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.     

Variational approach to spin fluctuations in the Hubbard model

We study a one parameter variational wave function to improve the spin density wave ground state of the Hubbard model by inclusion of quantum spin fluctuations. Using a perturbative approach and novel lattice summation techniques we present analytical as well as numerical results for the correlation energies and the staggered magnetizations in one and two dimensions. We find ground state energies which are satisfyingly close to known exact results and are significantly lower than those of existing Gutzwiller and numerical treatments.     

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.     

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     

Exact superconducting ground states of the extended Anderson model

We obtain exact ground states of an extended periodic Anderson model (EPAM) with non-local hybridization and Coulomb repulsion between f and c electrons (Falicov-Kimball term) in one dimension. We show that for a range of parameter values these ground states exhibit composite hole pairing and superconductivity that originate from purely electronic interactions.     

A variational treatment of the periodic Anderson model with antiferromagnetic order

We discuss a variational ground state wave function for the symmetric periodic Anderson model with commensurate spin density order. The energy of this ansatz is evaluated in closed form. Our approach generalizes a variational treatment proposed recently by Strack and Vollhardt and results in significantly lower energy. Contrary to the Gutzwiller ansatz the wave function recovers the Schrieffer-Wolff limit for large Coulomb repulsion. We clarify the relation of our approach to unrestricted Hartree-Fock and present a comparison with existing quantum Monte Carlo calculations for one dimension.     

Non-Fermi-liquid phases in the two-band Hubbard model: finite-temperature exact diagonalization study of Hund's rule coupling

The two-band Hubbard model involving subbands of different widths is investigated via finite-temperature exact diagonalization (ED) and dynamical mean field theory (DMFT). In contrast to the quantum Monte Carlo (QMC) method which at low temperatures includes only Ising-like exchange interactions to avoid sign problems, ED permits a treatment of Hund's exchange and other onsite Coulomb interactions on the same footing. The role of finite-size effects caused by the limited number of bath levels in this scheme is studied by analyzing the low-frequency behavior of the subband self-energies as a function of temperature, and by comparing with numerical renormalization group (NRG) results for a simplified effective model. For half-filled, non-hybridizing bands, the metallic and insulating phases are separated by an intermediate mixed phase with an insulating narrow and a bad-metallic wide subband. The wide band in this phase exhibits different degrees of non-Fermi-liquid behavior, depending on the treatment of exchange interactions. Whereas for complete Hund's coupling, infinite lifetime is found at the Fermi level, in the absence of spin-flip and pair-exchange, this lifetime becomes finite. Excellent agreement is obtained both with new NRG and previous QMC/DMFT calculations. These results suggest that-finite temperature ED/DMFT might be a useful scheme for realistic multi-band materials.     

Random dispersion approximation for the Hubbard model

We use the Random Dispersion Approximation (RDA) to study the Mott-Hubbard transition in the Hubbard model at half band filling. The RDA becomes exact for the Hubbard model in infinite dimensions. We implement the RDA on finite chains and employ the Lanczos exact diagonalization method in real space to calculate the ground-state energy, the average double occupancy, the charge gap, the momentum distribution, and the quasi-particle weight. We find a satisfactory agreement with perturbative results in the weak- and strong-coupling limits. A straightforward extrapolation of the RDA data for L ≤ 14 lattice results in a continuous Mott-Hubbard transition at U_c≈W. We discuss the significance of a possible signature of a coexistence region between insulating and metallic ground states in the RDA that would correspond to the scenario of a discontinuous Mott-Hubbard transition as found in numerical investigations of the Dynamical Mean-Field Theory for the Hubbard model.     

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     

Flow equations and extended Bogoliubov transformation for the Heisenberg antiferromagnet near the classical limit

The Heisenberg spin-S quantum antiferromagnet is studied near the large-spin limit, applying a new continuous unitary transformation which extends the usual Bogoliubov transformation to higher order in the 1/S-expansion of the Hamiltonian. This allows to diagonalize the bosonic Hamiltonian resulting from the Holstein-Primakoff representation beyond the conventional spin-wave approximation. The zero-temperature flow equations derived from the extension of the Bogoliubov transformation to order for the ground-state energy, the spin-wave velocity, and the staggered magnetization are solved exactly and yield results which are in agreement with those obtained by a perturbative treatment of the magnon interactions. Received: 19 March 1998 / Revised: 2 June 1998 / Accepted: 8 June 1998     

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.     

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     

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     

Short note on the excitonic Mott phase

An exciton gas on a lattice is analysed in terms of a convergent hopping expansion. For a given chemical potential, our calculation provides a sufficient condition for the hopping rate to obtain an exponential decay of the exciton correlation function. This result indicates the existence of a Mott phase in which strong fluctuations destroy the long range correlations in the exciton gas at any temperature, either by thermal or by quantum fluctuations.     

Magnetism and phase separation in the ground state of the Hubbard model

We discuss the ground state magnetic phase diagram of the Hubbard model off half filling within the dynamical mean-field theory. The effective single-impurity Anderson model is solved by Wilson's numerical renormalization group calculations, adapted to symmetry broken phases. We find a phase separated, antiferromagnetic state up to a critical doping for small and intermediate values of U, but could not stabilize a Néel state for large U and finite doping. At very large U, the phase diagram exhibits an island with a ferromagnetic ground state. Spectral properties in the ordered phases are discussed. Received 9 January 2002 Published online 25 June 2002     

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     

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     

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