Microscopic conditions favoring itinerant ferromagnetism: Hund's rule coupling and orbital degeneracy

The importance of Hund's rule coupling for the stabilization of itinerant ferromagnetism is investigated within a two-band Hubbard model. The magnetic phase diagram is calculated by finite-temperature quantum Monte-Carlo simulations within the dynamical mean-field theory. Ferromagnetism is found in a broad range of electron fillings whereas antiferromagnetism exists only near half filling. The possibility of orbital ordering at quarter filling is also analyzed. Received: 26 February 1998 / Accepted: 17 April 1998     

Modular invariant partition function of the Hubbard model

Summary By making use of the Abelian bosonization procedure, we obtain a Coulomb-gas picture of the continuum limit of the one-dimensional Hubbard model. It is shown clearly that the semi-direct product of two Virasoro algebras (c=1) denotes symmetry of excitations of the Hubbard model. A systematic study of modular invariant partition function for the Hubbard model is presented. Correlation functions are calculated explicitly and the result is in good agreement with those of numerical simulations and Tomonaga-Luttinger model.     

Renormalized quasiparticles in antiferromagnetic states of the Hubbard model

We analyze the properties of the quasiparticle excitations of metallic antiferromagnetic states in a strongly correlated electron system. The study is based on dynamical mean field theory (DMFT) for the infinite dimensional Hubbard model with antiferromagnetic symmetry breaking. Self-consistent solutions of the DMFT equations are calculated using the numerical renormalization group (NRG). The low energy behavior in these results is then analyzed in terms of renormalized quasiparticles. The parameters for these quasiparticles are calculated directly from the NRG derived self-energy, and also from the low energy fixed point of the effective impurity model. From these the quasiparticle weight and the effective mass are deduced. We show that the main low energy features of the k-resolved spectral density can be understood in terms of the quasiparticle picture. We also find that Luttinger's theorem is satisfied for the total electron number in the doped antiferromagnetic state.     

Two-parameter extended Hubbard Hamiltonian with supersymmetry

We investigate under which circumstances extended Hubbard models, including bond-charge, exchange, and pair-hopping terms, are invariant under gl (2,1) superalgebra. This happens for a two-parameter Hamiltonian which includes as particular cases the t - J, the EKS and the one-parameter BGLZ Hamiltonians, all integrable in one dimension. We show that the two parameter Hamiltonian can be recasted as the sum of the BGLZ Hamiltonian plus the graded permutation operator of electronic states on neighbouring sites. The integrability of the corresponding one-dimensional model is discussed. Received: 17 February 1998 / Received in final form: 6 March 1998 / Accepted: 17 April 1998     

Effective Hubbard model for Zn-doped CuO2 plane

In the framework of the cell-perturbation method for the original p-d model an effective two-band Hubbard model for the CuO₂ plane with Zn impurities is derived. Zn impurities are modelled by Wannir oxygen one-hole states at vacant Cu sites. The model is based on the results of band structure calculations carried out within the local-density approximation. Further reduction to an extended t-J model shows a large ferromagnetic superexchange interaction between the Cu spin with the nearest virtual oxygen spin in the Zn cell. Received 17 November 1998     

Magnetic fluctuations in coupled inequivalent Hubbard layers as a model for

We investigate, within the fluctuation-exchange approximation, a correlated-electron model for represented by two inequivalent Hubbard layers coupled by an interlayer hopping . An energy offset is introduced in order to produce a different charge carrier concentration in the two layers. We compare several single-particle and magnetic excitations, namely, the single particle scattering rate, the spectral function and the spin lattice as well as spin-spin relaxation times in the two layers as a function of . We show that the induced interlayer magnetic coupling produces a tendency to “equalization” of the magnetic properties in the two layers whereby antiferromagnetic fluctuations are suppressed in the less doped layer and enhanced in the heavily doped one.The strong antiferromagnetic bilayer coupling causes the charge carriers in the plane with larger doping concentration to behave similar to those of the underdoped layer, they are coupled to. This effect grows for decreasing temperature. For high temperatures or if both layers are optimally or overdoped, i.e. when the antiferromagnetic correlation length becomes of the order or smaller than one lattice site the charge carrier and magnetic dynamics of the two layers is disconnected and the equalization effect disappears. These results are in good agreement with NMR experiments on by Stern et al. [Phys. Rev B 51, 15478 (1995)]. We also compare the results with calculations on bilayer systems with equivalent layers as models for the constituent compounds and . Received: 28 August 1998     

