  Engineering long-range interactions in experimental platforms has been
achieved with great success in a large variety of quantum systems in recent
years. Inspired by this progress, we propose a generalization of the classical
Hamiltonian mean-field model to fermionic particles. We study the phase diagram
and thermodynamic properties of the model in the canonical ensemble for
ferromagnetic interactions as a function of temperature and hopping. At zero
temperature, small charge fluctuations drive the many-body system through a
first order quantum phase transition from an ordered to a disordered phase at
zero temperature. At higher temperatures, the fluctuation-induced phase
transition remains first order initially and switches to second order only at a
tricritical point. Our results offer an intriguing example of tricriticality in
a quantum system with long-range couplings, which bears direct experimental
relevance. The analysis is performed by exact diagonalization and mean-field
theory.
