Towards an ab-initio theory of correlated
materials . The challenge of the iron
pnictides.
Gabriel Kotliar
Physics Department and Center for Materials
Theory Rutgers University
Work with K. Haule Z. Ying A. Kutepov
(Rutgers) S. Savrasov (U.C. Davis)
Outline
• Quantifying the strength of the correlations.
First Principles DMFT –framework.
• Case study : Iron Pnictides, do correlations
matter ? Early DMFT results.
• Recent results for the optics.
• Outlook
Collaborators (cuprates) Kristjan Haule Andrey
Kutepov S.
Savrasov (UC Davis) K. Haule (Rutgers)
$upport : NSF -DMR , DOE-Basic Energy Sciences, MURI, NSF materials
1
world network.
The Great Solid State
Dream Machine
Instrument under constant
development/improvement.
Power-Limitations-Research Opportunities.
S. V. Faleev, M. van Schilfgaarde, and T. Kotani,
Phys. Rev. Lett. 93, 126406 (2004).
GW= First order PT in screened Coulomb
interactions around LDA
3
-
Dynamical Mean Field Theory. Cavity Construction.
A. Georges and G. Kotliar PRB 45, 6479 (1992).
å
J ij Si S j - h å Si
i, j

 (t
i , j  ,
D (w) =
ij
H MF = - heff So
i
†
H Anderson
† Imp   (V c0 A +c.c). 
  ij )(c c j  c j ci ), U  ni ni
†
i
 A A  



†
,
c0† c0  Uc0†c0c0† c0
,
i
å
a
*
Va Va
w - ea
A(w)
b
b
b
¶
c
(
t
)[
+ m- D (t - t ')]cos (t ') + U ò no­ no¯
òò
¶
t
0 0
0
†
os
10
Impurity Solver
D ( w) ®
A( w),
® Gimp (iwn ),
atomic levels
S (iwn )[D ]
Machine for
summing all local
diagrams in PT in
U to all orders.
mi = th[b å J ij m j + h ]
1
iwn - S (iwn )[D ] B - D (iwn ) +
Gimp (iwn )[D ]
j
Quantifying the degree of
localization/delocalization
Glatt (iwn , k )[D ] =
1
[iwn + m+ t (k ) - S imp (iwn )[D ]]
Gimp (iwn )[D ] =
å
k
G latt (iwn , k )[D ]
8
• The power of the method increased tremendously
fueled by advances in impurity solvers.
• Extensions to cluster of sites, CDMFT capture
short range correlations, k dependent self
Over the past few years evidence for the accuracy of the
method for Hubbard models accumulated very rapidly
from: a) comparison of different cluster sizes,
• b) comparison of dmft predictions with experiments
• c) experiments in cold atom traps realizing the Hubbard
model and compared with DMFT
• d) It’s now possible to compare with exact numerical
solutions of Hubbard model at high temperatures.
(agreement within a few percent) [Gull et. al.]
•
• Just as with LDA, we know how to interpret the results and where
and how ( in which direction ) it is biased. Local approximation is
very accurate in many regions of parameter space.
• Non locality in time is essential. [ Warning for other methods!!!]
LDA+DMFT. V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J.
Phys. Cond. Mat. 35, 7359 (1997). Lichtenstein and Katsnelson (1998) LDA++
1
G ( k , iw ) 
iw  t (k )  (iw )
Spectra=- Im G(k,w)
U
®U
S
abcd
t (k )
®
®
æ0
ö
0
÷
çç
÷
ççè0 S ff - Edc÷
÷
ø
æH [k ]spd ,sps
çç
ççè H [k ] f ,spd
| 0 > ,|­ > ,|¯> ,|­ ¯>
®
ö
H [k ]spd , f ÷
÷
÷
H [k ] ff ÷
ø
| LSJM J g... >
12
Pros------------------- Issues
•
•
•
•
•
Freed Model Hamiltonian
treatments from many
parameters.
