Gutzwiller Variational Wave Function Research Articles

A benchmark of Gutzwiller conjugate gradient minimization method in ground state energy calculations of dimers

We present numerical results of ground-state energies of 9 molecules in the well-established G2 molecule set given by the Gutzwiller conjugate gradient minimization (GCGM) method. The method, beyond the commonly used Gutzwiller approximation, was recently developed based on Gutzwiller variational wave functions. We find that compared to benchmark data given by full configuration interaction, GCGM total energies are reasonably well reproduced with the minimum basis set. To include the dynamical correlation beyond the minimal basis calculations, we adopt the local density approximation for the dynamical correlation energy Ec. By comparing the results with benchmark data given by experiments and large-basis configuration interaction, the GCGM total energies with Ec are in general better reproduced, but discrepancies are still observed for some dimers.

Signatures of gapless fermionic spinons on a strip of the kagome Heisenberg antiferromagnet

The search for exotic quantum spin liquid states in simple yet realistic spin models remains a central challenge in the field of frustrated quantum magnetism. Here we consider the canonical nearest-neighbor kagome Heisenberg antiferromagnet restricted to a quasi-1D strip consisting entirely of corner-sharing triangles. Using large-scale density matrix renormalization group calculations, we identify in this model an extended gapless quantum phase characterized by central charge $c=2$ and power-law decaying spin and bond-energy correlations which oscillate at tunably incommensurate wave vectors. We argue that this intriguing spin liquid phase can be understood as a marginal instability of a two-band spinon Fermi surface coupled to an emergent U(1) gauge field, an interpretation which we substantiate via bosonization analysis and Monte Carlo calculations on model Gutzwiller variational wave functions. Our results represent one of the first numerical demonstrations of emergent fermionic spinons in a simple SU(2) invariant nearest-neighbor Heisenberg model beyond the strictly 1D (Bethe chain) limit.

Infinite occupation number basis of bosons: Solving a numerical challenge

In any bosonic lattice system, which is not dominated by local interactions and thus "frozen" in a Mott-type state, numerical methods have to cope with the infinite size of the corresponding Hilbert space even for finite lattice sizes. While it is common practice to restrict the local occupation number basis to $N_c$ lowest occupied states, the presence of a finite condensate fraction requires the complete number basis for an exact representation of the many-body ground state. In this work we present a novel truncation scheme to account for contributions from higher number states. By simply adding a single \textit{coherent-tail} state to this common truncation, we demonstrate increased numerical accuracy and the possible increase in numerical efficiency of this method for the Gutzwiller variational wave function and within dynamical mean-field theory.

Sum-rule corrections: a route to error cancellations in correlation matrix renormalisation theory

ABSTRACTWe recently proposed the correlation matrix renormalisation (CMR) theory to efficiently and accurately calculate ground state total energy of molecular systems, based on the Gutzwiller variational wavefunction (GWF) to treat the electronic correlation effects. To help reduce numerical complications and better adapt the CMR to infinite lattice systems, we need to further refine the way to minimise the error originated from the approximations in the theory. This conference proceeding reports our recent progress on this key issue, namely, we obtained a simple analytical functional form for the one-electron renormalisation factors, and introduced a novel sum-rule correction for a more accurate description of the intersite electron correlations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.

Correlation Matrix Renormalization Theory: Improving Accuracy with Two-Electron Density-Matrix Sum Rules

We recently proposed the correlation matrix renormalization (CMR) theory to treat the electronic correlation effects [Phys. Rev. B 2014, 89, 045131 and Sci. Rep. 2015, 5, 13478] in ground state total energy calculations of molecular systems using the Gutzwiller variational wave function (GWF). By adopting a number of approximations, the computational effort of the CMR can be reduced to a level similar to Hartree-Fock calculations. This paper reports our recent progress in minimizing the error originating from some of these approximations. We introduce a novel sum-rule correction to obtain a more accurate description of the intersite electron correlation effects in total energy calculations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.

Gutzwiller wave function for finite systems: superconductivity in the Hubbard model

We study the superconducting phase of the Hubbard model using the Gutzwiller variational wave function (GWF) and the recently proposed diagrammatic expansion technique (DE-GWF). The DE-GWF method works on the level of the full GWF and in the thermodynamic limit. Here, we consider a finite-size system to study the accuracy of the results as a function of the system size (which is practically unrestricted). We show that the finite-size scaling used, e.g. in the variational Monte Carlo method can lead to significant, uncontrolled errors. The presented research is the first step towards applying the DE-GWF method in studies of inhomogeneous situations, including systems with impurities, defects, inhomogeneous phases, or disorder.

