1. 1 LDA+Gutzwiller Method for Correlated Electron Systems: Formalism and Its Applications Xi Dai Institute of Physics (IOP), CAS Beijing, China Collabrators: Zhong Fang (IOP) Students: X.Y. Deng, Mingfeng Tian IOP 2012

2. Contents 1. Introduction to Gutzwiller density functional theory. (Problems of LDA) 2. LDA+Gutzwiller Method 3.Applications to f-electron systems: Pu and Ce 4.conclusions XY Deng, L Wang, XD and ZF; PRB79, 075114 (2009) Deng, XD and ZF ， EPL83, 37008 （ 2008 ） MF Tian, et al., PRB 84, 205124 (2011)

3. The Kohn-Sham local density approximation KS ansatz: Take a non-interacting system as reference

4. 4 The problem of LDA when applied to strongly correlated systems Self interaction problem: spin and orbital physics The dynamical correlation effect: ?= The d and f electrons have both the band and atomic nature

5. 5 Methods to improve LDA for strongly correlated systems LDA+U: static mean field LDA+DMFT: introduce self energy LDA+Gutzwiller: using new variational wave fucntions

6. Using local density approximation in GDFT Generalized KS ansatz: Gutzwiller DFT Take a system with on-site interaction as reference H=H LDA +H U -E DC

7. Gutzwiller wave-function for multi-orbital system Γ: many body configurations on a single site. Single band: 2 2 =4 N-band: 2 2n Local many body density matrix

8. 8 LDALDA+ULDA+GLDA+DMF T Variational Parameters ψ nk Ψ nk & n ab Ψ nk & λ ΓΓ’ Ψ nk & Σ(iω) The variational parameters for different computational methods

9. Gutzwiller Approximation: Generalizing to Multi-orbital

10. Bench mark Gutzwiller Aproximation on two-band Hubbard model with DMFT+ED Gutzwiller Vs DMFT XY Deng, L Wang, XD and Zhong Fang; PRB79, 075114 (2009)

11. The flow chart of LDA+G: integrated mode XY Deng, L Wang, XD and Zhong Fang; PRB79, 075114 (2009)

12. Flow chart of LDA+G: the independent mode

13. LDA+G covers: From Weakly correlated metals to Strongly corrlated insulators (ordered state) If 0<q<1: Kinetic renormalization included If q=1: HF limit is recovered (LDA+U) Same as DMFT for ground state! Much cheaper than DMFT ! 5 orbitals can be solved by 1-min on PC. PRL (2008) for NaCoO2; EPL (2008) for details

14. Application: delta-Pu The bulk modules (U=4.5ev): 35Gpa

15. Application: Cerium metal under HP

16. Volume( ) B(GPa) PS-LDA23.358.7 FP-LMTO-LDA22.7460.5 PS-GGA26.3043.0 FP-LMTO-GGA26.0548.7 LDA+G28.9136.5 experiments28-2920-35 Equilibrium Volume and Bulk Modules for alpha-ce by LDA+G

17. Fcc 铈能量随体积的变化图 （固定 f 电子数目的 lda+g 计算）

18. 、 and bct phase a=b, c/a ： 1.414 ~1.5 ~1.65 ‘ phase The possible high pressure phases of Cerium metal

19. Enthalpy under pressure calculated by various of methods

20. 20

21. Phase diagram of Cerium metal under high pressure

22. 22 Conclusions: 1. We have developed LDA+Gutzwiller method 2. Accurate and Fast 3. Contains both correction of kinetic and interaction energy 4. Applied successfully to many correlated materials

23. 23 Thank you !