskiy
• Abstract summary: We study the isotropic Kitaev spin-$1/2$ model on the Bethe lattice. We take a straightforward approach of solving Heisenberg equations for a tailored subset of spin operators. As an example, we calculate the time-dependent expectation value of this observable for a factorized translation-invariant.
• Score: 23.87373187143897
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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