  We study entanglement in the Hatsugai-Kohmoto model, which exhibits a
continuous interaction-driven Mott transition. By virtue of the all-to-all
nature of its center-of-mass conserving interactions, the model lacks dynamical
spectral weight transfer, which is the key to intractability of the Hubbard
model for $d>1$. In order to maintain a non-trivial Mott-like electron
propagator, SU(2) symmetry is preserved in the Hamiltonian, leading to a ground
state that is mixed on both sides of the phase transition. Because of this
mixture, even the metal in this model is unentangled between any pair of sites,
unlike free fermions whose ground state carries a filling-dependent site-site
entanglement. We focus on the scaling behavior of the one- and two-site
entropies $s_1$ and $s_2$, as well as the entropy density $s$, of the ground
state near the Mott transition. At low temperatures in the two-dimensional
Hubbard model, it was observed numerically (Walsh et al., 2018,
arXiv:1807.10409) that $s_1$ and $s$ increase continuously into the metal,
across a first-order Mott transition. In the Hatsugai-Kohmoto model, $s_1$
acquires the constant value $\ln4$ even at the Mott transition. The ground
state's non-trivial entanglement structure is manifest in $s_2$ and $s$ which
decrease into the metal, and thereby act as sharp signals of the Mott
transition in any dimension. Specifically, we find that in one dimension, $s_2$
and $s$ exhibit kinks at the transition while in $d=2$, only $s$ exhibits a
kink.