Brought DMFT to the
attention of the electronic
stuture community.
Serious improvement over
LDA+U Multiplets!
Triggered numerous
collaborations between
electronic structure groups
and many body theorist
Proof of principle of a realistic
implementations of
multiorbital DMFT. Spectra of
LaSr TiO3
• H[k] is not affected by
correlations. No
feedback on the density.
• Parameters (i.e. U, Edc,)
• Not clear how to compute
total Energies.
• Primitive Impurity Solvers
(IPT)
• Embeddings in general basis
sets. Beyond LMTO-ASA
• Projectors to define Gloc.
•
Foundation ?
Conceptual Underpinning Diagrams: PT in W and G.
1
1
[G,W ]  TrLnG  Tr[G01  G 1 ]G  TrLnW  Tr[VC1  W 1 ]W  Ehartree  [G,W ]
2
2
Introduce projector Gloc
Wloc
: Chitra and Kotliar Phys. Rev. B 62, 12715
(2000) and Phys. Rev.B (2001).
Proof of Principle Implementation
Full implementation in the context of a a one orbital lattice model.
P Sun and G. Kotliar Phys. Rev. B 66, 85120 (2002). Propose GW+DMFT .
P.Sun and GK PRL (2004). Test various levels of self consistencyin Gnonloc Pinonloc
Test notion of locality in LMTO basis set in various materials.
N. Zeyn S. Savrasov and G. Kotliar PRL 96, 226403, 2006
N Zeyn S. Savrasov and G. K PRL 96, 226403 (2006)
GW self energy for Si
Beyond GW
0.04
0.03
0.008
0.02
0.006
0.01
0.004
Sigma s GW
Sigma p GW
0
-0.01
0.002
0
-0.02
-0.002
-0.03
-0.004
-0.04
0
1
Coordination Sphere
2
-0.006
Still, summing all
diagramas with
dynamical U and
obtaining the GW
s
starting point is DD Sigma
Sigma p
extremely expensive. So
this is still
0 a point
1
of 2principle rather
than a practical
tool.
Coordination
Sphere
LDA+DMFT as an approximation to the general scheme
S
®
æ0
ç
ç
ç
ç
è0
ö
0
÷
÷
+
÷
÷
S dmft ff - Edcø
æ[Wloc ]spd ,sps [Wloc ]spd , f
Wloc (iw) = ççç
çè [Wloc ] f ,spd
[Wloc ] ff
æVxc[k ]spd ,sps
ç
ç
ç
ç Vxc[k ] f ,spd
è
é0
ù
0
ö
÷
ê
ú
÷
®
÷
÷
ø
ê0 Uabcd ú
ë
û
Vxc[k ]spd , f
Vxc[k ] ff
U is parametrized in
terms of Slater
integrals F0 F2 F4 ….
Recent calculations using B3LYP hybrid + DMFT for Ce2O3. D. Jacob K. Haule and
GK EPL 84, 57009 (2008)
Total energy is derived from a functional of the density and Gloc
CHARGE SELF CONSISTENT LDA+DMFT.
S. Savrasov GK (2002)
Savrasov, Kotliar, Abrahams, Nature ( 2001)
12
LDA+DMFT Self-Consistency loop [Savrasov Kotliar 2002]
Derived from the functional.
c ka | ­ Ñ 2 + Vxc (r ) | c ka = H LMTO ( k )
Impurity
Solver
G
0
Edc
G
U

S.C.C.
DMFT
r (r) = T
å
iw
G( r, r, iw)e
iw0+
nHH = T
å
+
GHH ( r , r , iw)eiw 0
iw
REVIEW : G. Kotliar S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, C.A. Marianetti, RMP 78, 865
Total Energy as a function of volume for Pu W (ev) vs iw
(a.u. 27.2 ev)
Pu
Savrasov, Kotliar, Abrahams, Nature ( 2001)
Non magnetic correlated state of fcc Pu.
