  We show that strong electron-electron interactions in cavity-coupled quantum
materials can enable collectively enhanced light-matter interactions with
ultrastrong effective coupling strengths. As a paradigmatic example we consider
a Fermi-Hubbard model coupled to a single-mode cavity and find that resonant
electron-cavity interactions result in the formation of a quasi-continuum of
polariton branches. The vacuum Rabi splitting of the two outermost branches is
collectively enhanced and scales with $g_{\text{eff}}\propto\sqrt{2L}$, where
$L$ is the number of electronic sites, and the maximal achievable value for
$g_{\text{eff}}$ is determined by the volume of the unit cell of the crystal.
We find that $g_{\text{eff}}$ for existing quantum materials can by far exceed
the width of the first excited Hubbard band. This effect can be experimentally
observed via measurements of the optical conductivity and does not require
ultra-strong coupling on the single-electron level. Quantum correlations in the
electronic ground state as well as the microscopic nature of the light-matter
interaction enhance the collective light-matter interaction compared to an
ensemble of independent two-level atoms interacting with a cavity mode.
