Self-energy-functional approach to systems of correlated electrons

The grand potential of a system of interacting electrons is considered as a stationary point of a self-energy functional. It is shown that a rigorous evaluation of the functional is possible for self-energies that are representable within a certain reference system. The variational scheme allows to construct new non-perturbative and thermodynamically consistent approximations. Numerical results illustrate the practicability of the method. Received 13 January 2003 / Received in final form 5 March 2003 Published online 24 April 2003     

Electronic structure of LaNi and its hydride LaNi H

The electronic structure of LaNi₅ and its hydride LaNi₅H₇ are obtained using the self-consistent cluster-embedding calculation method. The Fermi level of LaNi₅H₇ is 5.172 eV higher than that of LaNi₅. In both materials, the La 5d electrons locate nearby the Fermi levels, and make only a small contribution to the density of states (DOS) of the valence bands. There is no significant charge transfer from La to Ni in LaNi₅. But for LaNi₅H₇, there is a charge transfer of 1.16 electrons from La to H, and H atoms are combined mainly with Ni to form hybridized orbitals in the energy regions far below the Fermi level. An explanation of hydrogenation of LaNi₅ is proposed: It is easy for hydrogens to take off some localized La 5 d electrons near the Fermi level, and combine with Ni to form hybridized orbitals in lower energy regions. This process is therefore in favor of energy, and forces a lattice expansion until the Fermi level rises to zero. Received 13 July 2001 / Received in final form 10 December 2001 Published online 17 September 2002     

Quantum statistical mechanics of ideal gas obeying fractional exclusion statistics: a systematic study

The quantum statistical mechanics of an ideal gas with a general free-particle energy obeying fractional exclusion statistics are systematically investigated in arbitrary dimensions. The pressure relations, the relation between pressure and internal energy, the equation of state, as well as the thermodynamic properties are thoroughly discussed. Some novel results are obtained. Received: 23 January 1998 / Accepted: 17 March 1998     

A theoretical analysis of the magnetic properties of La<Subscript>2</Subscript>CuO<Subscript>4</Subscript>

The magnetic properties of the La₂CuO₄ are analyzed by means of the paramagnetic solution of the Hubbard model within the composite operator method. The experimental findings of the inelastic neutron magnetic scattering [R. Coldea et al., Phys. Rev. Lett. 86, 5377 (2001)] for the spin spectrum, the spin-wave intensity and the behavior of the dispersion at the zone boundary are well described by our results although the difference in phase. The Hubbard model emerges has a minimal model capable to describe the anomalous magnetic behavior of such a strongly correlated material. Received 29 July 2002 / Received in final form 2 January 2003 Published online 14 March 2003     

Non-perturbative conserving approximations and Luttinger's sum rule

Weak-coupling conserving approximations can be constructed by truncations of the Luttinger-Ward functional and are well known as thermodynamically consistent approaches which respect macroscopic conservation laws as well as certain sum rules at zero temperature. These properties can also be shown for variational approximations that are generated within the framework of the self-energy-functional theory without a truncation of the diagram series. Luttinger's sum rule represents an exception. We analyze the conditions under which the sum rule holds within a non-perturbative conserving approximation. Numerical examples are given for a simple but non-trivial dynamical two-site approximation. The validity of the sum rule for finite Hubbard clusters and the consequences for cluster extensions of the dynamical mean-field theory are discussed.     

Interplay of charge, spin, orbital and lattice correlations in colossal magnetoresistance manganites

We derive a realistic microscopic model for doped colossal magnetoresistance manganites, which includes the dynamics of charge, spin, orbital and lattice degrees of freedom on a quantum mechanical level. The model respects the SU(2) spin symmetry and the full multiplet structure of the manganese ions within the cubic lattice. Concentrating on the hole doped domain ( 0≤x≤0.5) we study the influence of the electron-lattice interaction on spin and orbital correlations by means of exact diagonalisation techniques. We find that the lattice can cause a considerable suppression of the coupling between spin and orbital degrees of freedom and show how changes in the magnetic correlations are reflected in dynamic phonon correlations. In addition, our calculation gives detailed insights into orbital correlations and demonstrates the possibility of complex orbital states. Received 4 September 2002 / Received in final form 8 November 2002 Published online 31 December 2002     

Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice II

In this second paper, using N = 3 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion on a two dimensional L×L square lattice with periodic boundary conditions and nearest neighbor hopping t, we show that a single unpaired fermion can co-exist with a correlated two particle Wigner molecule for intermediate values of the Coulomb energy to kinetic energy ratio r _s = UL/(2t ). This supports in an ultimate mesoscopic limit a possibility proposed by Andreev and Lifshitz for the thermodynamic limit: a quantum crystal may have delocalized defects without melting, the number of sites of the crystalline array being smaller than the total number of particles. When L = 6, the ground state exhibits four regimes as r_s increases: a Hartree-Fock regime, a first supersolid regime where a correlated pair co-exists with a third fully delocalized particle, a second supersolid regime where the third particle is partly delocalized, and eventually a correlated lattice regime. Received 22 October 2002 Published online 23 May 2003 RID="a" ID="a"e-mail: jpichard@cea.fr     

Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice. I

In 1969, Andreev and Lifshitz have conjectured the existence of a supersolid phase taking place at zero temperature between the quantum liquid and the solid. In this and a succeeding paper, we re-visit this issue for a few polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion on a two dimensional L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. This paper is restricted to the magic number of particles N = 4 for which a square Wigner molecule is formed when U increases and to the size L = 6 suitable for exact numerical diagonalizations. When the Coulomb energy to kinetic energy ratio r _s = UL/(2t ) reaches a value r _s ^F ≈ 10, there is a level crossing between ground states of different momenta. Above r _s ^F, the mesoscopic crystallization proceeds through an intermediate regime ( r _s ^F < r _s < r _s ^W ≈ 28) where unpaired fermions with a reduced Fermi energy co-exist with a strongly paired, nearly solid assembly. We suggest that this is the mesoscopic trace of the supersolid proposed by Andreev and Lifshitz. When a random substrate is included, the level crossing at r _s ^F is avoided and gives rise to a lower threshold r _s ^F(W) < r _s ^F where two usual approximations break down: the Wigner surmise for the distribution of the first energy excitation and the Hartree-Fock approximation for the ground state. Received 21 June 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: jpichard@cea.fr     

From independent particle towards collective motion for two polarized electrons on a square lattice

The two dimensional crossover from independent particle towards collective motion is studied using 2 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion in a L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. Three regimes characterize the ground state when U/t increases. Firstly, when the fluctuation Δr of the spacing r between the two particles is larger than the lattice spacing a, there is a scaling length L ₀ = π²(t/U) such that the relative fluctuation Δr/〈r〉 is a universal function of the dimensionless ratio L/L ₀, up to finite size corrections of order L^-2. L < L ₀ and L > L ₀ are respectively the limits of the free particle Fermi motion and of the correlated motion of a Wigner molecule. Secondly, when U/t exceeds a threshold U ^*(L)/t, Δr becomes smaller than a, giving rise to a correlated lattice regime where the previous scaling breaks down and analytical expansions in powers of t/U become valid. A weak random potential reduces the scaling length and favors the correlated motion. Received 28 March 2002 Published online 19 November 2002     

A travelling cluster approximation for lattice fermions strongly coupled to classical degrees of freedom

We suggest and implement a new Monte Carlo strategy for correlated models involving fermions strongly coupled to classical degrees of freedom, with accurate handling of quenched disorder as well. Current methods iteratively diagonalise the full Hamiltonian for a system of N sites with computation time τ_N ∼N⁴. This limits achievable sizes to N ∼100. In our method the energy cost of a Monte Carlo update is computed from the Hamiltonian of a cluster, of size N_c, constructed around the reference site, and embedded in the larger system. As MC steps sweep over the system, the cluster Hamiltonian also moves, being reconstructed at each site where an update is attempted. In this method τ_N,Nc ∼NN_c³. Our results are obviously exact when N_c=N, and converge quickly to this asymptote with increasing N_c, particularly in the presence of disorder. We provide detailed benchmarks on the Holstein model and the double exchange model. The `locality' of the energy cost, as evidenced by our results, suggests that several important but inaccessible problems can now be handled with control. This method forms the basis of our studies in Europhys. Lett. 68, 564 (2004), Phys. Rev. Lett. 94, 136601 (2005), and Phys. Rev. Lett. 96, 016602 (2006).     

Coulomb repulsion versus Hubbard repulsion in a disordered chain

We study the difference between on site Hubbard and long range Coulomb repulsions for two interacting particles in a disordered chain. The system size L (in units of the lattice spacing) is of the order of the one particle localization length and the energies are taken near the band center. In the two cases, the limits of weak and strong interactions are characterized by uncorrelated energy levels and are separated by a crossover regime where the states are more extended and the spectra more rigid. U denoting the interaction strength and t the kinetic energy scale, the crossovers take place for interaction energy to kinetic energy ratios U/t and U/(2tL) of order one, for Hubbard and Coulomb repulsions respectively. While Hubbard repulsion can only yield weak critical chaos with intermediate spectral statistics, Coulomb repulsion can drive the two particle system to quantum chaos with Wigner-Dyson spectral statistics. The interaction matrix elements are studied to explain this difference. Received 21 March 2000 and Received in final form 5 February 2001     

Photonic band structure in the nearly plane wave approximation

For photons propagating in a periodic dielectric lattice, the dispersion curve forms photonic bands separated by forbidden gaps. When the dielectric lattice deviates only slightly from being homogenous, the photonic band structure resembles the linear dispersion relation for photons folded into the first Brillouin zone, i.e., the so-called empty lattice bands. Using group theoretical technique, we calculate the splitting of the accidental degeneracies in the empty lattice bands at symmetry points for a simple cubic dielectric lattice. Received 23 June 1998     