Comparison of two approaches for the treatment of Gutzwiller variational wave functions

In this work, we analyse the variational problem emerging from the Gutzwiller approach to strongly correlated systems. This problem comprises two main steps: evaluation and minimization of the ground state energy for the postulated Gutzwiller Wave Function. We discuss the available methods for evaluating , in particular the recently proposed diagrammatic expansion method. We compare the two existing approaches to minimize : the standard approach based on the effective single-particle Hamiltonian and the so-called Statistically-consistent Gutzwiller Approximation (SGA). On the example of the superconducting phase analysis, we show that these approaches lead to the same minimum as it should be. However, the calculations within the SGA method are easier to perform and the two approaches allow for a simple cross-check of the obtained results. Finally, we show two ways of solving the equations resulting from the variational procedure, as well as how to incorporate the condition for a fixed number of particles.

Gutzwiller study of phase diagrams of extended Bose—Hubbard models

Hard-core and soft-core extended Bose-Hubbard models with fixed boson densities are studied by using the Gutzwiller variational wave function. The phase diagram of the softcore model strongly depends on its transfer integral. Specifically, a supersolid phase can be the ground state even below half-filling for a large transfer integral. The density difference between nearest-neighbor sites, which is an order parameter of the supersolid phase, strongly depends on the boson density, especially for a small transfer integral.

Numerical minimisation of Gutzwiller energy functionals

AbstractWe give a comprehensive introduction into an efficient numerical scheme for the minimisation of Gutzwiller energy functionals for multi‐band Hubbard models. Our method covers all conceivable cases of Gutzwiller variational wave functions and has been used successfully in previous numerical studies.

Gutzwiller study of extended Hubbard models with fixed boson densities

We studied all possible ground states, including supersolid (SS) phases and phase separations of hard-core- and soft-core-extended Bose--Hubbard models with fixed boson densities by using the Gutzwiller variational wave function and the linear programming method. We found that the phase diagram of the soft-core model depends strongly on its transfer integral. Furthermore, for a large transfer integral, we showed that an SS phase can be the ground state even below or at half filling against the phase separation. We also found that the density difference between nearest-neighbor sites, which indicates the density order of the SS phase, depends strongly on the boson density and transfer integral.

Spin Bose-Metal and Valence Bond Solid Phases in a Spin-1/2Model with Ring Exchanges on a Four-Leg Triangular Ladder

We study a spin-1/2 system with Heisenberg plus ring exchanges on a four-leg triangular ladder using the density matrix renormalization group and Gutzwiller variational wave functions. Near an isotropic lattice regime, for moderate to large ring exchanges we find a spin Bose-metal phase with a spinon Fermi sea consisting of three partially filled bands. Going away from the triangular towards the square lattice regime, we find a staggered dimer phase with dimers in the transverse direction, while for small ring exchanges the system is in a featureless rung phase. We also discuss parent states and a possible phase diagram in two dimensions.

Real-space variational Gutzwiller wave functions for the Anderson-Hubbard model

Partially projected Gutzwiller variational wave functions are used to describe the ground state of disordered interacting systems of fermions. We compare several different variational ground states with the exact ground state for disordered one-dimensional chains, with the goal of determining a minimal set of variational parameters required to accurately describe the spatially inhomogeneous charge densities and spin correlations. We find that, for weak and intermediate disorder, it is sufficient to include spatial variations of the charge densities in the product state alone provided that screening of the disorder potential is accounted for. For strong disorder, this prescription is insufficient and it is necessary to include spatially inhomogeneous variational parameters as well.

Gutzwiller description of non-magnetic Mott insulators: Dimer lattice model

We introduce an extension of the Gutzwiller variational wave function able to deal with insulators that escape any mean-field-like description, as, for instance, nonmagnetic insulators. As an application, we study the Mott transition from a paramagnetic metal into a nonmagnetic Peierls, or valence-bond, Mott insulator. We analyze this model by means of our Gutzwiller wave function analytically in the limit of large coordination lattices, where we find that (1) the Mott transition is of first order; (2) the Peierls gap is large in the Mott insulator, although it is mainly contributed by the electron repulsion; and (3) singlet superconductivity arises around the transition.

