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.     

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.     

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     

Flow equations for the ionic Hubbard model

Taking the site-diagonal terms of the ionic Hubbard model (IHM) in one and two spatial dimensions, as H₀, we employ Continuous Unitary Transformations (CUT) to obtain a “classical” effective Hamiltonian in which hopping term has been renormalized to zero. For this Hamiltonian spin gap and charge gap are calculated at half-filling and subject to periodic boundary conditions. Our calculations indicate two transition points. In fixed Δ, as U increases from zero, there is a region in which both spin gap and charge gap are positive and identical; characteristic of band insulators. Upon further increasing U, first transition occurs at U=Uc₁, where spin and charge gaps both vanish and remain zero up to U=Uc₂. A gap-less state in charge and spin sectors characterizes a metal. For U>Uc₂ spin gap remains zero and charge gap becomes positive. This third region corresponds to a Mott insulator in which charge excitations are gaped, while spin excitations remain gap-less.     

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     

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.     

General spectral function expressions of a 1D correlated model

We introduce a method that allows the evaluation of general expressions for the spectral functions of the one-dimensional Hubbard model for all values of the on-site electronic repulsion U. The spectral weights are expressed in terms of pseudofermion operators such that the spectral functions can be written as a convolution of pseudofermion dynamical correlation functions. Our results are valid for all finite energy and momentum values and are used elsewhere in the study of the unusual finite-energy properties of quasi-one-dimensional compounds and the new quantum systems of ultra-cold fermionic atoms on an optical lattice.     

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     

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     

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.     

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.     

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     

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     

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.     

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