PreprintarXiv licencearXiv
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/√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.
Related
- Exact phase diagram of the XXZ Heisenberg chain in a staggered magnetic field
- Schwinger boson perturbation theory for spin-S Kitaev-Heisenberg magnets: phase diagram and dynamical response near Kitaev spin liquids
- Hypercontractivity and entropy decay for infinite-dimensional quantum Gibbs samplers
- Thermodynamic Cyclic Processes with Markov Samplers in Bayesian Inference
- Dephasing-Enhanced Response and Phase Transitions in Quantum Boltzmann Samplers
BibTeX
@misc{raikovich2026complete,
title = {{The complete phase diagram of detailed-balanced Gibbs samplers for the mean-field Heisenberg model}},
author = {Levente Raikovich and József Mák and Csaba Czabán and András Gilyén},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06818},
eprint = {2610.06818},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06818},
}
RIS
TY - UNPB
TI - The complete phase diagram of detailed-balanced Gibbs samplers for the mean-field Heisenberg model
AU - Levente Raikovich
AU - József Mák
AU - Csaba Czabán
AU - András Gilyén
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06818
UR - https://arxiv.org/abs/2610.06818
AB - 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/√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.
ER -