Academic literature on the topic 'Gutzwiller Variational Method'

Abstract We present a random-sampling (RS) method for evaluating expectation values of physical quantities using the variational approach. We demonstrate that the RS method is computationally more efficient than the variational Monte Carlo method using the Gutzwiller wavefunctions applied on single-band Hubbard models as an example. Non-local constraints can also been easily implemented in the current scheme that capture the essential physics in the limit of strong on-site repulsion. In addition, we extend the RS method to study the antiferromagnetic states with multiple variational parameters for 1D and 2D Hubbard models.

Abstract The ground state phases of ultracold bosons in a ladder optical lattice subjected to a magnetic field are studied. With the inhomogeneous Gutzwiller variational method, we find that a modulated supersolid phase appears as the magnetic flux increases. The dependence of the supersolid period on the magnetic flux satisfies the commensurate conditions of integer times of 2π/ϕ.

In this paper, a new Bosonic Gutzwiller projection approach is proposed to study the strongly correlated bosons in optical lattice. In this method, there exist many variational parameters which make us calculate the physical characters of states, including the double occupation rate and the higher occupation rates. Based on this approach, a quantum phase transition from superfluid state to Mott insulator state is obtained for the homogenous phase at unit filling.

We investigate the ground state of strongly correlated electron systems based on an optimization variational Monte Carlo method to clarify the mechanism of high-temperature superconductivity. The wave function is optimized by introducing variational parameters in an exponential-type wave function beyond the Gutzwiller function. The many-body effect plays an important role as an origin of superconductivity in a correlated electron system. There is a crossover between weakly correlated region and strongly correlated region, where two regions are characterized by the strength of the on-site Coulomb interaction U. We insist that high-temperature superconductivity occurs in the strongly correlated region.

The effective mass of phosphorus-doped silicon has been calculated in the light of the Gutzwiller method for highly correlated system. The many-valley nature of the host conduction band minima with a variational impurity concentration dependence is taken into account in the calculation. The results show fair agreement when compared to previous work and available experimental data. Calculation of the density of states at the Fermi energy is also presented for the sake of comparison.

We introduce a hybrid quantum-classical variational algorithm to simulate ground-state phase diagrams of frustrated quantum spin models in the thermodynamic limit. The method is based on a cluster-Gutzwiller ansatz where the wave function of the cluster is provided by a parameterized quantum circuit whose key ingredient is a two-qubit real XY gate allowing to efficiently generate valence-bonds on nearest-neighbor qubits. Additional tunable single-qubit Z- and two-qubit ZZ-rotation gates allow the description of magnetically ordered and paramagnetic phases while restricting the variational optimization to the U(1) subspace. We benchmark the method against the J1−J2 Heisenberg model on the square lattice and uncover its phase diagram, which hosts long-range ordered Neel and columnar anti-ferromagnetic phases, as well as an intermediate valence-bond solid phase characterized by a periodic pattern of 2×2 strongly-correlated plaquettes. Our results show that the convergence of the algorithm is guided by the onset of long-range order, opening a promising route to synthetically realize frustrated quantum magnets and their quantum phase transition to paramagnetic valence-bond solids with currently developed superconducting circuit devices.

We investigate the ground state of two-dimensional Hubbard model on the basis of the variational Monte Carlo method. We use wave functions that include kinetic correlation and doublon-holon correlation beyond the Gutzwiller ansatz. It is still not clear whether the Hubbard model accounts for high-temperature superconductivity. The antiferromagnetic correlation plays a key role in the study of pairing mechanism because the superconductive phase exists usually close to the antiferromagnetic phase. We investigate the stability of the antiferromagnetic state when holes are doped as a function of the Coulomb repulsionU. We show that the antiferromagnetic correlation is suppressed asUis increased exceeding the bandwidth. High-temperature superconductivity is possible in this region with enhanced antiferromagnetic spin fluctuation and pairing interaction.

