Estudo de propriedades do modelo exatamente solúvel de Hatsugai-Kohmoto bidimensional

Abstract

In this work, we examine various ordering tendencies exhibited by the exactly solvable two-dimensional Hatsugai–Kohmoto (HK) model on a square lattice. To this end, we investigate the competition among superconducting (SC), charge-density-wave (CDW), and pair-densitywave (PDW) orders as a function of the interaction strength, the doping, the magnetic field, and uniaxial strain. Consequently, the analysis confirms the interconnected nature of the fluctuations associated with the CDW and PDW phases for intermediate to strong couplings. It is also shown that, while the application of a magnetic field favors the formation of a CDW phase and subsequently enables the emergence of a PDW phase as a secondary order, strain effects favor the formation of a unidirectional PDW phase as the primary order, with a unidirectional CDW phase appearing only as a subdominant instability. Another line of investigation in this work concerns the analysis of the quantum Fisher information (QFI) as a function of temperature in the HK model. This quantity enables the detection, for instance, of the presence or absence of multipartite entanglement in the Mottinsulating phase that arises at half-filling for strong interactions, as well as in the non-Fermiliquid metallic phase that emerges at finite doping. The analysis of the QFI derivatives reveals a characteristic discontinuity in the transition between the weak- and strong-coupling regimes, suggesting an important influence of the Mott-insulating phase on the electronic phases that emerge as low-temperature instabilities of the non-Fermi-liquid-like metallic state exhibited by the system. All these results highlight the value of the HK model as a useful analytical platform for investigating, within an exact approach, the emergence of a Mott-insulating phase, a non-Fermiliquid-like phase, charge-ordered phases with d-wave symmetry, unconventional superconductivity, and other fundamental aspects related to strongly interacting electronic models. Finally, we briefly discuss an orbital generalization of the HK model, which has recently been identified as highly relevant for describing the properties of the paradigmatic two-dimensional Hubbard model.