  The quantum-classical correspondence between local minima on the classical
energy landscape and excited eigenstates in the energy spectrum is studied
within the context of many-body quantum spin systems. In mean-field
approximations of a quantum problem, one usually focuses on attaining the
global minimum of the resulting energy function, while other minimum solutions
are usually ignored. For frustrated systems, a strict distinction between
global and local minimum is often not tenable since first-order type
transitions can interchange the roles played by two different minima. This begs
the question of whether there is any physical interpretation for the local
minima encountered in mean-field approximations of quantum systems. We look at
the problem from the perspective of quantum spin systems. Two models are
studied, a frustrated model with quenched disorder, and a pure system without
frustration. Accurate classical energies of the minima are compared with the
full spectrum of energy levels, allowing us to search for signs of
correspondence between them. It is found that the local minima can generally be
interpreted as excited energy eigenstates. Instances of spurious minima are
also reported.
