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

Abstract

We introduce Gutzwiller conjugate gradient minimization (GCGM) theory, an ab initio quantum many-body theory for computing the ground-state properties of infinite systems. GCGM uses the Gutzwiller wave function but does not use the commonly adopted Gutzwiller approximation (GA), which is a major source of inaccuracy. Instead, the theory uses an approximation that is based on the occupation probability of the on-site configurations, rather than approximations that decouple the site-site correlations as used in the GA. We test the theory in the one-dimensional and two-dimensional Hubbard models at various electron densities and find that GCGM reproduces energies and double occupancies in reasonable agreement with benchmark data at a very small computational cost.

The Gutzwiller conjugate gradient minimization method for correlated electron systems

“…The GCGM method generally yields results in reasonable agreement with the reference data, i.e., the auxiliary-field quantum Monte Carlo (AFQMC) [35][36][37], density-matrix renormalization group (DMRG) [38,39], and density matrix embedding theory (DMET) [40,41] results provided in reference [42]. In reference [13], we also showcase several examples of the frustrated t − t Hubbard model (t stands for the 2nd nearest-neighbor hopping), where the GCGM method yields satisfying results compared with reference data. For conciseness, we do not show them in this review.…”

“…At the weak correlation regime, i.e., U = 2, the GCGM results agree reasonably well with DMRG. However, when it comes to the strong correlation regime, i.e., U = 8, the GCGM results do not agree well with DMRG, especially when t is comparable to t. Despite this inaccuracy in the estimation of the spin correlation, the energy calculation is reasonably accurate, as shown in reference [13].…”

“…Several ways have been proposed in reference [13] to evaluate p(Γ k ). Here, we only describe the most straightforward method.…”

“…In our previous work [13], the ground-state energy of 1D and 2D Hubbard model are studied. Firstly, p(Γ i ), the probability of the configuration Γ i at site i, is evaluated using equations ( 24)- (27).…”

“…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.…”