N, Zein Following Aryasetiwan Imada
Georges Kotliar Bierman and
Lichtenstein. PRB 70 195104. (2004)
DMFT Phonons in fcc -Pu
C11 (GPa)
C44 (GPa)
C12 (GPa)
C'(GPa)
Theory
34.56
33.03
26.81
3.88
Experiment
36.28
33.59
26.73
4.78
( Dai, Savrasov, Kotliar,Ledbetter, Migliori, Abrahams, Science, 9 May 2003)
(experiments from Wong et.al, Science, 22 August 2003)
Physical Picture of Plutonium as a Non Magnetic
Strongly Correlated Mixed Valent Metal.
Different Phases differ in the Redistribution of
Spectral Weight.
Remaining Practical Issues around 2003
• Spectra: no multiplet structure due to
solver limitations.
• Test quality and role of projectors / U’s
• Need Practical Solvers for Electronic
Structure.
• Need good criteria for good projectors.
• Problems largely solved in a series of works
by K. Haule.
Photoemission
Pu is non magnetic – Cm is magnetic TN ~ 150 K.
K.Haule J. Shim and GK Nature 446, 513 (2007)
Havela et. al. Phys. Rev. B
68, 085101 (2003)
Unresolved issues ( around 2008)
• STILL NEEDED Non empirical reliable
determinations of Uabcd and Edc
together with optimal projector, given finite
computational resources [ Wanniers,
projective LMTO’s etc ]
STILL NEEDED practical solvers with retarded
interactions.
• But then came the iron pnictides…………..
Iron Pnictides
FeSe1-0.08, (Tc=27K @ 1.48GPa),
Mizuguchi et.al., arXiv: 0807.4315
Broad Range of Viewpoints
• D. J Singh and M.H. Du Phys. Rev. Lett. 100, 237003
(2008). Itinerant magnetism.
• LDA+Spin Fluctuations.
• Haule K, Shim J H and Kotliar G Phys. Rev. Lett.
100, 226402 (2008) Correlated “Bad Semi-Metal” (U<
Uc2) Multi-orbital model. Z ~0.2–0.3.
• LDA+DMFT +extensions
• Q.Si and E.Abrahams Phys. Rev. Lett. 101, 076401.
(2008). Localized picture,frustration.
• t-J model S=3/2 1/2
LDA+ DMFT for LaFxO1-xFeAs
Correlations are important: LaOFeAs is on the itinerant side but not too far away
from the metal-insulator transition . Non trivial renormalizations Z~ .2 -.3
Typical parameters U=4eV, J=0.7eV. Bad semimetal at high temperatures. Large
scattering rate.
ALL 5 d bands important (for J>0.3) relatively small crystal fields
For J=0.7eV, Uc2 =4.5 Correlated insulator.
“Since the Coulomb correlation is below the
.
critical
U for this system to undergo a Mott
transition, an itinerant approach might be
adequate. This will involve a generalization of
the spin-fluctuation exchange mechanism to a
multiorbital situation. In adition the pairing
interaction might involve not just spin but also
orbital fluctuations within the d subshell. “
The electron phonon coupling is too small to
account for superconductivity. ( similar
results obtained by D. Singh and
Boeri et. al.)
K. Haule J. Shim and GK . PRL
31
100, 226402 (2008)
FeAs and Mott Hunds materials
Hubbard U is not the “relevant” parameter.
The Hund’s coupling brings correlations!
Specific heat within LDA+DMFT
for LaO1-0.1F0.1FeAs at U=4eV
Prediction
LDA value
For J=0 there is negligible mass enhancement at U~W!
K. Haule, G. Kotliar,
J~0.35 gives correct order ofMagnitude r.
