Magnetism and metallicity in the doped large-U triangular Hubbard model

With the advent of moire superlattice and cold atom emulators, the question of the nature of magnetic and conducting phases of doped triangular lattice systems both at zero and finite temperature has seen renewed interest [e.g., Y. Tang et al., Nature 579, 353 (2020), M. Xu et al., Nature 620, 971 (2023)], but still remains largely unexplored. Accurate treatments of effective model Hamiltonians have provided critical insights into the qualitative nature of these phases while also quantitatively explaining experiments [e.g., K. Lee et al., Phys. Rev. B 107, 235105 (2023)]. Inspired by these developments, we study the single-band Hubbard and t-J Hamiltonians on the triangular lattice, using a combination of ground state DMRG and finite temperature techniques to address the nature of magnetism and metallicity in the large U limit. We build on the framework of the Haerter-Shastry theory of kinetic frustration (valid for low hole density) by investigating the problem of multiple holes numerically for both infinite and large U, finding many qualitative similarities between them. We characterize the nature of metallicity by computing the quasiparticle residue and the charge structure factor and determine their impact on finite temperature properties, finding that a simple renormalization factor captures several aspects of our numerics. We identify signatures of magnetic order in the ground state as a function of hole density and clarify the interplay between charge and spin degrees of freedom.