On the Metastability of the Mean-Field Interchange Model for Local Dimension ≥ 3
Abstract
Many quantum systems are believed to thermalize slowly at low temperatures due to the existence of metastable phases. However, there are cases where further cooling can restore polynomial-time thermalization: we demonstrate that the Davies dynamics of the mean-field interchange model with local dimension d≥ 3 and single-site generalized Pauli couplings exhibits this behavior. The dynamical phase diagram is beholden to two distinguished inverse temperatures, βmin(d) and β=d, with the static first-order phase transition lying between them. At low and high temperatures surrounding the interval (βmin(d),d), the spectral gap of the Davies generator is bounded below by an inverse polynomial in system size n. Meanwhile, in this interval, the gap vanishes exponentially in n, indicating metastability. The proof uses Schur-Weyl duality to decompose the Davies generator into a classical Markov generator on Young diagrams, and the restriction to the remaining symmetry sectors whose gap is Ω(n−1). Thus, exponential slowdown arises entirely from the Young diagram chain.
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BibTeX
@misc{escobar2026metastability,
title = {{On the Metastability of the Mean-Field Interchange Model for Local Dimension $\geq 3$}},
author = {Sergio Escobar and Lin Lin and Michael Ragone and Kevin D. Stubbs},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01987},
eprint = {2610.01987},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01987},
}
RIS
TY - UNPB
TI - On the Metastability of the Mean-Field Interchange Model for Local Dimension ≥ 3
AU - Sergio Escobar
AU - Lin Lin
AU - Michael Ragone
AU - Kevin D. Stubbs
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.01987
UR - https://arxiv.org/abs/2610.01987
AB - Many quantum systems are believed to thermalize slowly at low temperatures due to the existence of metastable phases. However, there are cases where further cooling can restore polynomial-time thermalization: we demonstrate that the Davies dynamics of the mean-field interchange model with local dimension d≥ 3 and single-site generalized Pauli couplings exhibits this behavior. The dynamical phase diagram is beholden to two distinguished inverse temperatures, β_min(d) and β=d, with the static first-order phase transition lying between them. At low and high temperatures surrounding the interval (β_min(d),d), the spectral gap of the Davies generator is bounded below by an inverse polynomial in system size n. Meanwhile, in this interval, the gap vanishes exponentially in n, indicating metastability. The proof uses Schur-Weyl duality to decompose the Davies generator into a classical Markov generator on Young diagrams, and the restriction to the remaining symmetry sectors whose gap is Ω(n^−1). Thus, exponential slowdown arises entirely from the Young diagram chain.
ER -