Problem for us: Experimental evidences for
weak correlations. NO SATELITES
NOT SEEN
• XES: no lower Hubbard band or sharp
quasiparticle peak
• XAS: XAS and RIXS spectra are each qualitatively
similar to Fe metal
• XPS: itinerant character of Fe 3d electrons
• V. I. Anisimov, et al, PhysicaC 469, 442 (2009)
• W. L. Yang, et al, PRB 80, 014508 (2009)
Strong vs Weak Correlation. Transfer of Spectral
Weight . Naïve One Band Hubbard Picture
Z= 1- b(U/W)2
Z= 1-(U/Uc)
Z> .5
M*/M < 2
When U/W < 1 PT theory works
Z-1 -1 < 1
Spectral weight distributed within W
When U/W > 1 PT theory fails
Z-1-1 >1
Z < .5 W
Weight transferred outside
Hubbard Satellites M*/M > 2
YOU CANNOT HAVE THE CAKE [ substantial mass renormalization ] AND EAT IT TOO
[not have satellites ]
Z-1 -1 =.6
M*/M=1.6
Z=.5
pd model:
M*/M=2
OPTICAL CONDUCTIVITY TO THE RESCUE ?
wc=3000cm-1 ~ .3 ev
M. M. Qazilbash,1,, J. J. Hamlin,1 R. E. Baumbach,1 Lijun
Zhang,2 D. J. Singh,2 M. B. Maple,1 and D. N. Basov1
Nature Physics 5, 647 (2009)
Photoemission reveals now Z ~ .3
Go back to basics: U’s for DMFT. ( Kutepov et. al. building
on the PT in G and W by R. Chitra and G. K)
Rigorous Definition of the Hubbard U and the Weiss
Field
Delta in a Solid. Kutepov et.al (2010)
.
Define a projector. Use the same projector in calculating the U’s
that you will use in your DMFT calculation
Approximate Wloc and Piloc using Self
Consistent GW. Kutepov et. al. 2010
Eliminate the hybridization to the semicore states
included in GW but not in LDA +DMFT by rescaling
Freq. dep. U matrix well parametrized by F0 F2 F4
F0 = 4:9 eV, F2 = 6:4 eV and F4 = 4:3 eV., nc=6.2
Z =1/2 for x2- y2 and z2 , Z =1/3 f xz; yz zx orbitals.
Theory: Kutepove et.al. (2010) Expt:.
Quazilbash,et.al
DMFT F0 = 4:9 eV, F2 = 6:4 eV and F4 = 4:3 eV.,
nc=6.2
DOS [kutepov et.al. 2010]
There is transfer of spectral weight to high energies, spectral weight is conserved. But
the DOS is featuresless no satellites, and resembles the LDA!
Pnictides can have substantial
mass renormalizations and no sharp satellites!!!
Big difference between oxides and pnictides.
Theory: Kutepov et.al. Expt Brouet et.al.
Possible tests of these ideas and methods
• Coherent spectral weight in dispersive Fe and As
like features would only account for a fraction of
the total weight.
• Compute the properties in the ordered state
with the same parameters used for the PM
states.
• LDA has difficulties getting the right moment,
does LDA+DMFT solve that problem ?
Comparison across families. [ Yin et. al. Work in
progress]
Magnetic phase of the iron
arsenide compounds: important issues
.
• LDA predicted the correct magnetic
structure [ (0, pi) state [ stripe ]
Predicted a strong anisotropy of the magnetic
excitation spectra. J. Dong et al PRL 83, 27006
(2008). Z. P, Yin, et al, PRL 101, 047001 (2008).
• PROBLEMS WITH ITINERANT PICTURE
• LSDA predicts a moment of 2 muB . Expt ~
1mub. Origin of failure of LSDA ?
• Needs ad hoc adjustments i.e. negative U, still
the spectra does not fit.
• Anisotropy observed dc transport and in STM.
• Chu, J.-H. et al. Evidence for an electron nematic phase
transition in underdoped iron pnictide superconductors.
arXiv:1002.3364.
