The commensurate p/q-filled n-component Hubbard chain was investigated by bosonization and high-precision density-matrix renormalization-group analysis. It was found that depending on the relation between the number of components n, and the filling parameter q, the system shows metallic or insulating behavior, and for special fillings bond-ordered (dimerized, trimerized, tetramerized etc.) ground state develops in the insulating phase. A mean-field analysis shows that this bond ordering is a direct consequence of the spin-exchange interaction, which plays a crucial role in the one-parameter Hubbard model - not only for infinite Coulomb repulsion, but for intermediate values as well.
Recent scanning tunneling microscopy measurements which indicate the formation of two-dimensional density modulations at some doping levels in cuprates were reviewed. A model of hard-core bosons which represent bound hole pairs in the two-dimensional doped antiferromagnet was discussed in the context of these experimental results. By means of an exact numerical diagonalization it was shown that the Coulomb repulsion between bosons brings about the formation of charge modulations.
In this paper we focus on the anomalous temperature dependence of the in-plane conductivity and symmetry mixing of the superconducting order parameter observed in various experiments on cuprates. We show that the one-band Hubbard model is not capable of describing the physics of cuprates because the kinetic energy is lowered in this model in the superconducting state, which contradicts experimental observations. The proper model to investigate doped, short-range antiferromagnets is the t-J model, for which our results agree with experiments. We analyze a spin polaron model, that is an effective model for a doped antiferromagnet. In the framework of this model we also study the superconducting order-parameter symmetry-mixing phenomenon. We show that the expected mixing of d-wave symmetry with p-wave symmetry takes place in the superconducting order-parameter at a finite value of the doping parameter. This symmetry mixing brakes the time-reversal symmetry.
We study the antiferromagnetic phase of three-dimensional Hubbard model with nearest neighbors hopping on a bipartite cubic lattice. We use the quantum SU(2)×U(1) rotor approach that yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of the model and satisfies the Mermin-Wagner theorem. As our theory describes the evolution from a Slater (U ≪ t) to a Mott-Heisenberg (U ≫ t) antiferromagnet, we present the phase diagram of the antiferromagnetic Hubbard model as a function of the crossover parameter U/t.
We consider the iterative-perturbation theory and its generalization to multi-orbital Hubbard models. We discuss in detail all aspects of numerical implementations of the method.
We apply perturbation theory and cyclic spin permutation formalism to study the lowest energy states of the infinite-repulsion Hubbard model on n-leg ladders with alternating values of one-site energies α_{i} for neighboring rungs. We establish the "ferromagnetic" character of ladder ground-state at electron densities in the interval 1 - (2n)¯¹ ≤ ρ ≤ 1 and sufficiently large alternation of one-site energies of neighbor rungs of the ladder. We also show the stability of this state against the small deviations of the values of α_{i} in contrast to the case of two-leg ladder formed by weakly interacting neighbor rungs with equal one-site energies.
We study the single impurity Anderson model in an external magnetic field. There are no exact results for the spectral function in this situation. Using a resummation of the diagrammatic expansion we demonstrate that the strong coupling regime in a weak magnetic field is Kondo-like with a quasiparticle resonant peak split into two. We find two exponentially small Kondo scales (temperatures), one for transverse and one for longitudinal spin fluctuations. We show that the salient features of the spectral function in the Kondo regime can be seen already within an extended random phase approximation. To reveal the dependence of the Kondo scales on the bare electron interaction, however, one has to employ a two-particle self-consistency with renormalized vertices. We use the parquet approach to derive the dependence of the Kondo scales on magnetic field.
Results of Monte Carlo simulations for the spinless Falicov-Kimball model with the next-nearest-neighbor hopping are presented. We find the critical value of the next-nearest-neighbor hopping integral, below which the low temperature configuration of the localized particles is the same as in the presence of only the nearest-neighbor hopping. Beyond this critical value the localized particles form horizontal or vertical stripes.
The electron correlations in narrow energy bands are examined within the framework of the Hubbard model, generalized by taking into account the correlated hopping of electrons. Electronic conductivity and ferromagnetic ordering stabilization in the system with various forms of electronic density of states are studied. The influence of magnetic field, temperature and the form of density of states on concentration dependence of conductivity and magnetization is investigated. The correlated hopping is shown to cause the electron-hole asymmetry of transport and ferromagnetic properties of narrow band materials.
The p-d hybridised single-hole states of the transition-metal-oxygen tetrahedron (TMO_{4}) are collectivised due to the direct p-p hopping between oxygens of different clusters. The lowest-lying energy band is always narrow and fully occupied. The first excited band gets occupied as an effect of valence-uncompensated doping, so it can be almost localised. The possible hole excitations to the two higher energy bands, which are wider, may imply the Mott-like hopping form of charge transport in these systems.
