Quantum Phase Diagram of the Hamiltonian Mean Field Model

Quantum many body systems with long range interactions (LRIs) are increasingly both being realized in laboratory experiments, and recieving theoretical interest. The Hamiltonian Mean Field model (HMFm) is a 1-D model that has been extremely successful at helping to shed light on classical features of LRI systems such as self-gravitating fluids, and neutral plasmas. In this talk we investigate the bosonic HMFm's quantum phase diagram. Ignoring density and phase fluctuations, Chavanis (EPJ 2011) argued that a quantum phase transition, driven by a competition between LRIs and quantum pressure, is present. The ordered phase breaks translational symmetry, and is naively forbidden by the Mermin-Wagner theorem, however this allowed for LRI systems (e.g. Maghrebi PRL 119). In this talk we will discuss how to go beyond the mean-field approximation used by Chavanis, both numerically and analytically, and investigate the role of fluctuations in modifying the model's phase diagram, and the ultimate fate of the ordered phase.