Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the square lattice

The instability of the fully polarized ferromagnetic ground state (Nagaoka state) of the Hubbard model on the square lattice is investigated. We use single spin flip variational wave functions including majority spin correlation effects and calculate spin flip energies in the thermodynamic limit. With very local wave functions and with moderate numbers of variational parameters we reproduce the best known estimate for the critical hole density δ_cr = 0.29 and we obtain an estimate of U_cr = 63 t for the critical coupling which is considerably better than the best estimate of U_cr = 42 t previously known. The simplicity of our wave functions makes the physical origin of the various aspects of the instability particularly transparent.     

Ferromagnetism in the Hubbard model on the square lattice: Improved instability criterion for the Nagaoka state

The instability of the fully polarized ferromagnetic state (Nagaoka state) with respect to single spin flips is re-examined for the Hubbard model on the square lattice with a large family of variational wave functions which include correlation effects of the majority spins in the vicinity of the flipped spin. We find a critical hole density of δ_cr = 0.251 for U = ∞ and a critical coupling of U_cr = 77.7t. Both values improve previous variational results considerably.     

Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the triangular,honeycomb and kagome lattices

In order to analyse the lattice dependence of ferromagnetism in the two-dimensional Hubbard model we investigate the instability of the fully polarised ferromagnetic ground state (Nagaoka state) on the triangular, honeycomb and kagome lattices. We mainly focus on the local instability, applying single spin flip variational wave functions which include majority spin correlation effects. The question of global instability and phase separation is addressed in the framework of Hartree-Fock theory. We find a strong tendency towards Nagaoka ferromagnetism on the non-bipartite lattices (triangular, kagome) for more than half filling. For the triangular lattice we find the Nagaoka state to be unstable above a critical density of n = 1.887 at U = ∞, thereby significantly improving former variational results. For the kagome lattice the region where ferromagnetism prevails in the phase diagram widely exceeds the flat band regime. Our results even allow the stability of the Nagaoka state in a small region below half filling. In the case of the bipartite honeycomb lattice several disconnected regions are left for a possible Nagaoka ground state.     

Nagaoka Ferromagnetism in Two-Band Hubbard Model

In the present paper, we investigate the existence of ferromagnetism in a two-band Hubbard model, by applying a recently-introduced method by us to study ferromagnetism in metallic clusters. We prove rigorously that the ground state of this model is ferromagnetic if the intra-orbital Coulomb repulsion between electrons is infinitely strong and only one hole exists in the system. Our theorem improves a previous result. Furthermore, our method can also be applied to deal with the case of multiple holes.     

Ferromagnetism in the single-band Hubbard model: An exact high-temperature expansion

The first ten terms of the high-temperature expansion of the susceptibility of the single-band Hubbard model in the strong correlation limit are obtained for arbitrary electron density. The series is analyzed by ratio methods and Padé approximants. A critical temperature is found for 0.2 0.8; for > 1 further terms in the series are required.Supported in part by the National Research Council of Canada.     

Ferromagnetism,spiral magnetic structures and phase separation in the two-dimensional Hubbard model

The quasistatic approximation and equation-of-motion decoupling for the electron Green's functions are applied to trace the effect of electronic dispersion and electron correlations on the ferromagnetism of two-dimensional itinerant-electron systems. It is found that next-nearest-neighbor hopping t′$t\prime$ is of crucial importance for ferromagnetism formation yielding the magnetic phase diagram which is strongly asymmetric with respect to half-filling. At small t′$t\prime$ in the vicinity of half-filling the ferromagnetic phase region is restricted by the spin-density wave instability, and far from half-filling by one-particle (spin-polaron) instability. At t′$t\prime$ close to t/2$t/2$ ferromagnetism is stabilized at moderate Hubbard U   due to substantial curvature of the Fermi surface which passes in the vicinity of the van Hove singularity points. The results obtained are of possible importance for high-_Tc$T_{\mathrm{c}}$ compounds and layered ruthenates.     

