Quasiparticle density of states in the threedimensional Hubbard model

Quasiparticle densities of states are investigated for the threedimensional Hubbard model in the limit of strong coupling I >Δ (Δ = bandwidth) and for temperatures T → 0 by using the “method of spectral moments”. The densities of states depend on (i) the lattice structure, (ii) the band occupation and (iii) the magnetization of the system. Therefore these functions are evaluated for s.c.-, b.c.c.- and f.c.c.-lattices for some typical band occupations, and thereby first of all the influence of the magnetization is discussed.     

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     

Two-particle states in the 2D Hubbard model

An exact solution is proposed for the problem of two singlet electrons (zero-spin bosons) interacting through a Hubbard-type potential on a bounded quadratic lattice. Exact two-particle states and the energy spectrum are constructed.     

Spin-charge density waves in the Hubbard model

The ground state of the Hubbard model in a square lattice is examined in the Hartree-Fock mean field approximation at zero temperature. At small finite hole doping, the system has periodically distributed soliton like structures whose modulations are incommensurate. In a self-consistent way, the Fermi energy can always be located in a gap. The incommensurate states have lower energies than the commensurate antiferromagnetic states calculated at the same filling. These soliton structures persist even when a sizeable nearest neighbor repulsive interaction is included.     

Absence of highest-spin ground states in the Hubbard model

The Hubbard modelH=–tc _x c _y +U n _x n _x withN electrons and periodic boundary condition is studied onv-dimensionalL ₁ × ... ×L _v lattices. It is shown that for any value ofU there is no ground state with maximal spin (S=N/2) in the following cases: (i) ^v (v2) at low electron densities; with one hole ift>0 andL _i is odd for somei; with two holes ift<0, or ift>0 and all theL _i are even. (ii) Thebcc lattice at low densities; with two holes ift<0, or ift>0 and all theL _i are even; with 2, ..., 6 holes ifL _i =L andt<0, or ift>0 andL is even. (iii) The triangular lattice at densities near 0 and 1 ift>0; with two holes ift<0; with 2, 3, 4 holes ift<0 andL ₁=L ₂. (iv) Thefcc lattice at densities near 0 and 1 ift>0; with two holes ift<0. Some results for the one dimensional model are also presented.     

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.     

System-parameter dependence of the metallic phase of the non-doped 2D Hubbard model

Naito et al. reported that some non-doped T′-214-type compounds drive high-T_c superconductivity. The compounds are considered to be metallic since on-site Coulomb energy U is moderate and the Fermi surface is much deformed in these compounds. In order to confirm this picture and extract electronic structure information, we have examined the phase diagram of the metallic state of the 2D Hubbard model as a function of U and t′ (with t″ we fixed at − t′/2 here; t′ and t″ are the second- and third-neighbor transfer energies, respectively) by means of the variational Monte–Carlo method. We employed a Jastrow-type Gutzwiller trial wave function. In the studied range of U = 2–12, the boundary value for |t′| at which SDW disappears increases almost linearly with U. Jump-wise transition to the Mott insulator state was not observed. Using the boundary curve and experimental band parameter values, we estimate U  5 for T′-214 compounds. Preceding works are discussed in the last part.     

Doping dependence of the coupling of electrons to bosonic modes in the single-layer high-temperature Bi2Sr2CuO6 superconductor

A recent highlight in the study of high-T(c) superconductors is the observation of band renormalization or self-energy effects on the quasiparticles. This is seen in the form of kinks in the quasiparticle dispersions as measured by photoemission and interpreted as signatures of collective bosonic modes coupling to the electrons. Here we compare for the first time the self-energies in an optimally doped and strongly overdoped, nonsuperconducting single-layer Bi-cuprate (Bi2Sr2CuO6). In addition to the appearance of a strong overall weakening, we also find that the weight of the self-energy in the overdoped system shifts to higher energies. We present evidence that this is related to a change in the coupling to c-axis phonons due to the rapid change of the c-axis screening in this doping range.     

Density of states of two-dimensional aluminum nanoclusters in the Hubbard model

The density of states of a two-dimensional square nanosystem composed of N × N aluminum atoms (N = 3?30) is calculated in the framework of the Hubbard model. It is demonstrated that, at a small parameter N, the density of states depends substantially on the number of atoms and on the position of a particular atom in the lattice. As the parameter N increases, the density of states for the vertex and edge atoms tends to the value of the density of states for the bulk atoms. The temperature of the system is implicitly included by specifying the energy of hopping in the initial Hamiltonian.     

Continuum of many-particle states near the metal-insulator transition in the Hubbard model

The strong coupling diagram technique is used for investigating states near the metal-insulator transition in the half-filled two-dimensional repulsive Hubbard model. The nonlocal third-order term is included in the irreducible part along with local terms of lower orders. Derived equations for the electron Green’s function are solved by iteration for moderate Hubbard repulsions and temperatures. Starting iteration from Green’s functions of the Hubbard-I approximation with various distances of poles from the real frequency axis continua of different metallic and insulating solutions are obtained. The insulating solutions vary in the width of the Mott gap, while the metallic solutions differ in the shape of the spectral function in the vicinity of the Fermi level. Besides, different scenarios of the metal-insulator transition – with a sudden onset of a band of mobile states near the Fermi level and with gradual closure of the Mott gap – are observed with a change in temperature. In spite of these dissimilarities, all solutions have a common curve separating metallic and insulating states in the phase diagram. Near this curve metallic and insulating solutions coexist. For moderate Hubbard repulsions metallic solutions are not Fermi liquids.     

On the symmetries of the Hubbard model: application to finite-size clusters

We evaluate the density of states of the Hubbard model at half filling on a four-site cluster with periodic boundary conditions. The results are obtained from an exact diagonalization study of the model, where theSU(2) symmetry, the Yang\(\widetilde{SU}(2)\) pseudospin symmetry and the translational invariance of the Hamiltonian are explicitly taken into account.