Semiclassical representation of the Hubbard model

By revisiting the path-integral formulation of the Hubbard model, we propose a theoretical approach based on a semiclassical approximation employing an unconventional coherent-state representation. Within this framework, a subset of the dynamical variables is treated as static, yielding a nonperturbative scheme that is applicable at finite temperature, incorporates intersite correlations, and can be naturally extended to multiorbital systems. We assess the validity of the approximation by comparing its results with exact solutions for one- and two-site systems, focusing in particular on the particle number, double occupancy, hopping amplitude, and spin correlations, and find that the present approach qualitatively reproduces the exact behavior. Quantitatively, deviations arise, which is associated with the continuum (non-discretized) character of the underlying density of states. Furthermore, we derive the exact transformation associated with the coherent-state construction, thereby providing additional insight into the representation of the Hubbard model.