Phase diagram of the Mott transition in a two-band Hubbard model in infinite dimensions

The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory recently developed by Bulla and Potthoff. The phase boundary of the metal-insulator transition is obtained analytically as a function of the on-site Coulomb interaction at the d-orbital, the charge-transfer energy between the d- and p-orbitals and the hopping integrals between p-d, d-d and p-p orbitals. The result is in good agreement with the numerical results obtained from the exact diagonalization method. Received 5 October 2000 and Received in final form 8 December 2000     

Decomposition of the Fock space in two-dimensional triangle and honeycomb lattice systems

We consider the symmetry group inherent in two-dimensional triangle and honeycomb lattice systems. We find analytically and numerically the character of the reducible representation for the corresponding Fock space. Using the irreducible characters and the reducible character of the representation, we decompose the Fock space explicitly. For example, we calculate the multiplicity of each irreducible representation contained in the Fock space.     

Off-diagonal long-range order in a supersymmetric integrable model of correlated electrons

A new model for correlated electrons is presented which is integrable in one-dimension. The symmetry algebra of the model is the Lie superalgebra gl(2|1) which depends on a continuous free parameter. This symmetry algebra contains the pairing algebra as a subalgebra which is used to show that the model exhibits Off-Diagonal Long-Range Order in any number of dimensions. Received: 9 December 1997 / Revised: 12 February 1998 / Accepted: 17 March 1998     

Remnant Fermi surface in a pseudogap regime of the two-dimensional Hubbard model at finite temperature

A precursor effect on the Fermi surface in the two-dimensional Hubbard model at finite temperatures near the antiferromagnetic instability is studied using three different itinerant approaches: the second order perturbation theory, the paramagnon theory (PT), and the two-particle self-consistent (TPSC) approach. In general, at finite temperature, the Fermi surface of the interacting electron systems is not sharply defined due to the broadening effects of the self-energy. In order to take account of those effects we consider the single-particle spectral function A(, 0) at the Fermi level, to describe the counterpart of the Fermi surface at T = 0. We find that the Fermi surface is destroyed close to the pseudogap regime due to the spin-fluctuation effects in both PT and TPSC approaches. Moreover, the top of the effective valence band is located around = (π/2,π/2) in agreement with earlier investigations on the single-hole motion in the antiferromagnetic background. A crossover behavior from the Fermi-liquid regime to the pseudogap regime is observed in the electron concentration dependence of the spectral function and the self-energy. Received 8 September 2000 and Received in final form 20 December 2000     

Kondo insulators in the periodic Anderson model: a local moment approach

The symmetric periodic Anderson model is well known to capture the essential physics of Kondo insulator materials. Within the framework of dynamical mean-field theory, we develop a local moment approach to its single-particle dynamics in the paramagnetic phase. The approach is intrinsically non-perturbative, encompasses all energy scales and interaction strengths, and satisfies the low-energy dictates of Fermi liquid theory. It captures in particular the strong coupling behaviour and exponentially small quasiparticle scales characteristic of the Kondo lattice regime, as well as simple perturbative behaviour in weak coupling. Particular emphasis is naturally given to strong coupling dynamics, where the resultant clean separation of energy scales enables the scaling behaviour of single-particle spectra to be obtained. Received 19 December 2002 Published online 14 March 2003     

Possible phases of the two-dimensional Hubbard model

We present a stability analysis of the 2D t - t' Hubbard model on a square lattice for various values of the next-nearest-neighbor hopping t' and electron concentration. Using the free energy expression, derived by means of the flow equations method, we have performed numerical calculation for the various representations under the point group C _4ν in order to determine at which temperature symmetry broken phases become more favorable than the symmetric phase. A surprisingly large number of phases has been observed. Some of them have an order parameter with many nodes in -space. Commonly discussed types of order found by us are antiferromagnetism, d _{x2 - y2} -wave singlet superconductivity, d-wave Pomeranchuk instability and flux phase. A few instabilities newly observed are a triplet analog of the flux phase, a particle-hole instability of p-type symmetry in the triplet channel which gives rise to a phase of magnetic currents, an s^*-magnetic phase, a g-wave Pomeranchuk instability and the band splitting phase with p-wave character. Other weaker instabilities are found also. A comparison with experiments is made. Received 25 July 2002 / Received in final form 28 November 2002 Published online 14 February 2003 RID="a" ID="a"Current address: Département de physique and Centre de recherche sur les propriétés électroniques de matériaux avancés, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K 2R1 e-mail: vaha@physique.usherb.ca     

