Kinetic Magnetism in the Crossover between the Square and Triangular Lattice Fermi-Hubbard Models

We study the hard-core Fermi-Hubbard model in the crossover between square and triangular lattices near half-filling. In particular, we consider the square lattice with an additional hopping along one diagonal, whose strength is continuously varied.

As was recognized by Nagaoka in the 1960s, on the square lattice the presence of a single hole leads to ferromagnetic spin ordering. On the triangular lattice, geometric frustration instead leads to a spin-singlet ground state, which can be associated with a 120-degree spiral order. On lattices which interpolate between square and triangular, there is a phase transition at which the ferromagnetic order becomes unstable to a spin spiral. We model this instability, finding the exact critical point.

We then calculate the finite-temperature spin correlations that result from the motion of a single dopant (hole or particle) in the same model. 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 ~ 0.3|t|, 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 occurs at a similar value as the critical point. This crossover can be observed in current quantum gas microscopes.