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LDA+Gutzwiller Method for Correlated Electron Systems:  Formalism and Its Applications

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

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LDA+Gutzwiller Method for Correlated Electron Systems:  Formalism and Its Applications

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

  2. Contents • Introduction to Gutzwiller density functional theory. (Problems of LDA) • 2. LDA+Gutzwiller Method • Applications to f-electron systems: Pu and Ce • 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: Takea non-interacting system as reference

  4. The problem of LDA when applied to strongly correlated systems • Self interaction problem: spin and orbital physics • The dynamical correlation effect: <Q1Q2>?=<Q1><Q2> • The d and f electrons have both the band and atomic • nature

  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 Takea system with on-site interaction as reference H=HLDA+HU-EDC

  7. Gutzwiller wave-function for multi-orbital system Local many body density matrix Γ: many body configurations on a single site. Single band: 22=4 N-band: 22n

  8. 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 q=1: HF limit is recovered (LDA+U) If 0<q<1: Kinetic renormalization included 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. 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）Fcc铈能量随体积的变化图（固定f电子数目的lda+g计算）

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

  19. Enthalpy under pressure calculated by various of methods

  20. Phase diagram of Cerium metal under high pressure

  21. Conclusions: • 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

  22. Thank you !

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