In this work, we investigate the electronic and magnetic properties of the two-dimensional square-octagon structure (2DSOS) using a tight-binding framework augmented by on-site Coulomb interaction. We examine how varying hopping parameters, magnetic flux, and interaction strength influence the system’s band structure, dynamical transverse spin susceptibility (DTSS), and static spin structure factor (SSSF). Our findings reveal the emergence of a flat band when the third-nearest-neighbor hopping term t 3 equals the nearest-neighbor hopping t 1 , significantly affecting the magnetic response. The frequency dependence of the DTSS demonstrates that both magnetic flux and Coulomb repulsion shift the resonance peaks to higher frequencies and suppress their intensities, indicating a suppression of low-energy spin fluctuations. Moreover, the temperature dependence of the SSSF underlines a transition from paramagnetic to ferromagnetic behavior as the ratio t 2 /t 1 increases. These results highlight the crucial role of electronic correlations and lattice geometry in shaping the spin dynamics of flat-band systems and offer valuable insights for designing future spintronic and correlated electron devices.
In this work, we investigate the electronic and magnetic properties of the two-dimensional square-octagon structure (2DSOS) using a tight-binding framework augmented by on-site Coulomb interaction. We examine how varying hopping parameters, magnetic flux, and interaction strength influence the system’s band structure, dynamical transverse spin susceptibility (DTSS), and static spin structure factor (SSSF). Our findings reveal the emergence of a flat band when the third-nearest-neighbor hopping term t 3 equals the nearest-neighbor hopping t 1 , significantly affecting the magnetic response. The frequency dependence of the DTSS demonstrates that both magnetic flux and Coulomb repulsion shift the resonance peaks to higher frequencies and suppress their intensities, indicating a suppression of low-energy spin fluctuations. Moreover, the temperature dependence of the SSSF underlines a transition from paramagnetic to ferromagnetic behavior as the ratio t 2 /t 1 increases. These results highlight the crucial role of electronic correlations and lattice geometry in shaping the spin dynamics of flat-band systems and offer valuable insights for designing future spintronic and correlated electron devices.
We explore the magnetic properties of a two-dimensional Hubbard model on an inhomogeneous square lattice, which provides a platform for tuning the bandwidth of the flat band. In its limit, this inhomogeneous square lattice turns into a Lieb lattice, and it exhibits abundant properties due to the flat band structure at the Fermi level. By using the determinant quantum Monte Carlo simulation, we calculate the spin susceptibility, double occupancy, magnetization, spin structure factor, and effective pairing interaction of the system. It is found that the antiferromagnetic correlation is suppressed by the inhomogeneous strength and that the ferromagnetic correlation is enhanced. Both the antiferromagnetic correlation and ferromagnetic correlation are enhanced as the interaction increases. It is also found that the effective d-wave pairing interaction is suppressed by the increasing inhomogeneity. In addition, we also study the thermodynamic properties of the inhomogeneous square lattice, and the calculation of specific heat provides good support for our point. Our intensive numerical results provide a rich magnetic phase diagram over both the inhomogeneity and interaction.
The magnetic susceptibility of the two-dimensional repulsive Hubbard model with nearest-neighbor hopping is investigated using the diagram technique developed for the case of strong correlations. In this technique, a power series in the hopping constant is used. At half-filling, the calculated zero-frequency susceptibility and the square of the site spin reproduce adequately the results of Monte Carlo simulations. Also, in agreement with numerical simulations, no evidence of ferromagnetic correlations was found in the considered range of electron concentrations $0.8\ensuremath{\lesssim}\overline{n}\ensuremath{\lesssim}1.2$ for the repulsion parameters $8\ensuremath{\mid}t\ensuremath{\mid}\ensuremath{\leqslant}U\ensuremath{\leqslant}16\ensuremath{\mid}t\ensuremath{\mid}$. However, for larger $U∕\ensuremath{\mid}t\ensuremath{\mid}$ and $\ensuremath{\mid}1\ensuremath{-}\overline{n}\ensuremath{\mid}\ensuremath{\approx}0.2$, the nearest-neighbor correlations become ferromagnetic. For $\overline{n}\ensuremath{\lesssim}0.94$ and $\overline{n}\ensuremath{\gtrsim}1.06$, the imaginary part of the real-frequency susceptibility becomes incommensurate for small frequencies. The incommensurability parameter grows with departure from half-filling and decreases with increasing frequency. This behavior of the susceptibility can explain the observed low-frequency incommensurate response observed in normal-state lanthanum cuprates.