Resonance state in the 2D attractive Hubbard model

The systematic change of a resonance state with high momenta is studied with increasing particle density in the 2D attractive Hubbard model. Within the conserving self-consistent T-matrix approximation, we present the spectral functions for the one and two particle Green's functions as well as the self-energy. In the small density limit, the resonant state becomes stable and the result from the self-consistent calculations shows a good agreement with that from a simple analytical calculation. As particle density is increased, the resonance state acquires a short lifetime due to the increasing decay into two free particles.     

Spin waves in Hubbard model

Gutzwiller's variational method has been used to study the spin waves in the ferromagnetic state of a narrow band. The spin wave energies are investigated in both the nondegenerate and the doubly degenerate bands. The electron correlation restricts the spin excitations and so improves the RPA solutions of the magnon energies. It is found that the bare intra-atomic interaction energies in the RPA solutions are replaced by smaller effective ones. In the case of a degenerate band model, contrary to the constant value as predicted by RPA, the Stoner gap parameter is reduced by the correlation effect.     

Instability of the spiral state of the doped Hubbard model

It is shown that the homogeneous spiral state of the doped Hubbard model is unstable for infinitesimal doping concentration. The spin response about the Hartree-Fock spiral state is evaluated, considering both the interband and intraband processes. Driven by long-wavelength, intraband spin fluctuations, the instability towards infinitesimal fluctuations about the mean-field state is inferred from the nature of the static spin response.     

Quantum phase diagram of the half filled Hubbard model with bond-charge interaction

Using quantum field theory and bosonization, we determine the quantum phase diagram of the one-dimensional Hubbard model with bond-charge interaction X in addition to the usual Coulomb repulsion U at half-filling, for small values of the interactions. We show that it is essential to take into account formally irrelevant terms of order X  . They generate relevant terms proportional to X²$X^2$ in the flow of the renormalization group (RG). These terms are calculated using operator product expansions. The model shows three phases separated by a charge transition at U=Uc$U=U_c$ and a spin transition at U=Us>Uc$U=U_s>U_c$. For U<Uc$U<U_c$ singlet superconducting correlations dominate, while for U>Us$U>U_s$, the system is in the spin-density wave phase as in the usual Hubbard model. For intermediate values Uc<U<Us$U_c<U<U_s$, the system is in a spontaneously dimerized bond-ordered wave phase, which is absent in the ordinary Hubbard model with X=0$X=0$. We obtain that the charge transition remains at Uc=0$U_c=0$ for X≠0$X\ne 0$. Solving the RG equations for the spin sector, we provide an analytical expression for Us(X)$U_s(X)$. The results, with only one adjustable parameter, are in excellent agreement with numerical ones for X<t/2$X<t/2$ where t is the hopping.     

Ferromagnetism in the Hubbard model

Whether spin-independent Coulomb interaction can be the origin of a realistic ferromagnetism in an itinerant electron system has been an open problem for a long time. Here we study a class of Hubbard models on decorated lattices, which have a special property that the corresponding single-electron Schrödinger equation hasN _d-fold degenerate ground states. The degeneracyN _d is proportional to the total number of sites ||. We prove that the ground states of the models exhibit ferromagnetism when the electron filling factor is not more than and sufficiently close to=N _d/(2||), and paramagnetism when the filling factor is sufficiently small. An important feature of the present work is that it provides examples of three dimensional itinerant electron systems which are proved to exhibit ferromagnetism in a finite range of the electron filling factor.     

Generalized Hartree-Fock theory and the Hubbard model

The familiar unrestricted Hartree-Fock variational principles is generalized to include quasi-free states. As we show, these are in one-to-one correspondence with the one-particle density matrices and these, in turn, provide a convenient formulation of a generalized Hartree-Fock variational principle, which includes the BCS theory as a special case. While this generalization is not new, it is not well known and we begin by elucidating it. The Hubbard model, with its particle-hole symmetry, is well suited to exploring this theory because BCS states for the attractive model turn into usual HF states for the repulsive model. We rigorously determine the true, unrestricted minimizers for zero and for nonzero temperature in several cases, notably the half-filled band. For the cases treated here, we can exactly determine all broken and unbroken spatial and gauge symmetries of the Hamiltonian.Dedicated to Philippe Choquard on his 65th birthday.     

