Kinetic magnetism in the crossover between the square and triangular lattice Fermi-Hubbard models

TL;DR

This study investigates how the magnetic correlations caused by a dopant in the Fermi-Hubbard model change as the lattice geometry transitions from square to triangular, revealing a crossover from ferromagnetic to antiferromagnetic behavior.

Contribution

It introduces a high-temperature expansion combined with quantum Monte Carlo to analyze spin correlations in a tunable lattice geometry, overcoming finite-size and sign problem issues.

Findings

Crossover from kinetic ferromagnetism to antiferromagnetism observed

Method enables simulations at low temperatures without finite-size effects

Results applicable to current quantum gas microscope experiments

Abstract

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 [1,2], which is free of finite-size effects and allows us to simulate temperatures as low as $T \sim 0.3|t|$, 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 can be observed in current quantum gas microscopes.