Post on 17-Jan-2016
description
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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 !