Ground state wave functions for single-band Hubbard models from the Gutzwiller conjugate gradient minimisation theory

Abstract

The Gutzwiller conjugate gradient minimization (GCGM) theory is an ab initio quantum many-body theory for computing the ground-state properties of infinite systems. Previous applications of GCGM provides satisfying accuracy of ground-state energy of Hubbard models. In the current work, we address the problem of whether the obtained wave function is a good approximation for the true ground state by comparing the correlation functions with the benchmark data. Our results confirms the accuracy of the reproduced ground state of the regular Hubbard model, but with some exception for the frustrated Hubbard model.

Ground-state properties of the Hubbard model in one and two dimensions from the Gutzwiller conjugate gradient minimization theory

“…In our previous studies, we have developed the GCGM method for correlated electron systems and benchmarked it with molecules [3,4,7] and bulk systems, in particular, the Hubbard model [5,6]. As our previous study only focused on the single-band Hubbard model, in this work we continue our investigation and validate the GCGM method with a 2-band/orbital Hubbard model with demonstrated accuracy.…”

“…We have been developing such a many-body approach, namely, the Gutzwiller conjugate gradient minimization (GCGM) method [1][2][3][4][5][6][7]. The GCGM method is based on the Gutzwiller wave function (GWF) that was proposed by Gutzwiller in the 1960s [8][9][10].…”

The Gutzwiller conjugate gradient minimization method for correlated electron systems

“…Although the GCGM method generally produces energies in good agreement with benchmark data, it does not necessarily mean that the obtained wave function is a good approximation of the true ground state. In our recent work [14], we assess the quality of the wave function by comparing correlation functions, such as the joint probability of configuration pair p(Γ i , Γ i+1 ) and the spin correlation function, with the benchmark results. The estimate of p(Γ i , Γ i+1 ) is relatively accurate and the results are not presented here for conciseness.…”

“…Moving toward this goal, we have been developing an ab initio many-body approach, the Gutzwiller conjugate gradient minimization (GCGM) method [10][11][12][13][14], based on the Gutzwiller variational wave function (GWF) that were proposed by Gutzwiller in the 1960s [15][16][17]. The GWF introduces correlations into a trial wave function via an on-site correlation factor.…”

Ground and excited states of even-numbered Hubbard ring at half-filling: comparison of the extended Gutzwiller approach with exact diagonalization

“…For example, the quantum Monte Carlo method [7,8], the density matrix renormalization group (DMRG) scheme [9][10][11], the dynamical variational principle [12,13], and the symmetryprojected variational approach [6]. Our previously developed Gutzwiller conjugate gradient minimization (GCGM) theory [14,15] constitutes another efficient approach for describing strongly correlated electron systems, which has proved to provide satisfying accuracy of the ground-state (GS) energy and wavefunction of 1D and 2D Hubbard models [16,17]. GCGM is based on the Gutzwiller wave function (GWF) proposed by Gutzwiller in 1960s [18,19].…”