Gutzwiller Wave Function Research Articles

Off-Diagonal Wave Functions and Superconductivity in the Variational Monte Carlo Calculations.

We investigate the two-dimensional Hubbard model by the variational Monte Carlo method. We consider off-diagonal wave functions where we improve the Gutzwiller wave function by multiplying off-diagonal factors. In the 4×4 system, we compare our results with the exact diagonalization. The variational energies are fairly close to the exact values. We show the results for the 10×10 Hubbard model.

Gutzwiller wave function under magnetic field

Magnetization process of the Gutzwiller wave function is studied accurately by a variational Monte-Carlo method. We apply it to the one-dimensional (1D) and 2D Hubbard models (HM), and to the 1D periodic Anderson model (PAM) without orbital degeneracy. For the HM, magnetization varies discontinuously to the full moment, as the magnetic field increases. For the PAM, the paramagnetic state is unstable against ferromagnetism, although the energy reduction thereof is small.

Phase Diagram and Pairing Symmetry of the Two-Dimensionalt-JModel by a Variation Theory

Two-dimensional t-J model is studied by a variational Monte Carlo method, using Gutzwiller-Jastrow-type wave functions. Various kinds of superconducting pairing symmetries are compared in order to determine the phase diagram of the ground state in the full J/t-n plane. Near the half filling where the high temperature superconductivity is expected, the d_{x^2-y^2} wave pairing state is always the most stable among various symmetries. The three-site term hardly changes the phase diagram in this regime. In the low electron density, the extended s-type wave becomes a quantitatively good state for large J/t, although the energy gain is small. The Gutzwiller wave function is shown to be the exact ground state in the low-electron-density limit for the supersymmetric case (J/t=2).

Ground-state energy for periodic Anderson model

The ground-state properties of the asymmetric periodic Anderson model are investigated using a variational wave function recently proposed by us and the “Gutzwiller wave function”. We find that in the paramagnetic phase our wave function in the single site approximation and Gutzwiller wave function in the Gutzwiller approximation lead to an identical ground-state energy. For the first time the ground-state energy is calculated self-consistently for each of these two approaches.

Mott-Hubbard transition and antiferromagnetism on the honeycomb lattice

The Hubbard model is investigated for a halffilled honeycomb lattice, using a variational method. Two trial wave functions are introduced, the Gutzwiller wave function, well suited for describing the “metallic” phase at small U and a complementary wave function for the insulating regime at large values of U. The comparison of the two variational ground states at the mean-field level yields a Mott transition at U c /t ≈ 5:3. In addition, a variational Monte Carlo calculation is performed in order to locate the instability of the “metallic” wave function with respect to antiferromagnetism. The critical value U m/t ≈ 3:7 obtained in this way is considered to be a lower bound for the true critical point for antiferromagnetism, whereas there are good arguments that the mean-field value U c/t ≈ 5:3 represents an upper bound for the Mott transition. Therefore the “metal”- insulator transition for the honeycomb lattice may indeed be simultaneously driven by the antiferromagnetic instability and the Mott phenomenon.

One-dimensional t-J model from a variational viewpoint.

The one-dimensional (1D) t-J model is investigated by using a Gutzwiller-Jastrow-type variation method and the exact diagonalization of small systems. Variational expectation values are estimated by the variational Monte Carlo method with sufficient accuracy. First, we give detailed descriptions of the preceding paper [Phys. Rev. Lett. 67, 3610 (1991)], where we discussed the properties of the Fermi-liquid-type Jastrow wave function as well as the Gutzwiller wave function. Secondly, these wave functions are compared with the Tomonaga-Luttinger-liquid-type wave function proposed by Hellberg and Mele. It is found that the correlation factors in short distances control bulk quantities like energy and the magnitude of the correlation functions, while the long-range part of the correlation factors determines the critical behavior of correlation functions. Finally, using these functions, charge, spin susceptibilities, and magnetization curve are estimated, which agree with the exact results. It is shown that the Mott transition in the 1D t-J model is quite different from the Brinkman-Rice transition. \textcopyright{} 1996 The American Physical Society.

Alternative to Gutzwiller's approach.