We investigate the role of kinetic energy for the stability of superconducting state in the two-dimensional Hubbard model on the basis of an optimization variational Monte Carlo method. The wave function is optimized by multiplying by correlation operators of site off-diagonal type. This wave function is written in an exponential-type form given as ψλ=exp(−λK)ψG for the Gutzwiller wave function ψG and a kinetic operator K. The kinetic correlation operator exp(−λK) plays an important role in the emergence of superconductivity in large-U region of the two-dimensional Hubbard model, where U is the on-site Coulomb repulsive interaction. We show that the superconducting condensation energy mainly originates from the kinetic energy in the strongly correlated region. This may indicate a possibility of high-temperature superconductivity due to the kinetic energy effect in correlated electron systems.

The wavefunction method provides us with a useful tool to describe electron correlations in solids at the ground state. In this paper we review the recent development of the momentum-dependent local ansatz (MLA) wavefunction. It is constructed by taking into account two-particle excited states projected onto the local orbitals, and the momentum-dependent amplitudes of these states are chosen as variational parameters. The MLA describes accurately correlated electron states from the weak to the intermediate Coulomb interaction regime in infinite dimensions, and works well even in the strongly correlated region by introducing a new starting wavefunction called the hybrid (HB) wavefunction. The MLA-HB is therefore shown to overcome the limitation of the original local ansatz (LA) wavefunction as well as the Gutzwiller wavefunction. In particular, the calculated quasiparticle weight versus Coulomb interaction curve is shown to be close to that obtained by the numerical renormalization group approach. It is also shown that the MLA is applicable to the first-principles Hamiltonian.

The plan of this thesis is as follows. Chapt. 1 is devoted to the explanation of the main theoretical tool of our work, namely the GVM and GA. After introducing their earliest formulation by Martin C. Gutzwiller, we discuss their effectiveness in describing the physics of strongly correlated conductors, emphasizing the improvements they bring in comparison with mean-field, independent-electron approximations such as HF, and their limitations with respect to more refined, though computationally more costly, methods like DMFT and VQMC. We mention how the GA was initially exploited as an approximate tool for analytical calculation of expectation values on the GVW, and how later studies proved its exactness in the limit of infinite lattice coordination. After that, we discuss its more recent multi-band formulation which, together with the mixed-basis parametrization of Gutzwiller parameter matrix, is particularly important for combining the GVM with DFT. In Chapt. 2 we present our results for the strongly correlated Hubbard lattice with broken translational invariance due to the presence of a surface (panel (a) in Fig. 1), a metal-metal or metal-insulator junction (panel (b)), or a “sandwich” of Mott insulator or strongly correlated metal between metallic leads (panel (c)). For all geometries, we show the layer dependence of the quasi-particle weight and provide approximate analytical fits for the data, together with a comparison with DMFT calculations on similar systems. In Chapt. 3, we introduce the formalism of DFT, the Kohn-Sham self-consistent equations for the functional minimization and the LDA for exchange and correlation functionals. We further discuss the performance and limitations of LDA and present the LDA+U method as a way to correct the self-interaction error of LDA. We explain the details of the GDF in Chapt. 4, and underline its similarities and differences with respect to the LDA+U functional. In the same chapter we present our data for paramagnetic and ferromagnetic bcc iron obtained through our implementation of LDA+G in the Siesta code. We show energy differences between spin-polarized and unpolarized Iron computed within LDA, GGA and LDA+G and with different basis sets. We compare the band structure, lattice parameters and magnetic moments (some sample data is shown in Table 1) obtained with these functionals, and discuss the implications of our results on the understanding of the origin of magnetism in transition metals. In the appendices we list some important results that we believed too detailed or too marginal to be presented in the main body of the thesis. Appendix A is devoted to some proofs and detailed explanations related to the GVM. In Appendix B we include all details related to the calculations on the layered geometries of Chapt. 2. In Appendix C we explain how to implement spin and orbital symmetries in the parametrization of the Gutzwiller projector, while in Appendix D we give the details of the minimization algorithm we implemented for optimizing the variational energy of the LDA+G calculation with respect to Gutzwiller parameters. Finally, Appendix E contains various topics of DFT and LDA+U that are important for the understanding of the GDF we implemented and discussed in Chapt. 4.