{'fraction_non_alphanumeric': 0.027600849256900213, 'fraction_numerical': 0.004246284501061571, 'mean_word_length': 5.256637168141593, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
An extension of Tasaki's flat-band model

It is widely believed that the spin-independent Coulomb interaction and the Pauli exclusion principle can generate ferromagnetism in itinerant electron systems. One of the motivations to study the Hubbard model has been to establish and understand the generation of ferromagnetism in simplified situations taking account of these effects [1]. Mielke [2] and Tasaki [3], independently, presented Hubbard models which exhibit saturated ferromagnetism. These models have a common feature that single electron bands contain dispersionless bands, and are called flat-band models. In [4] and [5], Tasaki also discovered nonsingular Hubbard models which exhibit ferromagnetism. Recently Tanaka and Ueda succeeded in proving the existence of saturated ferromagnetism in a Hubbard model obtained by adding extra hopping terms to Mielke’s flat-band model on the kagomé lattice [6]. In this paper, we treat a class of Hubbard models in arbitrary dimensions with finite U and finite-range hopping. We prove that the models exhibit ferromagnetism in their ground states at two distinct electron numbers. The models are extensions of Tasaki’s flatband models, but the mechanism that leads to ferromagnetism is slightly different from that in Tasaki’s models. In our model, single-electron states each of which is localized around internal sites in a single cell play an important role.