Chuang, T.-M., et al. Nematic electronic structure in the
"parent" state of the iron-based superconductor
Ca(Fe1xCox)2As2. Science 327, 181 (2010).
• Is the origin of the anisotropy structural or electronic ?
• Does the nematic order drive the magnetic order or
visceversa ?
PROBLEMS WITH LOCALIZED PICTURE
• Short bond ferromagnetic, long bond antiferromangnetic.
• Short bond is less conductive than the long bond.
Is the magnetism itinerant or localized ?
• What drives the magnetism. Itinerant picture [
reduction in double occupancy, cost in kinetic
energy ]. Localized picture [ gain in
superexchange , pay double occupancy ].
• What selects the stripe state ?
• Conductivity measurments + theory should
help elucidate these issues.
LDA+DMFT Magnetic moment .95 muB
Expt 1 muB
EXPT: Hu, W. Z. et al. Phys. Rev. Lett. 101, 257005. (2008).
EXPT: Nakajima, M. et al. Phys. Rev. B 81, 104528 (2010)
LTheory Yin et. al. (2010)
Origin of the anisotropy is electronic
Optical features sharpen in the polarized spectra. Experimental predictions.
Measurements underway ( not easy !)
Spin polarization of the frequency dependent self
energy (real part). Frequency dependent exchange splitting. Large at high
energies.
Orbital polarization of the frequency dependent
hybridization Weiss field. Lives only at very low
energies.
Magnetic Stripe Phase of the FeAs
materials: new insights from LDA+DMFT Z.
Yin K. Haule and GK [ in preparation]
Focus on changes of Neff(L, T) at various energy
scales L, in going to the magnetic state.
a) At low energies conductivity goes up. Rapid
coherence crossover from an incoherent normal
state compensates for a loss of carriers. Gain
kinetic energy at very low energies!
b) For intermediate L, loss in carriers (kinetic
energy )
is a high energy phenomena, the exchange
splitting is three times bigger at infinity than at zero. LSDA
will miss that. [ Even with negative U, will not get both spectra
and moment right ! ]
• d) The cost in kinetic energy is compensated by a gain in
Hunds rule energy! Mott Hunds metal. [ Hunds is in, Hubbard
is out !]
• e) Validates our earlier view that the Hunds rule coupling
and its renormalization governs the physics of this material.
At high energies J is strong .7 ev, and induces the magnetic
moment.
• f) At low energies the Hunds rule coupling renormalizes down
to zero and good quasiparticles emerge. Coherence
incohrence crossover.
•
c) Spin polarization
• Orbital polarization is a LOW energy phenomena. [
Spin and orbital densities behave in complete opposite
ways ]. The most favorable form is orbital polarization
is ferromagnetic arrange so as to occupy the orbital
which can move better along the AF direction. [ i.e.
xz moves better along x direction ]
Does This Matter for
Superconductivity ??
The next step.
END OF THE EDUCATIONAL
PART
CMSN network for correlated materials
Postdocs –Student-Visitor-Resarch Scientist
positions Available!!!! kotliar@physics.rutgers.edu
IOWA
RUTGERS
DOE
BES
$$$
ARIZONA
UC DAVIS
When to use DMFT
• Designed to treat strongly correlated electron
materials in [ for example Mott transition problem in
3d transition metal oxides]
• Designed to compute one electron spectral functions,
photoemission and BIS
• Designed to treat finite electronic temperature
• Combines ideas of physics (bands ) and chemistry
(local CI). Cluster schemse become expensive!
• STILL ONLY GAME IN TOWN FOR A SMALL CALLS OF
SYSTEMS. AS A GENERAL PURPOSE TOOL AND IN THE
“GREY AREAS “ CONSIDER:
• Relatively new method. Still in rapid developing.