We analyze the influence of hopping interaction on magnetic ordering. Scattering scheme of the Hubbard III approximation with included inter-site kinetic electron-electron correlation is used. The hopping interaction and inter-site correlation lead to two spin dependent effects: the band width correction and the band-shift correction. The band-shift correction factor causes an exchange splitting between the spin-up and spin-down spectrum, and its role is similar to the exchange interaction in the classic Stoner model. The spin dependent band width correction enhanced strongly by the inter-site kinetic correlation lowers the kinetic energy of electrons by decreasing the majority spin band width for some electron occupations with respect to the minority spin band width. The results show that in the case of the symmetrical density of states there is only ferromagnetic enhancement. For the strongly asymmetrical density of states there is a ferromagnetic transition.
We analyze the possible occurrence of ferromagnetism in the Hubbard model, by means of an exact diagonalization study performed on 3- to 8-site chains with periodic boundary conditions. In the case of one hole in the half-filled configuration, we find that the Nagaoka state is reached only in the 3- and in the 4-site case. Ground states characterized by unsaturated ferromagnetism are found when the case of more than one hole is considered.
We provide a brief overview of recent theoretical results concerning the metallic and insulating states with very heavy quasiparticle masses and almost compensated magnetic moments, primarily in the antiferromagnetic state. The temperature dependence of the Kondo-insulator band gap is also discussed.
Two electrons on a lattice pose an interesting problem which can be solved exactly. When the effective interactions are strong enough, the bound states are formed. The properties of such bound pairs in an extended Hubbard model are examined for both signs of nearest neighbor hopping integral t. The stabilization of s*-wave pairing is found for t<0 and of f-wave for t>0. Phase diagrams for the existence of none, one or two s*-wave solutions are calculated.
The contractor renormalization group method was devised in 1994 by Morningstar and Weinstein. It was primarily aimed at extracting the physics of lattice quantum field theories (like lattice quantum chromodynamics). However, it is a general method of analyzing Hamiltonian lattice systems, e.g. Ising, Heisenberg or Hubbard models. The aim of this work is to show the application of contractor renormalization group method to one-dimensional quantum systems - the Heisenberg zig-zag model and the Hubbard chain. As a test of the method, the ground state energy of these systems will be calculated.
Using the self-consistent Born approximation we calculate Reiter's wave function for a single hole introduced into the undoped and orbitally ordered ground state of the t-J model with t_{2g} orbital degrees of freedom. While the number of excitations is similar to the spin t-J model for a given J/t, a distinct structure of the calculated wave function and its momentum dependence is identified suggesting the formation of a novel type of mobile polarons.
One-dimensional atomic chain with a variable-range hopping is described within the extended Hubbard model. The Gutzwiller-ansatz approximation is used to determine the optimized single-particle (Wannier) wave functions in the correlated state. Hopping integral up to the third neighbors is taken into account and the results are compared with those for the infinite hopping range. Ground state energy of the system is compared with that making use of the rigorous Lieb-Wu solution with the optimized wave functions. The evolution of the properties as a function of interatomic distance is discussed.
The paper examines part of the ground state diagram of the extended Hubbard model, with the on-site attraction U<0 and intersite repulsion W>0 in the presence of charge density waves, superconducting andη-superconducting order parameters. We show the possibility of the stabilization of the mixed state, with all three nonzero order parameters, in the model with nearest neighbor interactions. The other result of the paper is application of the exact solution of the Schrödinger equation for the two-electron bound state, as an additional bound for the phase diagram of the model, resulting in the partial suppression of the superconducting state of the s-wave symmetry, in favor of the normal state phase.
We analyse a behaviour of the order parameter and specific heat of the Falicov-Kimball model (FKM) on the Bethe lattice using the Dynamical Mean Field Theory (DMFT) formalism, which provides the exact solution in the limit of large spatial dimensions. In the large U limit, the FKM maps onto the effective Ising model, with the order parameter of the Curie-Weiss form. However, in the small U limit the order parameter takes on unusual shape, with a sharp reduction near T ≈ T_{c}/2. We focus our investigation on a crossover between these two limits, thus we perform our calculations for a set of intermediate and small values of U. We find the overall behaviour of the order parameter and specific heat as a function of temperature to be quite anomalous.
The mechanism of superconductivity generation by spin fluctuations in the electron doped canted antiferromagnet on the triangular lattice was analyzed. The underlying assumption is that the formation of the bound state is the prerequisite of pairing. The outcome of this analysis is also valid if an additional isotropic attraction is active but the anisotropic spin-fluctuation mediated force decides on the symmetry of the two-particle bound state. When the canted antiferromagnetic state is generated, the symmetry of the point group C_{6v} for the triangular lattice is lowered to the symmetry of C_{3v}. It is demonstrated that spin fluctuations definitely favor the p-wave bound state, which transforms according to the E representation of C_{3v}. Since the inversion is not an element of C_{3v}, the parity is not a good quantum number and thus the predicted paired state will be a mixture of singlet and triplet. Such a scenario may be relevant to physics of superconducting triangular cobaltates or organics.
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