Orbital-Selective Mott and Antiferromagnetic Phases in Diagonally Compressed Kagome Lattice

We perform determinant quantum Monte Carlo simulations of the half-filled Hubbard model on a diagonally compressed kagome lattice, introducing exponential decay long-range hopping $t(r)=t_0\exp (-r\mathrm{/}{r}_0)$ to account for the evolving bond length. By varying the lattice angle $\theta$ and the on-site interaction $U$, double occupancy, charge compressibility, and spin-spin correlation functions of the whole system and each sub-lattice are measured. We find that geometric compression induces a clear sublattice differentiation: for $\theta \gtrsim {52}^{\circ }$, the A sublattice establishes long-range hoppings, which in turn suppresses the metallic behavior of the $B\mathrm{/}C$ sublattice and drives a selective Mott transition; for $\theta \lesssim {52}^{\circ }$, the $B$-$C$ chains develop long-range antiferromagnetic correlations within the finite-size simulations, which in turn suppresses the metallic behavior of the $A$ sublattice and drives a selective Mott transition. The critical interaction $U_A^c$ for the $A$ sites decreases sharply near the onset of $B$-$C$ antiferromagnetic correlations, while $U_{B\mathrm{/}C}^c$ increases. These competing orders give rise to an orbital-selective Mott phase and a rich $U$-$\theta$ phase diagram featuring paramagnetic-metal, paramagnetic-Mott, antiferromagnetic-metal, and antiferromagnetic-Mott states. Our results highlight the complex interplay between lattice geometry, magnetic frustration, and strong correlations in frustrated two-dimensional systems.