DMFT : the middle way
• More expensive than density functional theory ( because it
targets spectral properties)
• Less expensive than direct application of QMC or CI (because it
only uses these tools locally )
• Utilizes advances in electronic structure [ DMFT can be built on
top of LDA, hybrid-DFT, GW ] and techniques such as QMC or CI,
and its various levels of approx to solve the impurity problem.
• Greens function method, based on a judicious use of the local
approximation. Proved its mettle in the Mott transition problem
in the context of the model Hamiltonians.
• Realistic DMFT Goal, combine those ideas with technology from
electronic structure methods to understand and predict properties
of correlated materials.
• Testing methods: “simple” models, experiments, predictive
power ? [ lots of fun !]
Thanks for your
Attention!!
Challenges
• Optimal choice of projectors.
• Basis sets [LMTO, LAPW, plane
waves+PAW’s…..]
• Optimal description of the “weakly correlated
sector” [ dft , GW, hybrids ]
• Cluster DMFT
• Determination of the screened F0, F2, F4
Challenges
• Non Equilibrium
• Longer Scales
Nanostructures-interfaces-impurities
Local self energy approximation
Practical Route to Total Energies LDA+DMFT functional
 LDA  DMFT [ r (r ) G a b VKS(r ) ab]
­ Tr log[iwn + Ñ 2 / 2 ­ VKS ­ c *a R ( r )S a b Rc b R ( r )] ­
ò
VKS ( r )r ( r )dr -
ò
å
Vext ( r )r ( r )dr +
å
TrS (iwn )G (iwn ) +
iwn
F [Ga b R ] - F DC
R
F DC [G ] = Un(n - 1)
1
2
1
2
ò
r ( r )r ( r ')
LDA
drdr '+ E xc
[r ] +
|r- r'|
 Sum of local 2PI graphs with
local U matrix and local G
n = T å (G (iw)e )
i 0+
aa
aiw
Notice Explicit Dependence on : U , DC, and Projectors
[ Orbitals ], and Independence of basis set.
R. Chitra and Gkotliar Phys.Rev.B62:12715 (2000). S. Savrasov and G. Kotliar PRB Phys.
Rev. B 69, 245101 (2004).
GW+DMFT Why it should work ?
GW+DMFT proposed and fully implmented in the context of a a one orbital lattice model.
P Sun and G. Kotliar Phys. Rev. B 66, 85120 (2002).
Test various levels of self consistency in Gnonloc Pinonloc P.Sun and GK PRL (2004). See
also GW+dc+U Biermann, F.Aryasetiawan. and A. Georges, PRL 90, 86402 (2003)
Test notion of locality in LMTO basis set in various materials. N. Zeyn S. Savrasov
and G. Kotliar PRL 96, 226403, (2006). Include higher order graphs, first
implementation of GW+DMFT (with a perturbative impurity solver).
GW self energy for Si
Beyond GW
0.04
0.03
0.008
0.02
0.006
0.01
0.004
Sigma s GW
Sigma p GW
0
-0.01
0.002
D Sigma s
D Sigma p
0
-0.02
-0.002
-0.03
-0.004
-0.04
0
1
2
-0.006
0
Coordination Sphere
1
2
Coordination Sphere
N Zeyn S. Savrasov and G. K PRL 96, 226403 (2006)
Cutoff Radius R
Impurity
Solver
Theoretical Spectroscopies.
Cerium 115Multiple hybridization gaps
eV
10K
non-f spectra
300K
In
Ce
In
•Larger gap due to hybridization with out of plane In
•Smaller gap due to hybridization with in-plane In
C. Yee G. Kotliar K. Haule Phys. Rev. B 81, 035105 (2010)
Conceptual Underpinning : Chitra and Kotliar Phys. Rev. B 62, 12715 (2000)
and Phys. Rev.B (2001).
