Enhanced entanglement in multi-bath spin-boson models

Charlie R. Hogg1, Federico Cerisola1,2, James D. Cresser1,3,4, Simon A. R. Horsley1, and Janet Anders1,5

1Department of Physics and Astronomy, University of Exeter, Stocker Road, Exeter EX4 4QL, United Kingdom.
2Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, United Kingdom.
3School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, United Kingdom.
4Department of Physics and Astronomy, Macquarie University, 2109 NSW, Australia.
5Institut für Physik und Astronomie, University of Potsdam, 14476 Potsdam, Germany.

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The spin-boson model usually considers a spin coupled to a single bosonic bath. However, some physical situations require coupling of the spin to multiple environments. For example, spins interacting with phonons in three-dimensional magnetic materials. Here, we consider a spin coupled isotropically to three independent baths. We show that coupling to multiple baths can significantly increase entanglement between the spin and its environment at zero temperature. The effect of this is to reduce the spin's expectation values in the mean force equilibrium state. In contrast, the classical three-bath spin equilibrium state turns out to be entirely independent of the environmental coupling. These results reveal purely quantum effects that can arise from multi-bath couplings, with potential applications in a wide range of settings, such as magnetic materials.

The spin-boson model describes the physics of a two-level system, such as a spin, which interacts with a single bosonic environment. However, in many physical situations, a spin couples to multiple environments. For example, the environment for a spin in a magnetic material, commonly modelled with the Landau-Lifshitz-Gilbert equation, consists of phonons and magnons, and couples to all three components of the spin.

In this paper, we establish the impact of coupling each of the three spin components to an independent environment and compare to the standard single-environment spin boson model. We show that coupling to multiple environments can significantly increase the entanglement between spin and environment at zero temperature. Practically, this entanglement leads to a reduction in the effective spin length. Furthermore, whilst the state of the quantum spin varies with environmental coupling strength, we find that the isotropic classical analogue is invariant. These results reveal purely quantum effects that can arise from multi-bath couplings.

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Cited by

[1] F. Hartmann, S. Scali, and J. Anders, "Anisotropic signatures in the spin-boson model", Physical Review B 108 18, 184402 (2023).

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