An efficient variational procedure to calculate the ground-state properties of the particle-hole symmetric periodic Anderson model is presented. Expectation values are calculated by using an approximate scheme. It is shown that the ground-state energy calculated with the one-site approximation, which essentially is a single-site mean-field approximation, is identical to the corresponding energy obtained by the well-known Gutzwiller wave function using the Gutzwiller approximation. The two-site approximation, in which intersite correlations are explicitly included, is shown to be a better approximation than the Gutzwiller approximation.

Correlation effects in fullerene molecule

Electron-correlation effects in fullerene molecule are investigated in the framework of the Hubbard model. The variational Monte Carlo method and the Gutzwiller wave function are used. The pairing energy of two electrons added to a fullerene molecule or ions is calculated. Contrary to the results obtained by second order perturbation theory the pair-binding is not found at intermediate interactions.

Helicity modulus and effective hopping in the two-dimensional Hubbard model using slave-boson methods

The slave-boson mean-field method is used to study the two-dimensional Hubbard model. A magnetic phase diagram allowing for paramagnetism, weak and strong ferromagnetism and antiferromagnetism is constructed and compared to the corresponding phase diagram using the Hartree-Fock approximation (HFA). Magnetically ordered regions are reduced by a factor of about three along both the t/U and density axes compared to the HFA. Using the spin-rotation-invariant formulation of the slave-boson method the helicity modulus is computed and for half filling is found practically to coincide with that found using variational Monte Carlo calculations with the Gutzwiller wave function. Off half filling the results can be used to compare with quantum Monte Carlo calculations of the effective hopping parameter. Contrary to the case of half filling, the slave-boson approach is seen to greatly improve the results of the HFA when off half filling.

Antiferromagnetic state in the three-band Hubbard model

The antiferromagnetic (AFM) state in the three-band Hubbard model on a CuO 2 plane is studied by using both the variational Monte Carlo (VMC) method based on the Gutzwiller wave function and the Rice-Ueda type Gutwiller approximation (GA). Near half-filling, the VMC energy is significantly improved by introducing AFM long range order. In the AFM state, the VMC energy is much lower than the GA energy. The AFM phase is suppressed by the direct O-O hopping more strongly in the hole-doped case than the electron doped case.

Electronic correlation effects in a fullerene molecule studied by the variational Monte Carlo method

Electron-correlation effects in the fullerene molecule and its ions are investigated in the framework of the Hubbard model. The variational Monte Carlo method and the Gutzwiller wave function are used. Most attention is paid to the case of intermediate interactions, but also the strong coupling limit, where the Hubbard model reduces to the antiferromagnetic Heisenberg model, is considered for the fullerene molecule. In this case we obtain a very low variational ground state energy. Futher, we have calculated the main spin correlation functions in the ground state. Only short-range order is found. The pairing energy of two electrons added to a fullerene molecule or to a fullerene ion is also calculated. Contrary to the results obtained by second-order perturbation theory, pair binding is not found.

Spin waves in the 2D Hubbard model beyond the RPA

Abstract The spin-wave velocity c for the repulsive Hubbard model on a square lattice at half-filling is calculated as the square root of spin stiffness over perpendicular susceptibility using the variational Monte Carlo method with Gutzwiller wave function. For 3 ≤ U / t ≤ 12, c increases by 34-15% compared to the RPA result.

Gutzwiller wave function in the three-band Hubbard model: A variational Monte Carlo study.

The Gutzwiller wave function for the three-band Hubbard model on a two-dimensional ${\mathrm{CuO}}_{2}$ plane is studied by using the variational Monte Carlo (VMC) method in the limit ${\mathit{U}}_{\mathit{d}}$\ensuremath{\rightarrow}\ensuremath{\infty}, where ${\mathit{U}}_{\mathit{d}}$ is the Coulomb repulsion between holes on a Cu site. The VMC results for the energy and the fraction of d holes are compared with those of the Rice-Ueda type Gutzwiller approximation (GA). The difference between the VMC and the GA results are most pronounced at half-filling, and away from half-filling the two results agree well in both the hole-doped and the electron-doped cases. The doping dependence of the momentum distribution function is also studied.

Gutzwiller approximation in the Fermi hypernetted-chain theory.

