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

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

Applications

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. conclusionsXY Deng, L Wang, XD and ZF; PRB79, 075114 (2009)Deng, XD and ZF ， EPL83, 37008 （ 2008）

MF Tian, et al., PRB 84, 205124 (2011)

The Kohn-Sham local density approximation

KS ansatz: Take a non-interacting system as reference

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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

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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=HLDA+HU-EDC

Gutzwiller wave-function for multi-orbital system

Γ: many body configurations on a single site.

Single band: 22=4

N-band: 22n

Local many body density matrix

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LDA LDA+U LDA+G LDA+DMFT

Variational Parameters

ψnk Ψnk & nab Ψnk & λΓΓ’ Ψnk & 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

GutzwillerVsDMFT

XY Deng, L Wang, XD and Zhong Fang; PRB79, 075114 (2009)

The flow chart of LDA+G: integrated mode

XY Deng, L Wang, XD and Zhong Fang; PRB79, 075114 (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 23.3 58.7

FP-LMTO-LDA 22.74 60.5

PS-GGA 26.30 43.0

FP-LMTO-GGA 26.05 48.7

LDA+G 28.91 36.5

experiments 28-29 20-35

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 phasea=b, c/a ： 1.414 ~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

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Conclusions:

1. We have developed LDA+Gutzwiller method2. Accurate and Fast3. Contains both correction of kinetic and

interaction energy4. Applied successfully to many correlated materials

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Thank you !