Triangular lattice Hubbard model physics at intermediate temperatures

Moire systems offer an exciting playground to study many-body effects of strongly correlated electrons in regimes that are not easily accessible conventional material settings. Motivated by a recent experiment on $\text{WSe}_2/\text{WS}_2$ moire bilayers [Y. Tang et al., Nature 579, 353-358 (2020)], which realizes triangular superlattice with small hopping (of approximately 10 Kelvin), tunable density holes, we explore the Hubbard model lattice for intermediate temperatures $t \lesssim T < U$. Employing finite temperature Lanczos calculations, and closely following fitting protocols used experiment, recover observed trends reported Curie-Weiss $\Theta$ filling, using interaction strength $U/t=20$. We focus large increase $|\Theta|$ decreasing below half filling sign change at higher fillings, signals onset ferromagnetism. The is also seen $t$-$J$ (the low energy limit model) range, clarify opposite trend its high limit. Differences between low, discussed. Our numerical calculations capture crossover short-range antiferromagnetic ferromagnetic order regime, result broadly consistent experimental findings. find this behavior finite-temperature remnant underlying zero phase transition, ground state matrix renormalization group calculations. provide evidence ferromagnetism characterized weak (but robust) correlations explain experiment.