We explore how the spiral spin (SP) state, a spin singlet known to accompany fully polarized ferromagnetic (F) states in the Hubbard model, is related with the F state in the thermodynamic limit using the density-matrix renormalization group and exact diagonalization. We first obtain an indication that when the F state is the ground state the SP state is also eligible as the ground state in that limit. We then follow the general argument by Koma and Tasaki [J. Stat. Phys. 76, 745 (1994)] to find that (i) the SP state possesses a kind of order parameter, and (ii) although the SP state does not break the SU(2) symmetry in finite systems, it does so in the thermodynamic limit by making a linear combination with other states that are degenerate in that limit. We also calculate the one-particle spectral function and dynamical spin and charge susceptibilities for various one-dimensional finite-size lattices. We find that the excitation spectra of the SP state and the F state are almost identical. The present results suggest that the SP and the F states are equivalent in the thermodynamic limit. These properties may be exploited to determine the magnetic phase diagram from finite-size studies.
We explore how the spiral spin (SP) state, a spin singlet known to accompany fully polarized ferromagnetic (F) states in the Hubbard model, is related with the F state in the thermodynamic limit using the density-matrix renormalization group and exact diagonalization. We first obtain an indication that when the F state is the ground state the SP state is also eligible as the ground state in that limit. We then follow the general argument by Koma and Tasaki [J. Stat. Phys. 76, 745 (1994)] to find that (i) the SP state possesses a kind of order parameter, and (ii) although the SP state does not break the SU(2) symmetry in finite systems, it does so in the thermodynamic limit by making a linear combination with other states that are degenerate in that limit. We also calculate the one-particle spectral function and dynamical spin and charge susceptibilities for various one-dimensional finite-size lattices. We find that the excitation spectra of the SP state and the F state are almost identical. The present results suggest that the SP and the F states are equivalent in the thermodynamic limit. These properties may be exploited to determine the magnetic phase diagram from finite-size studies.
We investigate magnetic properties in the ground state of the one-dimensional flat-band Hubbard model in high electron filling. Until now, we found the new saturated ferromagnetism for odd numbers of holes, and its properties were investigated in detail. However, it was remained as a problem how we understand the complete alternation of magnetism between saturated ferromagnetism and singlet for odd and even numbers of holes, respectively. This alternation causes a difficulty when we consider the thermodynamic limit. In order to solve this difficulty, we investigate, at first, the change of the magnetization for systems with various boundary conditions, and we find that even for the even numbers of holes, the ground states are saturated ferromagnetic under the antiperiodic boundary condition. Furthermore, we explicitly investigate the spin-spin correlation functions < S z i S z j > to see the spin ordering. These calculations shows that all ground states in this filling region are the spiral state under a suitable boundary condition, and that the singlet states in these ground states, therefore, have a ferromagnetic order within, approximately, a half of the system size, although the total spin is still zero. From these results, we conclude that the properties in this region are by no means ill, and all ground states are essentially ferromagnetic in the sense that the spins in the singlet states are also ordered ferromagnetically if we take in the half of the system size.
We present an unbiased mean-field analysis of magnetic and charge orders in the two-dimensional Hubbard model on a square lattice, at both zero and finite temperatures. Unrestricted Hartree-Fock calculations on large finite lattices are complemented by solutions restricted to N\'eel and circular spiral order in the thermodynamic limit. The magnetic states are classified by a systematic scheme based on the dominant Fourier components of the spin texture. On finite lattices a whole zoo of ordering patterns appears. We show that many of these states are finite-size artifacts related to the limited choice of ordering wave vectors on a finite lattice. In the thermodynamic limit only three classes of states with a relatively simple structure survive: N\'eel, circular spiral, and stripe states. Stripes involve also charge order and can be unidirectional or bidirectional, with horizontal and/or vertical orientation. We present complete phase diagrams in the plane spanned by electron density and temperature, for a moderate Hubbard interaction and various choices of the next-nearest-neighbor hopping amplitude.
In this work we obtain the magnetic and thermodynamic properties of the classical Hubbard model. This one is easier to handle than the original Hubbard model, and it maintains fundamental aspects like charge and particle-hole symmetry. We find the relationship between this and the Ising model. For square and simple cubic lattices, the thermodynamic properties and phase diagrams were calculated by Monte Carlo method. We show the behavior of internal energy, specific heat, and magnetic susceptibility as a function of the temperature. For the considered lattices, the ground state is anti-ferromagnetic. The Néel temperatures were found as a function of the electronic interaction in the case of half-filled band. In the limit of vanishing of diverging interaction, our results agree with the Ising model.
We study the phase diagram of one-dimensional quantum ferrimagnets by using a numerical exact diagonalization of a finite size system along with a field-theoretical nonlinear $\ensuremath{\sigma}$ model of the quantum ferrimagnets at zero temperature and its effective description in the presence of the external magnetic field in terms of the quantum XY model. The low- and high-field phases correspond, respectively, to the classical N\'eel and the fully polarized ferromagnetic states where in the intermediate magnetic field (hc1<h<hc2), it is an XXZ+h model with easy plane anisotropy, which possess the spiral (superfluid) states that carry the dissipationless spin supercurrent. We derive the critical exponents, and then will study the stability of the XY spiral state against these spin-supercurrents and the hard axis fluctuations. We will show a first order phase transition from the easy plane spiral state to a saturated ferromagnetic state occurs at h=hc2 if the spin supercurrent reaches its critical value.
In this work we obtain the magnetic and thermodynamic properties of the classical Hubbard model. This one is easier to handle than the original Hubbard model, and it maintains fundamental aspects like charge and particle-hole symmetry. We find the relationship between this and the Ising model. For square and simple cubic lattices, the thermodynamic properties and phase diagrams were calculated by Monte Carlo method. We show the behavior of internal energy, specific heat, and magnetic susceptibility as a function of the temperature. For the considered lattices, the ground state is anti-ferromagnetic. The Néel temperatures were found as a function of the electronic interaction in the case of half-filled band. In the limit of vanishing of diverging interaction, our results agree with the Ising model.
The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ 0 (1) (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ 0(n)<ɛ FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m.