In itinerant systems, electron-electron interactions may lead to the formation of local magnetic moments and their effective exchange coupling, which in turn gives rise to long-range magnetic order. Therefore, when moment formation is weakened, such as in the single-band Hubbard model on a square lattice with the on-site repulsion being randomly switched off on a fraction x of sites, magnetic order is suppressed beyond some critical xc, which was found to lie below the classical percolation threshold xc(perc,sq). Here we study dilute magnetism in flat band systems, namely, in the Hubbard model on a ``Lieb'' lattice. Interestingly, we show that magnetic order persists to x almost twice as large as the classical percolation threshold for the lattice, thus emphasizing the central role of electron itinerancy to the magnetic response. The analysis of the orbital-resolved order parameters reveals that the contribution of the fourfold coordinated ``d'' sites to magnetism is dramatically affected by dilution, while the localized ``p'' states of the flat band provide the dominant contribution to long-range correlations. We also examine the transport properties, which suggest the existence of an insulator-to-metal transition in the same range of the critical magnetic dilution.
Correlation and magnetic effects in narrow bands are studied using a new type of self-consistent cluster treatment of Hubbard's Hamiltonian. Here the dynamics consist of electron hopping between lattice sites and Coulomb repulsion between electrons only on the same site. The environment of the cluster is regarded as a particle reservoir, one such for each spin. Hopping between the cluster and reservoirs is described by fermion source terms. It is required that the thermodynamic average of the particle currents of each spin within the cluster equal the corresponding particle exchange between cluster and reservoir. Electron motion in the system is examined for varying ratios of the strength of the hopping to the Coulomb repulsion. This is done as a function of electron density, spin, temperature, and external magnetic field. A Mott transition is found under dynamical conditions close to those predicted by Hubbard when there is one particle per site. For 〈n〉 ≠ 1, no metal insulator transition exists although discontinuous changes in the cluster-reservoir coupling occur. The magnetic susceptibility of the cluster reveals antiferromagnetic behavior for 〈n〉 = 1, ferromagnetic behavior for 〈n〉 > 1, and partial ferromagnetic character for n < 1. This appears to agree with Nagoaka's results.
The description of a solid at a microscopic level is complex, involving the interaction of a huge number of its constituents, such as ions or electrons. The Hubbard model used in this research describes interacting electrons in narrow energy bands, with application to problems as diverse as high – Tc superconductivity, band magnetism and the metal-insulator transition. This research seeks to solve one of the most challenging problems in Theoretical physics which is to describe electronic correlations. In this research the t – U Hubbard model is used to solve analytically and numerically using the exact diagonalization techniquesThis research work focused on the spin interaction and magnetic behavior of some systems and it is therefore an investigation into the various phenomena seen in the phase diagram of ferromagnetic systems. We studied the 2 electrons on 2 sites, 2 electrons on 3 sites and 2 electrons on 4 sites all in One-Dimension (1-D), where the onsite coulomb repulsion, U, and the hopping matrix element, t, were varies to determine their magnetic phase diagram.This results obtained shows that, as the values of the onsite coulomb repulsion, U, increases in all the lattice systems studied, the electronic correlation that favours ferromagnetism gets stronger, but there were no clear transition, and at some point the lattices loss its antiferromagnetic properties, hence the instability of ferromagnetism were established. It was also observed that as the hopping matrix element, t, increases the electronic correlation that favours ferromagnetism get stronger and the lattice begins to loss antiferromagnetic properties but beyond the transition point the lattice began to gain a much stronger antiferromagnetism, hence the ferromagnetism is unstable.
The description of a solid at a microscopic level is complex, involving the interaction of a huge number of its constituents, such as ions or electrons.The Hubbard model used in this research describes interacting electrons in narrow energy bands, with application to problems as diverse as high -Tc superconductivity, band magnetism and the metal-insulator transition.This research seeks to solve one of the most challenging problems in Theoretical physics which is to describe electronic correlations.In this research the t -U Hubbard model is used to solve analytically and numerically using the exact diagonalization techniques This research work focused on the spin interaction and magnetic behavior of some systems and it is therefore an investigation into the various phenomena seen in the phase diagram of ferromagnetic systems.We studied the 2 electrons on 2 sites, 2 electrons on 3 sites and 2 electrons on 4 sites all in One-Dimension (1-D), where the onsite coulomb repulsion, U, and the hopping matrix element, t, were varies to determine their magnetic phase diagram.This results obtained shows that, as the values of the onsite coulomb repulsion, U, increases in all the lattice systems studied, the electronic correlation that favours ferromagnetism gets stronger, but there were no clear transition, and at some point the lattices loss its antiferromagnetic properties, hence the instability of ferromagnetism were established.It was also observed that as the hopping matrix element, t, increases the electronic correlation that favours ferromagnetism get stronger and the lattice begins to loss antiferromagnetic properties but beyond the transition point the lattice began to gain a much stronger antiferromagnetism, hence the ferromagnetism is unstable.