QUANTUM MATTER SEMINAR

FERROMAGNETISM IN HUBBARD-LIKE MODELS

IN TWO-DIMENSIONAL LATTICES

Ravin Bhatt, Princeton University

The two-dimensional Hubbard model for electrons is known to have an antiferromagnetically ordered ground state at half-filling (one electron per site) for both square and triangular lattices. Interestingly, for infinite e-e repulsion (U = ¥), it was shown by Nagaoka almost six decades back, that putting a single hole in the half-filled Hubbard model on bipartite lattices (e.g. square lattice in 2D), results in a ferromagnetic ground state. However, to-date, no analog of Nagaoka ferromagnetism has been seen in naturally occurring solid-state materials, presumably because U is not large enough. One exception is lightly doped semiconductors, where the ratio of e-e interaction (U) and hopping (t), U/t, can be made arbitrarily large, but in that system, the dopants are not on a lattice, but are randomly distributed, precluding Nagaoka type ferromagnetism.

In recent years, two synthetic platforms have emerged to test the possibility of Nagaoka type ferromagnetism in finite two-dimensional lattices described by Hubbard-like Hamiltonians: (a) ultracold fermionic atoms in optical lattices, and (b) a superlattice of quantum dots or monodispersed dopant clusters in semiconductors. In this work, we describe our attempts to model the behavior of such engineered structures using appropriate Hubbard-like Hamiltonians. We use the Density-Matrix Renormalization Group (DMRG) method to determine the magnetic structure of the ground states of large but finite sized square and triangular lattices, using additional tools such as pinning potentials, to achieve a detailed understanding of ferromagnetism in the Hubbard model. We find that in the strongly interacting regime, ferromagnetism at long length scales emerges from local ferromagnetic polarons dressing the charge carriers. Our results are in quantitative agreement with experiments on ultracold atoms on a triangular lattice, and provide specific suggestions for seeing ferromagnetic behavior in square arrays in semiconductor platforms.