Two-dimensional Single-band Hubbard Model Research Articles

Variational cluster approach to thermodynamic properties of interacting fermions at finite temperatures: A case study of the two-dimensional single-band Hubbard model at half filling

We formulate a finite-temperature scheme of the variational cluster approximation (VCA) particularly suitable for an exact-diagonalization cluster solver. Based on the analytical properties of the single-particle Green's function matrices, we explicitly show the branch-cut structure of logarithm of the complex determinant functions appearing in the self-energy-functional theory (SFT) and whereby construct an efficient scheme for the finite-temperature VCA. We first apply the method to explore the antiferromagnetic order in a half-filled Hubbard model by calculating the entropy, specific heat, and single-particle excitation spectrum for different values of on-site Coulomb repulsion $U$ and temperature $T$. We also calculate the $T$ dependence of the single-particle excitation spectrum in the strong coupling region, and discuss the overall similarities to and the fine differences from the spectrum obtained by the spin-density-wave mean-field theory at low temperatures and the Hubbard-I approximation at high temperatures. On the basis of the thermodynamic properties, we obtain a crossover diagram in the $(U,T)$-plane which separates a Slater-type insulator and a Mott-type insulator. Next, we demonstrate the finite-temperature scheme in the cluster-dynamical-impurity approximation (CDIA) and study the paramagnetic Mott metal-insulator transition in the half-filled Hubbard model. Formulating the finite-temperature CDIA, we first address a subtle issue regarding the treatment of the artificially introduced bath degrees of freedom which are absent in the originally considered Hubbard model. We then apply the finite-temperature CDIA to calculate the finite-temperature phase diagram in the $(U,T)$-plane. We find that the Mott transition at low temperatures is discontinuous, and the coexistence region of the metallic and insulating states persists down to zero temperature.

Optimized wave function by kinetic renormalization effect in strongly correlated region of the three-band Hubbard model

We investigate the ground state of the two-dimensional single-band Hubbard model and three-band Hubbard model (d-p model) by using a variational Monte Carlo method. We employ an optimization variational Monte Carlo method. In this method the many-body wave function is improved and optimized by introducing variational parameters in the form: ψ = exp(-S)ψ0 where ψ0 is a wave function, for example, the Gutzwiller function, and S is an operator used to include the many-body effect.The strong magnetic correlation is induced by the on-site Coulomb repulsive interaction U. The magnetic correlation plays a significant role in correlated electron systems as an origin of electron pairing as well as a main competitor of superconductivity. High-temperature superconductivity occurs in the strongly correlated region where U is greater than the bandwidth. We investigate the stability of antiferromagnetic state in the three-band d-p model.

Brillouin-zone integration scheme for many-body density of states: Tetrahedron method combined with cluster perturbation theory

By combining the tetrahedron method with the cluster perturbation theory (CPT), we present an accurate method to numerically calculate the density of states of interacting fermions without introducing the Lorentzian broadening parameter $\eta$ or the numerical extrapolation of $\eta \to 0$. The method is conceptually based on the notion of the effective single-particle Hamiltonian which can be subtracted in the Lehmann representation of the single-particle Green's function within the CPT. Indeed, we show the general correspondence between the self-energy and the effective single-particle Hamiltonian which describes exactly the single-particle excitation energies of interacting fermions. The detailed formalism is provided for two-dimensional multi-orbital systems and a benchmark calculation is performed for the two-dimensional single-band Hubbard model. The method can be adapted straightforwardly to symmetry broken states, three-dimensional systems, and finite-temperature calculations.

Effect of thermal fluctuations on magnetic phase separation and on the parameters of spin-spiral waves

Effects of temperature on magnetic phase separation and on the parameters of spin-spiral waves are studied. The study is performed using the two-dimensional single-band Hubbard model and the Hubbard-Stratonovich transformation. Both commensurate (antiferromagnetic, ferromagnetic) and incommensurate (spiral) magnetic phases are considered. The problem is solved using the static approximation with allowance for transverse fluctuations of the magnetic moment. It is shown that the temperature significantly affects the collinear and spiral magnetic phases. With an increase in the temperature, the phase-separation region near the half-filling is sufficiently reduced and substituted by the antiferromagnetic phase. The results are used for the interpretation of the magnetic properties of cuprates.