Magnetism in the single-band Hubbard model

A self-consistent spectral density approach (SDA) is applied to the Hubbard model to investigate the possibility of spontaneous ferro- and antiferromagnetism. The starting point is a two-pole ansatz for the single-electron spectral density, the free parameter of which can be interpreted as energies and spectral weights of respective quasiparticle excitations. They are determined by fitting exactly calculated spectral moments. The resulting self-energy consists of a local and a non-local part. The higher correlation functions entering the spin-dependent local part can be expressed as functionals of the single-electron spectral density. Under certain conditions for the decisive model parameters (Coulomb interaction U, Bloch bandwidth W, band occupation n, temperature T) the local part of the self-energy gives rise to a spin-dependent band shift, thus allowing for spontaneous band magnetism. As a function of temperature, second-order phase transitions are found away from half-filling, but close to half-filling, the system exhibits a tendency towards first-order transitions. The non-local self-energy part is determined by use of proper two-particle spectral densities. Its main influence concerns a (possibly spin-dependent) narrowing of the quasiparticle bands with the tendency to stabilize magnetic solutions. The non-local self-energy part disappears in the limit of infinite dimensions. We present a full evaluation of the Hubbard model in terms of quasiparticle densities of states, quasiparticle dispersions, magnetic phase diagram, critical temperatures (T_c, T_N) as well as spin and particle correlation functions. Special attention is focused on the non-locality of the electronic self-energy, for which some rigorous limiting cases are worked out.     

Nagaoka ferromagnetism in the two-dimensional infinite-U Hubbard model

We present different numerical calculations based on variational quantum Monte Carlo simulations supporting a ferromagnetic ground state for finite and small hole densities in the two-dimensional infinite-U Hubbard model. Moreover, by studying the energies of different total spin sectors, these calculations strongly suggest that the paramagnetic phase is unstable against a phase with a partial polarization for large hole densities delta approximately 0.40 with evidence for a second-order transition to the paramagnetic large doping phase.     

半满Hubbard模型的新处理方法

从标准Hubbard模型出发,对半满狭带强关联系统,在讨论自旋为δ的电子运动时,忽略自旋为-δ的电子在格点间的跳跃,得到不对称哈密顿量,并运用平均场近似求得相应准粒子谱．在绝对零度时,与Green函数近似解作了比较;在有限温度时,讨论了从绝缘体到金属相变的可能．     

Flow equations and the strong-coupling expansion for the Hubbard model

Applying the method of continuous unitary transformations to a class of Hubbard models, we reexamine the derivation of thet/U expansion for the strong-coupling case. The flow equations for the coupling parameters of the higher order effective interactions can be solved exactly, resulting in a systematic expansion of the Hamiltonian in powers oft/U, valid for any lattice in arbitrary dimension and for general band filling. The expansion ensures a correct treatment of the operator products generated by the transformation, and only involves the explicit recursive calculation of numerical coefficients. This scheme provides a unifying framework to study the strong-coupling expansion for the Hubbard model, which clarifies and circumvents several difficulties inherent to earlier approaches. Our results are compared with those of other methods, and it is shown that the freedom in the choice of the unitary transformation that eliminates interactions between different Hubbard bands can affect the effective Hamiltonian only at ordert ³/U² or higher.     

Ferromagnetism in the degenerate Hubbard model

We study the ground state of the doubly degenerate Hubbard model in the strong coupling limit. For this limit, we obtain new exact results: when there are N ? 1 electrons, the ground state is ferromagnetic and there is a ferromagnetic orbital ordering; when the number of electrons is between N and 2N, the ground state is also ferromagnetic due to the intra-atomic Hund's coupling. For this second case, we give an estimate of the Curie temperature.