Local entropies across the Mott transition in an exactly solvable model

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 the intractability of the Hubbard model for d>1. In order to maintain a nontrivial 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 s1 and s2, as well as the entropy density s, of the ground state near the Mott transition. At low temperatures in the two-dimensional Hubbard model, Walsh et al. [Phys. Rev. B 99, 075122 (2019)PRBMDO2469-995010.1103/PhysRevB.99.075122] observed numerically that s1 and s increase continuously into the metal, across a first-order Mott transition. In the Hatsugai-Kohmoto model, s1 acquires the constant value ln 4 even at the Mott transition. On the other hand, s2 and s each act as a sharp signal of the Mott transition, in any dimension, by decreasing at the transition into the metal. Specifically, we find that in one dimension, s2 and s exhibit kinks at the transition while in two dimensions, only s exhibits a kink.