Using the solution of the near-neighbor hopping Hubbard model in one dimension by Leib and Wu, it is shown that in the limit of interaction energy much greater than hopping energy, this system has the temperature dependence of magnetization of a free-spin system even for temperatures much less than the bandwidth, for nearly all occupancies of the band.
Using the solution of the near-neighbor hopping Hubbard model in one dimension by Leib and Wu, it is shown that in the limit of interaction energy much greater than hopping energy, this system has the temperature dependence of magnetization of a free-spin system even for temperatures much less than the bandwidth, for nearly all occupancies of the band.
Nagoaka's result that the ground state of the near-neighbor-hopping Hubbard model, for a nearly half-filled band and for interaction strength much greater than hopping energy, is ferromagnetic, is shown to be valid for bosons with spin, as well as fermions, in a finite system. In the thermodynamic limit, the boson system is shown to be nonmagnetic. Ferromagnetism is argued to exist at nonzero temperatures for fermions in an infinite system, and upper and approximate lower bounds are obtained for the Curie temperature.
Correlated electron systems with competing interactions provide a valuable platform for examining exotic magnetic phases. Theoretical models often focus on nearest-neighbor interactions, although long-range interactions can have a considerable impact on the behavior of the system, creating distinct and complicated magnetic phases. We investigate the consequences of competing interactions in a half-filled one-band Hubbard model on a simple cubic lattice, incorporating hopping processes up to third-nearest-neighbors, to explore the underlying magnetotransport properties. Our magnetic phase diagrams at low temperatures, obtained using semiclassical Monte Carlo analysis, reveal that the long-range interactions can disrupt one form of magnetic phase while creating a new type of magnetic order. For the nonperturbative regime (on-site Hubbard repulsive strength $U\ensuremath{\sim}$ bandwidth), the C-type antiferromagnetic ground state is preferred over the G-type antiferromagnetic phase when the interaction between second-nearest-neighbor sites becomes significant relative to the nearest-neighbor interactions. However, interactions beyond the second-nearest-neighbors are required to stabilize the A-type antiferromagnetic ground state. Remarkably, at low temperatures, a highly correlated paramagnetic insulating phase develops at the intersection between the antiferromagnetic phases, which might promote a three-dimensional spin-liquid state.
The magnetic susceptibility at absolute-zero temperature for the one-dimensional Hubbard model is studied exactly as a function of the concentration of electrons by using Lieb and Wu's theory for this system. Our analysis essentially follows Griffiths's method for the magnetic susceptibility of the one-dimensional Heisenberg antiferromagnet, and is a generalization of Takahashi's calculation to the systems with an arbitrary concentration of electrons. The ground-state energy and the magnitude of local moments at each site are also studied. Combined with the results on the susceptibility, they should suggest how the effect of the Coulomb interaction on the properties of the system at low temperatures changes with the concentration of electrons.
With the aim of contributing to a better understanding of the finite-temperature properties of low-dimensional strongly correlated systems we study a one-dimensional half-filled-band extended Hubbard model with a term of exchange interaction between neighboring sites. We analyze the temperature dependence of the specific heat, internal energy, entropy, number of doubly occupied sites, magnetic susceptibility, spin-spin correlation functions, and also investigate a detailed diagram of magnetic correlations. We use the method of small-cluster exact diagonalization calculations with the application of the grand canonical ensemble and of extrapolation techniques to the infinite chain. Our results show that the examined model exhibits a rich structure of magnetic properties due to the competition between the onsite Coulombian repulsion and the exchange interaction.
Abstract. We study the influence of on-site disorder on the magnetic properties of the ground state of the infinite-U one-dimensional (1D) Hubbard model. We find that the ground state is not ferromagnetic. This is analysed in terms of the algebraic structure of the spin dependence of the Hamiltonian. A simple explanation is derived for the 1=N periodicity in the persistent current for this model. The Hubbard model is the simplest model one can study to examine the effects of correlations between electrons in narrow energy bands. The Hamiltonian consists of a nearest neighbour hopping term and an electron–electron repulsion, U, which acts only when two electrons are on the same site. The Hubbard model is also the canonical model for the study of itinerant ferromagnetism. The strong coupling regime is of special importance for the study of ferromagnetism, since a theorem by Nagaoka [1] states that in theU D 1 limit, the ground state (GS) is ferromagnetic given some connectivity property of the lattice (which holds in most cases for d> 1). The model is solvable in one dimension and it was shown [2] that for open boundary conditions (BCs) the GS for finiteU is a singlet, i.e. there can be no ferromagnetism unless one postulates explicitly spin- or velocity-dependent forces. For infinite U, the GS of
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.