Magneto-electronic properties of the AA- and ABC-stacked graphites

In this study, we apply the tight-binding method to magneto-electronic properties of the AA- and ABC-stacked graphites, which are strongly dependent on the interlayer interactions, the magnetic field, and the stacking sequences. First of all, the interlayer interactions induce the significant changes in the energy dispersions, the band symmetry about the Fermi level, the overlap between valence and conduction bands, the band width, and the band-edge states or the symmetry points. Then, the magnetic field induces the Peierls phase in the Bloch functions and thus strongly affects the energy dispersions of the Landau Levels, the subband spacings, the energy width, and the special structures in density of states (DOS). Finally, the stacking sequences dominates over the low-energy band overlap and the anisotropy of energy bands. The effects mentioned above are exactly reflected in the density of state. Here, DOS exhibits the 3D, 2D, and 1D characteristics.     

LOCV calculation for the uniform electron fluid at finite temperature

The free energy of the homogeneous electron fluid at finite temperature is obtained using the lowest order constrained variational (LOCV) method. In order to test the convergence of cluster expansion series the three-body cluster terms are calculated with the LOCV correlation functions. The results agree reasonably with those of Monte Carlo, coupled-cluster, perturbational expansion etc, techniques at zero temperature. The flashing and critical temperatures as well as the critical exponent are found to be about 0.6, 1.3 eV and 0.384 respectively. A similar liquid-gas phase transition to that of nuclear matter and liquid He³ is observed. Received 15 April 2002 / Received in final form 19 October 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: modarres@khayam.ut.ac.ir     

Parity law of the singlet-triplet gap in graphitic ribbons

This work explores the possibility to transfer the parity law of the singlet-triplet gap established for square ladders (gapped for even number of legs, gapless for odd number of legs) to fused polyacenic 1-D systems, i.e., graphite ribbons. Qualitative arguments are presented in favor of a gapped character when the number n_ω of benzene rings along the ribbon width is odd. A series of numerical calculations (quantitative mapping on spin 1/2 chains, renormalized excitonic treatments and Quantum Monte Carlo) confirms the parity law and the gapless character of the ribbon for even n_ω.     

The two-dimensional t-t'-U model as a minimal model for cuprate materials

The addition to the Hubbard Hamiltonian of a t' diagonal hopping term, which is considered to be material dependent for high-T _c cuprate superconductors, is generally suggested to obtain a model capable to describe the physics of high-T _c cuprate materials. In this line of thinking, the two-dimensional t-t'-U model has been studied by means of the Composite Operator Method, which allows to determine the dynamics in a fully self-consistent way by use of symmetry requirements, as the ones coming from the Pauli principle. At first, some local quantities have been calculated to be compared with quantum Monte Carlo data. Then, the structure of the energy bands, the shape of the Fermi surface and the position of the van Hove singularity have been computed as functions of the model parameters and studied by the light of the available experimental data. The results of our study show that there exists two sets of parameters that allows the model to describe the relevant features of the 1-layer compounds Nd_2-xCe_xCuO₄ and La_2-xSr_xCuO₄. On the other hand, for the 2-layer compound YBa₂Cu₃O _{7 - δ} is not possible to find a reasonable set of parameters which could reproduce the position of the van Hove singularity as predicted by ARPES experiments. Hence, it results questionable the existence of an unique model that could properly describe the variety of cuprate superconductors, as the two-dimensional t-t'-U model was thought to be. Received 29 March 2000 and Received in final form 10 August 2000     

Enumeration of many-body skeleton diagrams

The many-body dynamics of interacting electrons in condensed matter and quantum chemistry is often studied at the quasiparticle level, where the perturbative diagrammatic series is partially resummed. Based on Hedin's equations for self-energy, polarization, propagator, effective potential, and vertex function, dressed (skeleton) Feynman diagrams are enumerated. Such diagram counts provide useful simple checks for extensions of the theory for future realistic simulations.     

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.     

Extended Hubbard model in the presence of a magnetic field

Within the Green’s function and equations of motion formalism it is possible to exactly solve a large class of models useful for the study of strongly correlated systems. Here, we present the exact solution of the one-dimensional extended Hubbard model with on-site U and first nearest neighbor repulsive V interactions in the presence of an external magnetic field h, in the narrow band limit. At zero temperature our results establish the existence of four phases in the three-dimensional space (U, n, h) – n is the filling – with relative phase transitions, as well as different types of charge ordering. The magnetic field may dramatically affect the behavior of thermodynamic quantities, inducing, for instance, magnetization plateaus in the magnetization curves, and a change from a single to a double-peak tructure in the specific heat. According to the value of the particle density, we find one or two critical fields, marking the beginning of full or partial polarization. A detailed study of several thermodynamic quantities is also presented at finite temperature.