Electronic state in the 2D Hubbard model

Electronic state of the 2D Hubbard model near the half-filling is analyzed by use of the composite operator method. Doping and temperature dependence of density of states show similar behaviors obtained in numerical simulation. The weight of the upper and lower Hubbard bands at the half filling are not evenly distributed in the Brillouin zone, keeping roughly the original band distribution. With hole doping the lower Hubbard band spreads in the whole zone.     

Resonance state in the 2D attractive Hubbard model

The systematic change of a resonance state with high momenta is studied with increasing particle density in the 2D attractive Hubbard model. Within the conserving self-consistent T-matrix approximation, we present the spectral functions for the one and two particle Green's functions as well as the self-energy. In the small density limit, the resonant state becomes stable and the result from the self-consistent calculations shows a good agreement with that from a simple analytical calculation. As particle density is increased, the resonance state acquires a short lifetime due to the increasing decay into two free particles.     

Single-hole state in half-filled 2D Hubbard model

Summary We have investigated the ground state of a single hole in the half-filled Hubbard model on a 2D square lattice using the coupled-cluster method. In particular we obtained an analytical expression of the hole energy dispersion function ɛ(k) which is consistent with earlier studies on thet-J model in the strong-coupling limit. An appreciable discrepancy on the hole energy bandwidth is, however, observed between the Hubbard model and thet-J model. We believe that this discrepancy is due to the absence of the three-site interaction term in thet-J model.     

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.     

Evidence for Luttinger-liquid behavior in crossed metallic single-wall nanotubes

Transport measurements through crossed metallic single-wall nanotubes are presented. We observe a zero-bias anomaly in one tube which is suppressed by a current flowing through the other nanotube. These results are compared with a Luttinger-liquid model which takes into account electrostatic tube-tube coupling together with crossing-induced backscattering processes. Explicit solution of a simplified model is able to describe qualitatively the observed experimental data with only one adjustable parameter.     

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.     

An investigation of the 2D attractive Hubbard model

We present an investigation of the 2D attractive Hubbard model, considered as an effective model relevant to superconductivity in strongly interacting electron systems. We use both hybrid Monte-Carlo simulations and existing hopping parameter expansions to explore the low temperature domain. The increase of the static S-wave pair correlation with decreasing temperature, which depends weakly on the band filling in the explored temperature range, is analyzed in terms of an expected Kosterlitz-Thouless superconducting transition. Using both our data and previously published results, we show that the evidence for this transition is weak: If it exists, its temperature is very low. The number of unpaired electrons remains nearly constant with temperature at fixed attractive potential strength. In contrast, the static magnetic susceptibility decreases fast with temperature, and cannot be related only to pair formation. We introduce a method by which the Padé approximants of the existing series for the susceptibility give sensible results down to rather low temperature region, as shown by comparison with our numerical data. Received: 30 October 1996 / Revised: 23 October 1997 / Accepted: 29 January 1998     

Correlated ground state of the Hubbard model

The variational many-body approach or, more generally, the method of correlated basis functions initiated for a quantitative analysis of strongly interacting quantum fluids may be adapted with minor modifications for exploring the properties of lattice models. This is demonstrated by performing an explicit analysis of the paramagnetic ground state of the Hubbard model. In a first step of the approximation scheme we represent the correlated state by a spin-dependent wave function of Jastrow-type. We analyze in detail the associated density-matrix elements and set up the corresponding Fermi hypernetted-chain equations which determine the irreducible constituents of these quantities. The solutions are discussed and constructed by iteration in terms of cluster approximants. Specializing the input data and the formal results provides a Fermi hypernetted-chain analysis of the correlations induced by a ground state wave function of the Gutzwiller form.     

