The fate of entanglement in quantum antiferromagnets under Lindbladian dynamics of their localized spins

It is commonly assumed in antiferromagnetic spintronics that localized spins within such materials are in the Neel ground state [1,2] and they obey Landau-Lifshitz-Gilbert (LLG) equation when pushed out of equilibrium by electrons or external fields [3]. However, it is well-known that the ground state of antiferromagnets is highly entangled [4], as confirmed in very recent neutron scattering experiments [5] witnessing their entanglement up to some finite temperature. In this study, we either start from the ground state of quantum Heisenberg antiferromagnet or excited state generated by flipping one of its spins [2], and then evolve them for an open quantum system subject to decoherence [1] and dissipation via the Lindblad quantum master equation obtained [6] by integrating out bosonic bath interacting with the spins. We find that some degree of entanglement always persists, thereby shrinking the length of the vector magnitude of spin expectation values, which makes the LLG equation (operating with classical vectors of localized spins of fixed length) inapplicable.

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