Ferromagnetism, spiral magnetic structures and phase separation in the two-dimensional Hubbard model (original) (raw)
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Ferromagnetism in the Two Dimensional t-t′ Hubbard Model at the Van Hove Density
Physical Review Letters, 1997
Using an improved version of the projection quantum Monte Carlo technique, we study the square-lattice Hubbard model with nearest-neighbor hopping t and next-nearest-neighbor hopping t ′ , by simulation of lattices with up to 20×20 sites. For a given R = 2t ′ /t, we consider that filling which leads to a singular density of states of the noninteracting problem. For repulsive interactions, we find an itinerant ferromagnet (antiferromagnet) for R = 0.94 (R = 0.2). This is consistent with the prediction of the T -matrix approximation, which sums the most singular set of diagrams. 75.10.Jm, 71.20.Ad, 71.27.+a Typeset using REVT E X
Physical Review B, 2003
Models with range-free frustrated Ising spin interaction and additional Hubbard interaction are treated exactly by means of the discrete time slicing method of Grassmann field theory. Critical and tricritical points, spin-and charge correlations, and the fermion propagator, are derived as a function of temperature, chemical potential µ, of the Hubbard coupling U , and of the spin glass energy J. U is allowed to be either repulsive (U > 0) or attractive (U < 0). Cuts through the multi-dimensional phase diagram are obtained. Analytical and numerical evaluations take important replica symmetry breaking (RSB)-effects into account. Results for the ordered phase are given at least in one-step approximation (1RSB), for T = 0 we report the first two-, three-, and four-step calculations (4RSB) for fermionic spin glasses. The use of exact relations and invariances under RSB together with 2RSB-calculations for all fillings and 4RSB-solutions for half filling allow to model exact solutions by interpolation. For T = 0, our numerical results provide strong evidence that the exact spin glass pseudogap obeys ρ(E) = c1|E − EF | for energies close to the Fermi level with c1 ≈ 0.13. Rapid convergence of ρ ′ (EF) under increasing order of RSB is observed and ρ ′′ (E) is evaluated to estimate subleading powers. Over a wide range of the pseudogap and after a small transient regime ρ(E) regains a linear shape with larger slope and a small S-like perturbation. The leading term resembles the Efros-Shklovskii Coulomb pseudogap of two-dimensional localized disordered fermionic systems. Beyond half filling we obtain a ν − 1 ∼ (µ − U) 2 , µ ≥ U, dependence of the fermion filling factor ν. We find a half filling transition between a phase for U > µ, where the Fermi level lies inside the Hubbard gap, into a phase where µ(> U) is located at the center of the upper spin glass pseudogap (SG-gap). For µ > U the Hubbard gap combines with the lower one of two SG-gaps (phase I), while for µ < U it joins the sole SG-gap which exists in this half-filling regime (phase II). Shoulders of the combined gaps are shaped by RSB due to spin glass order. We predict scaling behaviour at the half filling transition which becomes continuous due to ∞RSB. Implications of the half-filling transition between the deeper insulating phase II and phase I for the eventual delocalization by additional hopping processes in itinerant model extensions are discussed. Possible metal-insulator transition scenarios are described. Generalizations to random Hubbard coupling and alloy models as well as frustrated magnetic interactions with ferro-or antiferromagnetic components are also considered separately.
physica status solidi (b), 2014
We consider a Hubbard model (HM) with occupation dependent hopping integrals. Using the Hartree-Fock (H-F) approximation and the new Green's function approach with inter-site kinetic averages included, we analyze the influence of the correlated hopping on ferromagnetic ordering. The influence of correlated hopping on the nonlocal quasiparticle energies and corresponding k-dependent spectral weights is included. In addition, we obtain the shift of the spin bands, which is a major factor in creating spontaneous ferromagnetism. At some parameters of the model, the correlated hopping effect is strong enough to achieve saturated ferromagnetism. This state may be obtained at the asymmetric density of states (DOS) and the Fermi energy located in the region of large spectral weight near the band edge. The results are compared with DMFT-Quantum Monte Carlo calculations and with the Hubbard III approximation, which includes the correlated hopping effect.
