Interplay of magnetic and thermodynamic responses in the kagome-triangular system

Inspired by the recent experimental progress in pyrochlore derivative RE$_3$Sb$_3$A$_2$O$_{14}$ (A = Mg, Zn), we investigate the Hubbard model on the kagome lattice with an additional hopping $t'/t$, which enables continuous interpolation between the kagome and triangular lattices by using determinant quantum Monte Carlo simulations. We find that increasing $t'/t$ suppresses the nearest-neighbor antiferromagnetic correlations. Concurrently, the next-nearest-neighbor antiferromagnetic correlations are enhanced and closely associated with the emergence of a pronounced low-temperature peak in the specific heat. Increasing on-site interaction $U$ enhances magnetic correlations and shifts the associated $t'/t$ crossover points to larger values. We also discuss the sign problem to clarify which parameter region of our numerical simulations is accessible and reliable. Our results uncover the competition between frustration and correlations and the interplay of magnetic and thermodynamic responses in the kagome lattice, providing insights into correlated states in frustrated materials.