2026/07/23 by Joao Basso, Thiago Bergamaschi, Lin Lin +2
#quant-ph #math-ph #math.MP
The mean-field Heisenberg ferromagnet is a quantum spin model on the complete graph with isotropic spin-1/2 interactions. This non-commuting Hamiltonian is permutation and SU(2) invariant, and its Gibbs states undergo an SU(2) symmetry breaking phase transition at inverse temperature β=2. We consider the associated Davies generator, a canonical model of open-system thermalization, and prove tight asymptotic estimates for its spectral gap at all noncritical temperatures. For fixed β<2, the gap as a function of number of qubits n is Θ(1), while for fixed β>2 the gap is Θ(n-1). The matching upper bound of the spectral gap is witnessed by the total magnetization order parameter, suggesting that the low-temperature (β>2) slowdown is associated with broken continuous symmetry. Two key ingredients in our approach are a comparison argument, which introduces auxiliary generators to bound dissipation on nontrivial representations of the symmetry groups SU(2) and Sn, and a decomposition of the space of observables into spherical tensor operators to reveal a form of monotonicity.