Charge and spin criticality for the continuous Mott transition in a two-dimensional organic conductor

We study the continuous bandwidth-controlled Mott transition in the two-dimensional single-band Hubbard model with a focus on the critical scaling behavior of charge and spin degrees of freedom. Using plaquette cluster dynamical mean-field theory, we find charge and spin criticality consistent with experimental results for organic conductors. In particular, the charge degree of freedom measured via the local density of states at the Fermi level shows a smoother transition than expected for the Ising universality class and in single-site dynamical mean-field theory, revealing the importance of short-ranged nonlocal correlations in two spatial dimensions. The spin criticality measured via the local spin susceptibility agrees quantitatively with nuclear magnetic resonance measurements of the spin-lattice relaxation rate.

Fidelity study of the superconducting phase diagram in the two-dimensional single-band Hubbard model

Extensive numerical studies have demonstrated that the two-dimensional single-band Hubbard model contains much of the key physics in cuprate high-temperature superconductors. However, there is no definitive proof that the Hubbard model truly possesses a superconducting ground state or, if it does, of how it depends on model parameters. To answer these longstanding questions, we study an extension of the Hubbard model including an infinite-range d-wave pair field term, which precipitates a superconducting state in the d-wave channel. Using exact diagonalization on 16-site square clusters, we study the evolution of the ground state as a function of the strength of the pairing term. This is achieved by monitoring the fidelity metric of the ground state, as well as determining the ratio between the two largest eigenvalues of the d-wave pair/spin/charge-density matrices. The calculations show a d-wave superconducting ground state in doped clusters bracketed by a strong antiferromagnetic state at half filling controlled by the Coulomb repulsion U and a weak short-range checkerboard charge ordered state at larger hole doping controlled by the next-nearest-neighbor hopping t'. We also demonstrate that negative t' plays an important role in facilitating d-wave superconductivity.

Fermi-liquid, non-Fermi-liquid, and Mott phases in iron pnictides and cuprates

The role of Coulomb correlations in the iron pnictide LaFeAsO is studied by generalizing exact diagonalization dynamical mean field theory to five orbitals. For rotationally invariant Hund's rule coupling a continuous transition from a paramagnetic Fermi-liquid phase to a non-Fermi-liquid metallic phase exhibiting frozen moments is found at moderate Coulomb energies. For Ising-like exchange, this transition is first order and occurs at a lower critical Coulomb energy. The correlation-induced scattering rate as a function of doping relative to half-filling, i.e., delta = n/5-1, where n=6 for the undoped material, is shown to be qualitatively similar to the one in the two-dimensional single-band Hubbard model. In this scenario, the parent Mott insulator of LaFeAsO is the half-filled n=5 limit, while the undoped n=6 material corresponds to the critical doping region delta_c ~ 0.2 in the cuprates, on the verge between the Fermi-liquid phase of the overdoped region and the non-Fermi-liquid pseudogap phase in the underdoped region.

Rotationally invariant slave-boson formalism and momentum dependence of the quasiparticle weight

We generalize the rotationally invariant formulation of the slave-boson formalism to multiorbital models, with arbitrary interactions, crystal fields, and multiplet structure. This allows for the study of multiplet effects on the nature of low-energy quasiparticles. Nondiagonal components of the matrix of quasiparticle weights can be calculated within this framework. When combined with cluster extensions of dynamical mean-field theory, this method allows us to address the effects of spatial correlations, such as the generation of the superexchange and the momentum dependence of the quasiparticle weight. We illustrate the method on a two-band Hubbard model, a Hubbard model made of two coupled layers, and a two-dimensional single-band Hubbard model (within a two-site cellular dynamical mean-field approximation).

