On the Metastability of the Mean-Field Interchange Model for Local Dimension $\geq 3$

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 $d\geq 3$ and single-site generalized Pauli couplings exhibits this behavior. The dynamical phase diagram is beholden to two distinguished inverse temperatures, $β<em>{\mathrm{min}}(d)$ and $β=d$, with the static first-order phase transition lying between them. At low and high temperatures surrounding the interval $(β</em>{\mathrm{min}}(d),d)$, 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 $Ω(n<sup>{-1})$. Thus, exponential slowdown arises entirely from the Young diagram chain.