Seminarium Fizyki Materii Skondensowanej

Exactly solvable models play an important role in the understanding of physical phenomena, as they often provide reference points and intuitions for more accurate, but usually not solvable in general, models. One such model is the Hasugai-Kohmoto model. It circumvents the biggest obstacle of the Hubbard model, the non-commutative nature of the interaction and kinetic terms, by postulating Hubbard-like interaction in the momentum space. Despite this simplification, it is capable of describing a Mott gap opening and the model belongs to the same high-temperature universality class as the Hubbard model. Yet, the exact solvability of this model relies on a silent assumption of the periodicity of the system under consideration. In my talk, I will address this interaction from the real-space perspective and discuss its peculiarities. One of which is that it is highly sensitive to the boundary conditions and their influence is felt even in the thermodynamic limit. For example, the presence of the hard edges leads to the formation of a ferromagnetic ground state of the gapped phase, which is not the case for the periodic system. I will also present other properties of this model and put them in the context of the analogous results for the Hubbard model.