Landau-Fermi liquid analysis of the 2D t-t' Hubbard model

We calculate the Landau interaction function f (k,k') for the two-dimensional t-t' Hubbard model on the square lattice using second and higher order perturbation theory. Within the Landau-Fermi liquid framework we discuss the behavior of spin and charge susceptibilities as function of the onsite interaction and band filling. In particular we analyze the role of elastic umklapp processes as driving force for the anisotropic reduction of the compressibility on parts of the Fermi surface. Received 18 March 2002 Published online 9 July 2002     

Dynamical spin magnetic susceptibility in the 2D Hubbard model

Magnetic properties of the two-dimensional Hubbard model are investigated by studying the imaginary part of the dynamical spin magnetic susceptibility as a function of momentum and doping. The calculations are performed by means of the composite operator method in the static approximation. It is shown that the results are in good qualitative agreement with the experimental data for LaSrCuO compounds.     

Ground state of Hubbard model on 2 × 2 × 2 lattice

The energy and the total spin of the ground state of Hubbard model on 2 × 2 × 2 lattice are calculated for various values of the intra-atomic Coulomb repulsion I. The total spin S of the ground state assumes the smallest value when the electron number N is 2, 3 or 6, irrespective of the value of I. For N = 5, S is $\text{3}\text{2}$ and is independent of I, too. For N = 4 or 7, S assumes the smallest value when I is not very large, and the ground state becomes completely ferromagnetic when I exceed 39 or 200 times the inter atomic transfer energy, respectively.     

Electron-doping versus hole-doping in the 2D t-t' Hubbard model

We compare the one-loop renormalization group flow to strong coupling of the electronic interactions in the two-dimensional t-t'-Hubbard model with t' = - 0.3t for band fillings smaller and larger than half-filling. Using a numerical N-patch scheme ( N = 32, ..., 96) we show that in the electron-doped case with decreasing electron density there is a rapid transition from a d _{x2 - y2}-wave superconducting regime with small characteristic energy scale to an approximate nesting regime with strong antiferromagnetic tendencies and higher energy scales. This contrasts with the hole-doped side discussed recently which exhibits a broad parameter region where the renormalization group flow suggests a truncation of the Fermi surface at the saddle points. We compare the quasiparticle scattering rates obtained from the renormalization group calculation which further emphasize the differences between the two cases. Received 19 December 2000 and Received in final form 28 February 2001     

The ground state of the neutral Hubbard model

The ground state energy of the neutral Hubbard model is calculated by BCS methods for all values of total spinS _z . Numerical results are given for the simple cubic and for the body centred cubic lattice. Antiferromagnetic ordering and a finite paramagnetic susceptibility is found for all values of the coupling constantV ₀.     

Fermi surface of the 2D Hubbard model at weak coupling

We calculate the interaction-induced deformation of the Fermi surface in the two-dimensional Hubbard model within second order perturbation theory. Close to half-filling, interactions enhance anisotropies of the Fermi surface, but they never modify the topology of the Fermi surface in the weak coupling regime.     

On the ground state of the half-filled Hubbard model

We calculate the ground state of the half-filled Hubbard model and its energy by starting from a spindensity wave approximation and improving it by incorporating transverse spin fluctuations. The calculations are done by employing a projection method. The quality of the proposed approximation is particularly high for intermediate and large Coulomb repulsionU, where it exceeds considerably e.g. that of the Gutzwiller projected spin-density wave state. To ordert ²/U (wheret is the hopping matrix element), our approximation is shown to be equivalent to a recent Coupled Cluster calculation for the Heisenberg antiferromagnet. Finally we show how to ordert ²/U the linear spin-wave approximation for the Heisenberg antiferromagnet may be obtained.     

Systematic study of d-wave superconductivity in the 2D repulsive Hubbard model

The cluster size dependence of superconductivity in the conventional two-dimensional Hubbard model, commonly believed to describe high-temperature superconductors, is systematically studied using the dynamical cluster approximation and quantum Monte Carlo simulations as a cluster solver. Because of the nonlocality of the d-wave superconducting order parameter, the results on small clusters show large size and geometry effects. In large enough clusters, the results are independent of the cluster size and display a finite temperature instability to d-wave superconductivity.     

The ground state problem in the infinite-U Hubbard model

The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ ₀ ⁽¹⁾ (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ _FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M _k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ ₀(n)<ɛ _FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m. Fiz. Tverd. Tela (St. Petersburg) 39, 193–203 (February 1997)