Quantum Mean-Fields Spin Systems in a Random External Field

In this work, we consider general exchangeable quantum mean-field Hamiltonian such as the prominent quantum Curie-Weiss model under the influence of a random external field. Despite being arguably the simplest class of disordered quantum systems, the random external field breaks the symmetry of the mean-field Hamiltonian and hence standard quantum de Finetti type or semiclassical arguments are not directly applicable. We introduce a novel strategy in this context, which can be seen as non-commutative large deviation analysis, allowing us to characterize the limiting free energy in terms of a simple and explicit variational formula. The proposed method is general enough to be used for other classes of mean-field models such as multi species Hamiltonians.