Fate of entanglement in open quantum spin liquid: Time evolution of its genuine multipartite negativity upon sudden coupling to a dissipative bosonic environment

Many-body entanglement properties of quantum spin liquids (QSLs), persisting at arbitrarily long distances, have been intensely explored over the past two decades, but mostly for QSLs viewed as {\em closed} quantum systems. However, in experiments and potential quantum computing applications, candidate materials for this exotic phase of quantum matter will always interact with a dissipative environment, such as the one generated by bosonic quasiparticles in solids at finite temperature. Here we investigate both the {\em stability} and {\em spatial distribution} of entanglement for the Kitaev model of QSL, which is made {\em open} by its sudden coupling to an infinite bosonic bath of Caldeira-Leggett type and then time-evolved in both Markovian and non-Markovian regimes. From the time-dependent density matrix of QSL subregions, we extract genuine multipartite negativity (GMN), quantum Fisher information, spin-spin correlators, and the expectation value (EV) of the Wilson loop operator. In particular, time dependence of GMN offers the most penetrating insights: ({\em i}) in the Markovian regime, it remains nonzero only in hexagonal loopy subregions of QSL (as also discovered very recently for closed QSLs), eventually vanishing on the same timescale on which the EV of the Wilson loop operator vanishes; ({\em ii}) in the non-Markovian regime with pronounced memory effects, surprisingly, GMN remains nonzero up to much higher temperatures while also remaining zero in non-loopy subregions. In addition, the non-Markovian dynamics generates emergent interactions between spins, thereby opening avenues for tailoring properties of QSL via engineering of dissipation.

💡 Research Summary

The paper investigates how multipartite quantum entanglement in a Kitaev quantum spin liquid (QSL) behaves when the system is suddenly coupled to an infinite bosonic bath of Caldeira‑Leggett type. Two dynamical regimes are considered: a weak‑coupling, short‑memory Markovian regime described by a universal Lindblad quantum master equation (QME), and a strong‑coupling, long‑memory non‑Markovian regime treated with tensor‑network techniques (process‑tensor MPO combined with TEBD) and, for the steady‑state limit, a reaction‑coordinate plus polaron transformation that yields an effective Hamiltonian.

The authors compute, from the time‑dependent reduced density matrix of selected subregions, four observables: (i) genuine multipartite negativity (GMN) for up to six spins, (ii) quantum Fisher information (QFI) for a wave‑vector mode, (iii) equal‑time spin‑spin correlators ⟨σ_i^z σ_j^z⟩, and (iv) the expectation value of the Wilson loop operator ⟨W_p⟩, which signals the underlying Z₂ gauge structure.

In the Markovian case, GMN is non‑zero only for hexagonal “loop” subregions (six spins forming a honeycomb plaquette) and vanishes for non‑loop subregions (five spins). The decay of GMN follows the same timescale on which the Wilson loop expectation collapses, indicating that the loop‑shaped region uniquely protects multipartite entanglement against weak dissipation. QFI and spin‑spin correlations decay synchronously, confirming a global loss of quantum coherence.

In contrast, the non‑Markovian dynamics exhibits pronounced memory effects. Even at temperatures as high as T≈0.7 J_z (significantly above the Markovian threshold), GMN remains finite for the loop subregion, while it stays zero for non‑loop subregions. The Wilson loop expectation decays much more slowly, sometimes reaching a non‑zero plateau, and QFI retains appreciable values, demonstrating that strong system‑bath coupling can actually stabilize multipartite entanglement in specific geometries. Moreover, the reaction‑coordinate analysis reveals emergent renormalized exchange interactions: the effective Kitaev couplings are modified, generating longer‑range spin‑spin terms that are absent in the closed model. This “environment‑induced interaction” suggests a route to engineer the Hamiltonian of a QSL by tailoring the spectral density of the bath.

A comparative study with an open quantum antiferromagnet on the same honeycomb lattice shows that, unlike the QSL, the antiferromagnet retains non‑zero GMN in both loop and non‑loop regions under Markovian dissipation, highlighting the special topological protection of multipartite entanglement in the Kitaev liquid.

The work therefore provides the first systematic, quantitative picture of how genuine multipartite entanglement survives (or disappears) in an open QSL. By linking GMN dynamics to experimentally accessible quantities such as QFI and Wilson loop measurements, the authors outline realistic diagnostic protocols for solid‑state QSL candidates. The findings also open the possibility of “dissipation engineering”: by designing structured bosonic environments (e.g., phononic crystals, cavity‑mediated baths) one could enhance memory effects, suppress decoherence, and even induce desirable effective interactions, paving the way for robust topological quantum memories and quantum simulators based on spin liquids.