Including many-body screening into self-consistent calculations: Tight-binding model studies with the Gutzwiller approximation

Y. X. Yao, C. Z. Wang, and K. M. Ho

Phys. Rev. B 83, 245139 – Published 30 June 2011

Abstract

We introduce a scheme to include many-body screening processes explicitly into a set of self-consistent equations for electronic-structure calculations using the Gutzwiller approximation. The method is illustrated by the application to a tight-binding model describing the strongly correlated $γ$ -Ce system. With the inclusion of the $5 d$ electrons into the local Gutzwiller projection subspace, the correct input Coulomb repulsion $U_{f f}$ between the $4 f$ electrons for $γ$ -Ce in the calculations can be pushed far beyond the usual screened value $U_{f f}^{scr}$ and close to the bare atomic value $U_{f f}^{bare}$ . This indicates that the $d$ - $f$ many-body screening is the dominant contribution to the screening of $U_{f f}$ in this system. The method provides a promising way toward the ab initio Gutzwiller density functional theory.

Received 15 December 2010

DOI:https://doi.org/10.1103/PhysRevB.83.245139

Authors & Affiliations

Y. X. Yao, C. Z. Wang, and K. M. Ho

Ames Laboratory–US DOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 83, Iss. 24 — 15 June 2011

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Upper left panel shows the comparison between ab initio plane-wave based band structure (red thick lines) and the downfolded tight-binding result (black thin lines). The other three panels show the projected weight of $6 s$ , $5 d$ , and $4 f$ orbitals for each band.Reuse & Permissions
Figure 2
Orbital renormalization factors $z_{γ}$ (left axis, blue solid symbols) and orbital occupations $n_{γ}^{0}$ (right axis, red open symbols) as functions of the Coulomb repulsion parameter between $4 f$ electrons $U_{f f}$ . Square and circle are for the first two groups of $4 f$ orbitals with a degeneracy of 3. The third singly degenerate group is symbolized by an up-triangle. For paramagnetic solution, we have $z_{γ} = z_{γ ↑} = z_{γ ↓}$ and $n_{γ}^{0} = n_{γ ↑}^{0} = n_{γ ↓}^{0}$ .Reuse & Permissions
Figure 3
The dependence of the orbital renormalization factor $z_{γ}$ on the Coulomb repulsion parameter between the $4 f$ electrons $U_{f f}$ , that between the $4 f$ and $5 d$ electrons $U_{fd}$ , and the number of many-body screening $5 d$ channels explicitly included in the Hamiltonian, which is 1 for the left panel (one of the $e_{g}$ orbitals), 2 for the middle (two $e_{g}$ orbitals), and 5 for the right (two $e_{g}$ orbitals and three $t_{2 g}$ orbitals). The set of values of $U_{fd}$ scanned in the calculation are 1 eV indicated by black solid symbols with solid lines, 3 eV by red half-filled symbols with short-dashes, and 5 eV by blue open symbols with short dots. The three distinct $z$ factors of $4 f$ orbitals are depicted by the same symbols as in Fig. 2 with the average $z$ factor for the participating $d$ channels by down-triangles.Reuse & Permissions
Figure 4
The dependence of the orbital occupation $n_{γ}^{0}$ on the Coulomb repulsion parameter between the $4 f$ electrons $U_{f f}$ , that between the $4 f$ and $5 d$ electrons $U_{fd}$ , and the number of many-body screening $5 d$ channels explicitly included in the Hamiltonian. Plot settings are the same as Fig. 3.Reuse & Permissions
Figure 5
The sum of occupation probabilities of some group of local electronic configurations as a function of $U_{f f}$ and $U_{fd}$ with all the $5 d$ and $4 f$ orbitals in the Gutzwiller local subspace. Squares are for the configurations with no $f$ electron occupied, circles for those with one $f$ electron, and up-triangles for those with two $f$ electrons. $U_{fd} = 0$ eV is indicated by black solid symbols with solid lines, 3 eV by red half-filled symbols with short-dashes, and 5 eV by blue open symbols with short dots. The results with $U_{fd} = 0$ are the same as those with only $4 f$ orbitals included in the Gutzwiller local subspace since there are no Coulomb interactions between $5 d$ and $4 f$ electrons.Reuse & Permissions

Physical Review B

covering condensed matter and materials physics