Role of electron-phonon interaction on quasiparticle dispersion in the strongly correlated cuprate superconductors

The role of the electron-phonon (el-ph) interaction in high-${T}_{c}$ cuprates is investigated theoretically by considering correlated electrons interacting with Holstein phonons within the two-dimensional single-band Hubbard model in the limit of large Coulomb interaction. It is shown that the electron-phonon interaction gives rise to a kink in the dispersion along the nodal direction and to a peak/dip/hump structure in the one-electron spectral weight whose dependence on temperature, isotope substitution, and doping is discussed in relation to recent photoemission experiments on the nodal quasiparticles in Bi2201 and LSCO. A comparison with these experiments shows that electron correlations play a crucial role in the determination of the kink position, size, and doping dependence. We also show that the ``unusual'' oxygen isotope shift in the real part of the self-energy, experimentally observed in the optimally doped Bi2212 samples, can be qualitatively explained within the framework that incorporates both strong electron correlations and the adiabatic electron-phonon interaction.

PHASE SEPARATION IN THE TWO-DIMENSIONAL HUBBARD MODEL

In this paper, we study phase separation in the two-dimensional single-band Hubbard model with the unrestricted Hartree-Fock(UHF) method and the restricted Hartree-Fock (RHF) method. We perform the calculation for square lattices and rectangle lattices. It is observed that the stripe phase exists and it depends on three aspects: geometry of the lattice, Coulomb interaction U and band filling n. To gain more physical insights, we consider the Hubbard model with spin dependent hoppings: t↑ and t↓, and study the effect of varying [Formula: see text] on the phase separation.

Effect of vertex corrections on the correlation functions and the gap equation in the spin fluctuation-induced superconductors

We calculate self-consistently the Green's function and dynamical spin susceptibility on the basis of the self-consistent renormalization (SCR) theory for the two-dimensional single-band Hubbard model near half-filling. Not only the vertex corrections to the susceptibility but also those to the self-energy are incorporated in our theory. The particle–particle irreducible vertex in the linearized gap equation is approximated by the maximally crossed diagrams generated by the bare interactions and the interactions resulting from the spin fluctuations. We find that the vertex corrections generally tend to enhance both antiferromagnetic fluctuations and the d-wave superconductivity.

The superconducting gap in the two-dimensional Hubbard model

Superconductivity with singlet d-wave pairing has been studied for the two-dimensional single-band Hubbard model by means of the composite operator method. Results are given for the one-particle energy gap as a function of wave vector.

Doping dependence of optical conductivity and photoemission spectra in high Tc copper oxides

The optical conductivity σ(ω) and photoemission spectra in high T c copper oxides are examined by diagonalizing exactly the three-band and single-band Hubbard Hamiltonians of finite size clusters. The calculated results are compared with the experimental ones. The origin of the mid-infrared absorption in σ(ω) is also discussed by using two-dimensional single-band Hubbard model.

Quasiparticle bands of the two-dimensional Hubbard model.

We present a mean-field calculation of the two-dimensional single-band Hubbard model based on a Mori-projection-operator formalism. Various physical properties including the energy, effective hopping matrix element, local moment, momentum distribution function, and Fermi surface are calculated. The results are compared with those of the Hubbard-I approximation, the four-boson mean-field theory of Kotliar and Rockenstein (SBMF), and quantum Monte Carlo simulations. Systematic improvement over the Hubbard-I approximation is seen, and good agreements are obtained between our calculation and the SBMF theory.

Local anharmonic vibrations strong correlations and superconductivity: A quantum simulation study

We investigate the importance of local anharmonic vibrations of the bridging oxygen in the copper oxide high-T c materials in the context of superconductivity. For the numerical simulation we employ the projector quantum Monte Carlo method to study the ground state properties of the coupled electron-phonon system. The quantum Monte Carlo simulation allows an accurate treatment of electronic interactions which investigates the influence of strong correlations on superconductivity mediated by additional quantum degrees of freedom. As a generic model for such a system, we study the two-dimensional single band Hubbard model coupled to local pseudo spins (bridging oxygen), which mediate an effective attractive electron-electron interaction leading to superconductivity. The results are compared to those of an effective negativeU model.