We present a general formalism for the variational calculation of the one-body density-matrix and correlation functions for strongly correlated lattice electrons in terms of the Fermi hypernetted-chain (FHNC) diagrammatic expansion. It is shown that, in the limit of infinite spatial dimensions, the local-field-approximate FHNC scheme yields the exact solution for the Gutzwiller wave function, which is equivalent to the result of the Gutzwiller approximation.

Gutzwiller wave-function approach to spiral magnetic order in the two-dimensional Hubbard model: A variational Monte Carlo study

The magnetic groundstate properties of the two-dimensional Hubbard model are investigated using generalized Gutzwiller wave-functions with spiral magnetic order. Employing variational Monte Carlo simulations these wave-functions are treated without approximations on finite lattices. The resulting phase diagram shows para-, ferro-, antiferro- and spiral magnetic phases of different types.

A new expansion for generalized Gutzwiller wave functions: Antiferromagnetic case

We propose an alternative approach to the 1/D-type expansions for evaluating properties of generalized Gutzwiller wave functions (GWF’s) in low dimensions. Our expansion uses the sum rule and symmetries of the trial wave function explicitly. We apply the scheme to an antiferromagnetic generalization of the GWF for the 1D Hubbard model. We find good agreement with known results from variational Monte Carlo calculations and a significant improvement over previous approximations.

A variational Monte Carlo study of the three-band Hubbard model

The three-band Hubbard model on a two-dimensional CuO 2 plane is studied based on a Gutzwiller wavefunction using the variational Monte Carlo (VMC) method. We calculate the energy, the number of holes on Cu sites, the momentum distribution function, and the spin and charge structure factors in the strong coupling limit, where the Coulomb repulsion between holes on the Cu site is U d=∞.

High-order perturbation expansion for the two-dimensional Hubbard model using the Gutzwiller wave function.

A variational approach of the two-dimensional Hubbard model is presented, based on the Gutzwiller wave function, making no use of the Gutzwiller approximation. We calculated exactly the coefficients of the (${\mathit{g}}^{2}$-1${)}^{\mathit{m}}$ expansion of the ground-state energy (g is the Gutzwiller variational parameter) up to the m=8 order. The mg8 terms were deduced with an acuracy O[(n/2${)}^{18}$] as a function of the electron concentration n. Double occupancy, expectation value of the interaction energy, average kinetic energy, and the minimized ground-state energy are determined and their electron concentration and dimensionality dependence are discussed. An evaluation of the nonanalyticities for any dimension is also presented.

Brinkman-Rice transition in the three-band Hubbard model

The ${\mathit{U}}_{\mathit{d}}$=\ensuremath{\infty} three-band Hubbard model on a two-dimensional ${\mathrm{CuO}}_{2}$ network is studied based on a Gutzwiller wave function by use of the variational Monte Carlo (VMC) method, where ${\mathit{U}}_{\mathit{d}}$ is the Coulomb repulsion between holes on the Cu site (hole picture). The VMC results are compared with those of the Rice-Ueda-type Gutzwiller approximation (GA) in a half-filled band, where the average number of holes per Cu site is n=1. In the GA the Brinkman-Rice (BR) transition occurs at a finite value of ${\mathrm{\ensuremath{\Delta}}}_{0}$=(${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{p}}$-${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{d}}$)/2, and then the number of d holes becomes ${\mathit{n}}_{\mathit{d}}$=n=1. Whether the BR transition really occurs or not within the Gutzwiller wave function is discussed in detail. In finite systems the absence of the BR transition is shown analytically. The thermodynamic limit is examined assuming the asymptotic behavior of ${\mathit{n}}_{\mathit{d}}$ is given by a scaling function. The results of the finite-size scaling analysis suggest the absence of the BR transition as that in the single-band Hubbard model.

Sum rule and symmetry-controlled expansion for generalized Gutzwiller wave functions.

A systematic expansion scheme that goes beyond the Gutzwiller-type approximation is developed for generalized Gutzwiller wave functions. The expansion satisfies sum rules and symmetries of the trial wave function in a self-consistent way. We apply the scheme to an antiferromagnetic generalization of the Gutzwiller wave function for the one-dimensional Hubbard model. We find good agreement with known results from variational Monte Carlo calculations. We also demonstrate that the expansion scheme converges rapidly.