Ferromagnetism in the Hubbard model on fcc-type lattices

The Hubbard model on fcc-type lattices is studied in the dynamical mean-field theory of infinite spatial dimensions. At intermediate interaction strength finite temperature Quantum Monte Carlo calculations yield a second order phase transition to a highly polarized, metallic ferromagnetic state. The Curie temperatures are calculated as a function of electronic density and interaction strength. A necessary condition for ferromagnetism is a density of state with large spectral weight near one of the band edges. Received: 6 August 1997 / Accepted: 20 August 1997     

Anisotropy of the energy gap in the insulating phase of the U-t-t' Hubbard model

We apply a diagrammatic expansion method around the atomic limit () for the U-t-t ' Hubbard model at half filling and finite temperature by means of a continued fraction representation of the one-particle Green's function. From the analysis of the spectral function we find an energy dispersion relation with a modulation of the energy gap in the insulating phase. This anisotropy is compared with experimental ARPES results on insulating cuprates. Received 18 May 2000 and Received in final form 9 August 2000     

Phase diagram of the spin extended model

The quantum phase transition in the ground state of the extended spin S = 1/2 XY model has been studied in detail. Using the exact solution of the model the low temperature thermodynamics, as well as the ground state phase diagram of the model in the presence of applied uniform and/or staggered magnetic field are discussed. Received 29 November 2002 / Received in final form 24 February 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: japa@iph.hepi.edu.ge     

Construction of localized basis for dynamical mean field theory

Many-body Hamiltonians obtained from first principles generally include all possible non-local interactions. But in dynamical mean field theory the non-local interactions are ignored, and only the effects of the local interactions are taken into account. The truncation of the non-local interactions is a basis dependent approximation. We propose a criterion to construct an appropriate localized basis in which the truncation can be carried out. This involves finding a basis in which a functional given by the sum of the squares of the local interactions with appropriate weight factors is maximized under unitary transformations of basis. We argue that such a localized basis is suitable for the application of dynamical mean field theory for calculating material properties from first principles. We propose an algorithm which can be used for constructing the localized basis. We test our criterion on a toy model and find it satisfactory.     

Thermodynamic properties of the spin-1/2 antiferromagnetic ladder under magnetic field

Specific heat (C_V) measurements in the spin-1/2 Cu₂(C₂H₁₂N₂)₂Cl₄ system under a magnetic field up to H =8.25 T are reported and compared to the results of numerical calculations based on the 2-leg antiferromagnetic Heisenberg ladder. While the temperature dependences of both the susceptibility and the low-field specific heat are accurately reproduced by this model, deviations are observed above the critical field H_C1 at which the spin gap closes. In this Quantum High Field phase, the contribution of the low-energy quantum fluctuations are stronger than in the Heisenberg ladder model. We argue that this enhancement can be attributed to dynamical lattice fluctuations. Finally, we show that such a Heisenberg ladder, for H > H C1, is unstable, when coupled to the 3D lattice, against a lattice distortion. These results provide an alternative explanation for the observed low temperature ( K-0.8 K) phase (previously interpreted as a 3D magnetic ordering) as a new type of incommensurate gapped state. Received: 23 July 1998 / Accepted: 24 August 1998     

Violation of the Luttinger sum rule within the Hubbard model on a triangular lattice

The frequency-moment expansion method is developed to analyze the validity of the Luttinger sum rule within the Mott-Hubbard insulator, as represented by the generalized Hubbard model at half filling and large U. For the particular case of the Hubbard model with nearest-neighbor hopping on a triangular lattice lacking the particle-hole symmetry results reveal substantial violation of the sum rule.     

Long-range spin-pairing order and spin defects in quantum spin- $${1 \over 2}$$ ladders

For w-legged antiferromagnetic spin-1/2 Heisenberg ladders, a long-range spin pairing order can be identified which enables the separation of the space spanned by finite-range (covalent) valence-bond configurations into w +1 subspaces. Since every subspace has an equivalent counter subspace connected by translational symmetry, twofold degeneracy, breaking translational symmetry is found except for the subspace where the ground state of w = even belongs to. In terms of energy ordering, (non)degeneracy and the discontinuities introduced in the long-range spin pairing order by topological spin defects, the differences between even and odd ladders are explained in a general and systematic way. Received 19 July 1999 and Received in final form 8 October 1999