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 in 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 a triangular superlattice with a small hopping (of approximately 10 Kelvin), with tunable density of holes, we explore the Hubbard model on the triangular lattice in the regime $t \ll U$ for intermediate temperatures $t < T < U$. Using finite temperature Lanczos calculations, we quantitatively recover the observed trends in the reported Curie-Weiss temperature $\Theta_c$ at various charge densities using the reported value of interaction strength $U/t=20$. In particular, we focus on the large increase of $|\Theta_c|$ on doping away from the half-filled antiferromagnet, with a sign change above half-filling, which signals the appearance of ferromagnetism. Remnants of the underlying zero temperature phase transition, which we explore with ground state DMRG, appear as crossovers at intermediate temperature.