Correspondence between excited energy eigenstates and local minima of the energy landscape in quantum spin systems

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.