New Green function approach describing the ferromagnetic state in the simple Hubbard model
We consider a Hubbard model with occupation dependent hopping integrals. Using the Hartree-Fock (H-F) approximation and the new Green function approach with inter-site kinetic averages included, we analyze the influence of the correlated hopping on ferromagnetic ordering. The influence of correlated hopping on the nonlocal quasiparticle energies and corresponding k-dependent spectral weights is included. In addition we obtain the shift of the spin bands which is a major factor in creating spontaneous ferromagnetism. At some parameters of the model the correlated hopping effect is strong enough to achieve saturated ferromagnetism. This state may be obtained at the asymmetric density of states (DOS) and the Fermi energy located in the region of large spectral weight near the band edge. The results are compared with DMFT-Quantum Monte Carlo calculations and with the Hubbard III approximation which includes the correlated hopping effect.
Physical Review B, 2007
The magnetic susceptibility of the two-dimensional repulsive Hubbard model with nearestneighbor 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 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 < ∼n < ∼ 1.2 for the repulsion parameters 8|t| ≤ U ≤ 16|t|. However, for larger U/|t| and |1 −n| ≈ 0.2 the nearest neighbor correlations become ferromagnetic. Forn < ∼ 0.94 andn > ∼ 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 the frequency. This behavior of the susceptibility can explain the observed low-frequency incommensurate response observed in normal-state lanthanum cuprates.
The European Physical Journal B, 1998
A systematic investigation of the microscopic conditions stabilizing itinerant ferromagnetism of correlated electrons in a single-band model is presented. Quantitative results are obtained by quantum Monte Carlo simulations for a model with Hubbard interaction U and direct Heisenberg exchange interaction F within the dynamical mean-field theory. Special emphasis is placed on the investigation of (i) the distribution of spectral weight in the density of states, (ii) the importance of genuine correlations, and (iii) the significance of the direct exchange, for the stability of itinerant ferromagnetism at finite temperatures. We find that already a moderately strong peak in the density of states near the band edge suffices to stabilize ferromagnetism at intermediate U -values in a broad range of electron densities n. Correlation effects prove to be essential: Slater-Hartree-Fock results for the transition temperature are both qualitatively and quantitatively incorrect. The nearestneighbor Heisenberg exchange does not, in general, play a decisive role. Detailed results for the magnetic phase diagram as a function of U , F , n, temperature T , and the asymmetry of the density of states are presented and discussed. 71.27.+a,75.10.Lp
Journal of Magnetism and Magnetic Materials, 2009
The quasistatic approach is used to analyze the criterion of ferromagnetism for two-dimensional (2D) systems with the Fermi level near Van Hove (VH) singularities of the electron spectrum. It is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction between electrons and paramagnons, determined by the Hubbard on-site repulsion U, is sufficiently large. Due to incommensurate spin fluctuations near the ferromagnetic quantum phase transition, the critical interaction U c remains finite at VH filling and exceeds considerably its value obtained from the Stoner criterion. A comparison with the functional renormalization group results and mean-field approximation which yields a phase separation is also performed. Crown (P.A. Igoshev).
Journal of the Physical Society of Japan, 2011
We study a ferromagnetic tendency in the two-dimensional Hubbard model near van Hove filling by using a functional renormalization-group method. We compute temperature dependences of magnetic susceptibilities including incommensurate magnetism. The ferromagnetic tendency is found to occur in a dome-shaped region around van Hove filling with an asymmetric property: incommensurate magnetism is favored near the edge of the dome above van Hove filling whereas a first-order-like transition to the ferromagnetic ground state is expected below van Hove filling. The dome-shaped phase diagram is well captured in the Stoner theory by invoking a smaller Coulomb interaction. Triplet p-wave superconductivity tends to develop at low temperatures inside the dome and extends more than the ferromagnetic region above van Hove filling.