The complete phase diagram of detailed-balanced Gibbs samplers for the mean-field Heisenberg model

Abstract:We study the spectral gap of recently discovered families of KMS-detailed-balanced Gibbs-sampler Lindbladians for the mean-field Heisenberg model on $n$ spins. We show that the spectral gaps of these natural families of Lindbladians admit the same phase diagram: the gap is constant above the critical temperature (i.e., in the disordered phase), scales as $1/\sqrt{n}$ at the critical temperature, and as $1/n$ below the critical temperature (i.e., in the ordered phase). Our result builds on and extends the recent work of Basso et al.~(2026) which characterized this phase diagram for the GNS-detailed-balanced Davies generator, but only partially resolved the gap scaling at the critical temperature.

arXiv:2610.06818 [quant-ph]

(or arXiv:2610.06818v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.06818 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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