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

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, (2009) Deng, XD and ZF ， EPL83, （ 2008 ） MF Tian, et al., PRB 84, (2011)

The Kohn-Sham local density approximation KS ansatz: Take a 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: ?= 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

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

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 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

Gutzwiller Approximation: Generalizing to Multi-orbital

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

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

Flow chart of LDA+G: the independent mode

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

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

Application: Cerium metal under HP

Volume( ) B(GPa) PS-LDA FP-LMTO-LDA PS-GGA FP-LMTO-GGA LDA+G experiments Equilibrium Volume and Bulk Modules for alpha-ce by LDA+G

Fcc 铈能量随体积的变化图 （固定 f 电子数目的 lda+g 计算）

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

Enthalpy under pressure calculated by various of methods

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Phase diagram of Cerium metal under high pressure

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 Thank you !