+
G = - < y ( x ') y † ( x ) >
1
f ( x)VC - 1 ( x, x ')f ( x ') +
ò
ò
2
ò if ( x)y
†
( x )y ( x )
< f ( x ')f ( x ) > - < f ( x ') > < f ( x ) > = W
1
1
[G,W , M , P ]  TrLn[G0 1  M ]  Tr[G ]  TrLn[VC1  P ]  Tr[ P ]W  Ehartree  [G,W ]
2
2
C-.O.Almbladh, U.von Barth and R.vanLeeuwen Int.J.Mod.Phys. B13, 535 (1999)
Introduce Notion of Local Greens functions, Wloc, Gloc
Ex. Ir>=|R, r> Gloc=G(R r, R r’)
[G,W ]   EDMFT [Gloc ,Wloc , Gnonloc  0,Wnonloc  0]
G=Gloc+Gnonloc
.
R,R’

Sum of 2PI graphs
One can also view as an approximation to an exact Spectral Density
Functional of Gloc and Wloc . One can do further PT in Gloc Gnonloc by
keeping perturbative corrections in

Pros-------------------Remaining Issues
• Freed Model Hamiltonian
treatments from many
parameters.
• Brought DMFT to the
attention of the electronic
stuture community.
• Serious improvement over
LDA+U
• Triggered numerous
collaborations between
electronic structure groups
and many body theorist
• Implementation for
Spectra of LaSr TiO3
• H[k] is not affected by
correlations. No
feedback on the density.
• Parameters (i.e. U)
• Not clear how to compute
total Energies.
• Primitive Impurity Solvers
(IPT)
• Not very accurate basis
sets to write H[k] LMTOASA
• Very primitive projectors
to define Gloc.
An exact impurity solver,
continuous time QMC - expansion in terms of hybridization
P. Werner et. al. PRL (2006) K.H.aule Phys. Rev. B 75, 155113 (2007)
General impurity problem
Diagrammatic expansion in terms of hybridization D
+Metropolis sampling over the diagrams
•Exact method: samples all diagrams!
•Allows correct treatment of multiplets
K.Haule J. Shim and GK Nature 446, 513 (2007)
Photoemission in Actinides
alpa->delta volume collapse transition
F0=4,F2=6.1
F0=4.5,F2=7.15
F0=4.5,F2=8.11
Curium has large magnetic moment and orders
antiferromagnetically Pu does is non magnetic.
Keep all bands, no downfolding, apply
correlations to Fe orbitals. Use realistic
parameters CAN HAVE MASS
RENORMALIZATIONS AND NOT SATELLITES!!!
K Haule J.Shim and G. K PRL 100, 226402 (2008)
• Since the Coulomb correlation is below the critical U for this system to
undergo a Mott transition, an itinerant approach might be adequate. This
will involve a generalization of the spin-fluctuation exchange mechanism
to a multiorbital situation. In adition the pairing interaction might involve
not just spin but also orbital fluctuations within the d subshell.
• The DMFT approach predicts a renormalized low energy band with a
fraction of the original width (Z 0.2 – 0.3) . At high temperatures, bad
(semi-)metal with large scattering rate. Coherence incoherence
crossover.
Main DMFT Concepts in electronic structure
Local Self Energies and Correlated Bands
Orbitally Resolved Spectral Functions
Transfer of spectral weight.
.
1
G ( k , iw ) 
iw  H k  (iw )
Weiss Weiss field, collective
hybridization function, quantifies
the degree of localization
ab
D (w) =
å
a
a *
b
a a
V V
w - ea
Valence Histograms. Describes the
Probability of finding the correlated
state site in the solid in a given
configuration
J. H. Shim, K. Haule, and G. Kotliar, Nature London 446, 513 (2007).
Functionals of density and
spectra, total energies: spectral
density functional.
Review: Realistic DMFT. Rev. Mod. Phys. G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko,
O. Parcollet, and C. A. Marianetti Rev. Mod. Phys. 78,865 (2006).
13
Second problem: soft underbelly of the interface between
electronic structure and DMFT .