We calculate the spin correlations that result from the motion of a single dopant in the hard-core Fermi-Hubbard model, as the geometry evolves from a square to a triangular lattice. In particular, we consider the square lattice with an additional hopping along one diagonal, whose strength is continuously varied. We use a high-temperature expansion which expresses the partition function as a sum over closed paths taken by the dopant. We sample thousands of diagrams in the space of closed paths using the quantum Monte Carlo approach of Raghavan and Elser [Phys. Rev. Lett. 75, 4083 (1995)], which is free of finite-size effects and allows us to simulate temperatures as low as $T\sim 0.3\left|t\right|$, even in cases where there is a sign problem. For the case of a hole dopant, we find a crossover from kinetic ferromagnetism to kinetic antiferromagnetism as the geometry is tuned from square to triangular, which can be observed in current quantum gas microscopes.

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• Fermi gases
• Magnetism
• Polarons
• Quasiparticles & collective excitations
• Thermal properties
• Strongly correlated systems
• Quantum Monte Carlo