  The suppression of antiferromagnetic ordering in geometrically frustrated
Hubbard models leads to a variety of exotic quantum phases including quantum
spin liquids and chiral states. Here, we focus on the Hubbard model on one of
the simplest frustrated lattice geometries, a triangular lattice. Motivated by
the recent realization of ultracold fermionic atoms in triangular optical
lattices, we study the properties of the triangular-lattice Hubbard model
through a Numerical Linked-Cluster Expansion algorithm. We investigate the Mott
insulator transition finding a critical interaction $U_c/t = 7.0(2)$ and use
spatial two- and three-point correlation functions to explore doped and
imbalanced systems. Our results demonstrate that many interesting features
occur at temperatures previously obtained for ultracold fermions in optical
lattices and are accessible by upcoming experiments. Our calculations will be
helpful for thermometry in ultracold atom quantum simulators and can guide
experimental searches for exotic quantum phases in atomic triangular Hubbard
quantum simulators.