Extended Gutzwiller wave function for the Hubbard-Holstein model

We introduce a new type of Gutzwiller variational wave function for correlated electrons coupled to phonons, able to treat on equal footing electronic and lattice degrees of freedom. We benchmark the wave function in the infinite-U Hubbard-Holstein model away from half-filling on a Bethe lattice, where we can directly compare with exact results by the Dynamical Mean-Field Theory. For this model, we find that variational results agree perfectly well with the exact ones. In particular the wave function correctly describes the crossover to a heavy polaron gas upon increasing the electron-phonon coupling.

Quantum Lifshitz Point in the Infinite-Dimensional Hubbard Model

We show that the Gutzwiller variational wave function is very accurate for the computation of magnetic phase boundaries in the infinite-dimensional Hubbard model. This allows us to substantially extend known phase diagrams. For both the half-hypercubic and the hypercubic lattice, a large part of the phase diagram is occupied by an incommensurate phase, intermediate between the ferromagnetic and the paramagnetic phase. In case of the hypercubic lattice, the three phases join at a new quantum Lifshitz point at which the order parameter is critical and the stiffness vanishes.

Dynamical behavior across the Mott transition of two bands with different bandwidths

We investigate the role of the bandwidth difference in the Mott metal-insulator transition of a two-band Hubbard model in the limit of infinite dimensions, by means of a Gutzwiller variational wave function as well as by dynamical mean-field theory. The variational calculation predicts a two-stage quenching of the charge degrees of freedom, in which the narrower band undergoes a Mott transition before the wider one, both in the presence and in the absence of a Hund's exchange coupling. However, this scenario is not fully confirmed by the dynamical mean-field theory calculation, which shows that, although the quasiparticle residue of the narrower band is zero within our numerical accuracy, low-energy spectral weight still exists inside the Mott-Hubbard gap, concentrated into two peaks symmetric around the chemical potential. This spectral weight vanishes only when the wider band ceases to conduct too. Although our results are compatible with several scenarios, e.g., a narrow gap semiconductor or a semimetal, we argue that the most plausible one is that the two peaks coexist with a narrow resonance tied at the chemical potential, with a spectral weight below our numerical accuracy. This quasiparticle resonance is expected to vanish when the wider band undergoes the Mott transition.

Possibility of a First-Order Superfluid–Mott-Insulator Transition of Spinor Bosons in an Optical Lattice

We study the superfluid-Mott-insulator transition of antiferromagnetic spin-1 bosons in an optical lattice described by a Bose-Hubbard model. Our variational study with the Gutzwiller variational wave function determines that the superfluid-Mott-insulator transition is a first-order one at a part of the phase boundary curve, contrary to the spinless case.

The Gutzwiller wave function as a disentanglement prescription

The Gutzwiller variational wave function is shown to correspond to a particular disentanglement of the thermal evolution operator, and to be physically consistent only in the temperature range $U\ll kT\ll E_F$ , the Fermi energy of the non-interacting system. The correspondence is established without using the Gutzwiller approximation. It provides a systematic procedure for extending the ansatz to the strong-coupling regime. This is carried out to infinite order in a dominant class of commutators. The calculation shows that the classical idea of suppressing double occupation is replaced at low temperatures by a quantum RVB-like condition, which involves phases at neighboring sites. Low-energy phenomenologies are discussed in the light of this result.

Exact analytic results for the Gutzwiller wave function with finite magnetization

We present analytic results for ground-state properties of Hubbard-type models in terms of the Gutzwiller variational wave function with nonzero values of the magnetization m. In dimension $D=1$ approximation-free evaluations are made possible by appropriate canonical transformations and an analysis of umklapp processes. We calculate the double occupation and the momentum distribution, as well as its discontinuity at the Fermi surface, for arbitrary values of the interaction parameter g, density n, and magnetization m. These quantities determine the expectation value of the one-dimensional Hubbard Hamiltonian for any symmetric, monotonically increasing dispersion ${\ensuremath{\epsilon}}_{k}.$ In particular for nearest-neighbor hopping and densities away from half filling the Gutzwiller wave function is found to predict ferromagnetic behavior for sufficiently large interaction U.

Dispersion relation of a single hole in the t-J model determined by a variational Monte Carlo method.

We use a simple Gutzwiller variational wave function to study the dispersion relation of one single hole in the t-J model. Such a wave function gives a minimum of energy for the hole at (\ensuremath{\pi}/2,\ensuremath{\pi}/2), in agreement with previous results, and both a band width and an energy that are linear in J for moderate values of J.