Stability of Itinerant Ferromagnetism versus Antiferromagnetism in the Single Band Hubbard Model

Hal Tasaki

Hal Tasaki

Akinori Tanaka, Hal Tasaki

Pavol Farkašovský

Since its introduction in 1963, the Hubbard model has becomes one of the most popular models used in the literature to study cooperative phenomena in narrow-band metals (ferromagnetism, metal-insulator transitions, charge-density waves, high-Tc superconductivity). Amongst all these cooperative phenomena, the problem of itinerant ferromagnetism in the Hubbard model has the longest history. However, in spite of an impressive research activity in the past, the underlying physics (microscopic mechanisms) that leads to the stabilization of itinerant ferromagnetism in Hubbard model (narrow-band metals) is still far from being understood. In this review we present our numerical results concerning this subject, which have been reached by small cluster exact diagonalization, density matrix renormalization group and quantum Monte Carlo calculations within various extensions of the Hubbard model. Particular attention is paid to a description of crucial mechanisms (interactions) that support the stabilization of the ferromagnetic state, and namely: (i) the long-range hopping, (ii) the correlated hopping, (iii) the long-range Coulomb interaction, (iv) the flat bands and (v) the lattice structure. Most of the presented results have been obtained for the one-dimensional case, but the influence of the increasing dimension of the system on the ferromagnetic state is also intensively discussed.

Koichi Kusakabe, Hideo Aoki

Junha Kang, Taekoo Oh, Junhyun Lee +1 more

Despite its abundance in nature, predicting the occurrence of ferromagnetism in the ground state is possible only under very limited conditions such as in a flat band system with repulsive interaction or in a band with a single hole under infinitely large Coulomb repulsion, etc. Here, we propose a general condition to achieve saturated ferromagnetism based on the quantum geometry of electronic wave functions in itinerant electron systems. By analyzing the spin excitations of multi-band repulsive Hubbard models with an integer band filling, relevant to either ferromagnetic insulators or semimetals, we show that quantum geometry stabilizes the Goldstone mode in the strongly correlated limit. Our theory indicates the stability of ferromagnetism in a large class of insulators and semimetals other than the previously studied flat band systems and their variants. Moreover, we rigorously prove that saturated ferromagnetism is forbidden in any system with trivial quantum geometry, which includes every half-filled system. We believe that our findings reveal a profound connection between quantum geometry and ferromagnetism, which can be extended to various symmetry-broken ground states in itinerant electronic systems.