Metal-insulator transition and intermediate phases in the kagome lattice Hubbard model

Motivated by the recent discovery of metallic kagome lattice materials, ${\mathrm{AV}}_{3}{\mathrm{Sb}}_{5}$ (A = K, Rb, Cs), we investigate ground state half-filled Hubbard model employing density-matrix renormalization group method. We identify a metal-insulator transition around $U\ensuremath{\sim}{U}_{c1}$ and four distinct phases as function $U/t$ on narrower cylinders, including phase at $U<{U}_{c1}$, two insulating intermediate (a translational symmetry breaking ${U}_{c1}<U<{U}_{c2}$ quantum spin liquid ${U}_{c2}<U<{U}_{c3}$), antiferromagnetic $U>{U}_{c3}$. confirm that is robust for wider while smoothly connected to with increasing system width. Moreover, our numerical observations indicate continuous ${U}_{c1}$ whose nature consistent Slater's scenario. The magnetic between ${U}_{c2}$ first order. Our findings may provide insights into exotic materials.