Transcript Challenges in Strongly Correlated Electron Systems: A Dynamical Mean Field Theory Perspective Gabriel Kotliar and Center for Materials Theory & CPHT Ecole Polytechnique Palaiseau &

Challenges in Strongly Correlated Electron
Systems: A Dynamical Mean Field Theory
Perspective
Gabriel Kotliar
and Center for Materials Theory &
CPHT Ecole Polytechnique Palaiseau & SPHT CEA Saclay, France
EPS 21st General Conference of the Condensed matter
Division and DPG Spring Meeting
March 26 - 31, 2006 In Dresden, Germany
$upport : NSF -DMR DOE-Basic Energy Sciences . Chaire Blaise Pascal
Fondation de l’Ecole Normale.
Fermi Liquid Theory (Landau 1957)
Density Functional Theory (Kohn Sham 1964)
- Ñ 2 / 2 + VKS (r)[r ] y kj = ekj y kj
Static Mean Field Theory.
Starting point for perturbation theory in the screened interactions (Hedin 1965)
G
1
1
0KS
 G
+[
-
VKS
]
Strong Correlation Challenges
Approach fails for strongly correlated systems
•Fermi Liquid Parameters Non Perturbative.
•Regimes where FLT Does NOT Apply. Need new
concepts to replace rigid KS bands !
Mott transition: how does the electron go
from the localized to itinerant ?
Matsuura et.
al.(2000)
k -(BEDT-TTF)2Cu[N(CN)2]Cl Lefevre et.al.
(2000)Limelette et al.,(2003)
Kagawa et al. (2003)
Dynamical Mean Field Theory. Cavity Construction.
A. Georges and G. Kotliar PRB 45, 6479 (1992).
Inspiration: Weiss (1907), Onsager (1936), DMFT for spin
glasses, Fermions in d=∞ Metzner and Vollhardt (1989)
Reviews: A. Georges W. Krauth G.Kotliar and M. Rozenberg RMP (1996)G.
Kotliar and D. Vollhardt Physics Today (2004).
Mean-Field : Classical vs Quantum
Classical case
-
å
Quantum case
J ij Si S j - hå Si
i, j

i , j  ,
i
HMF = - heff So
Easy!!!
h
áS ñ=eff
th[b heff ]
 (t
b
ij
  ij )(ci† c j  c†j ci )  U  ni  ni 
i
b
b
¶
†
m- D (t - t ')]cos (t ') + U ò no- no¯
ò ò cos (t )[ ¶ t + Hard!!!
0 0
0
QMC: J. Hirsch R. Fye (1986)
NCA : T. Pruschke and N. Grewe (1989)
PT : Yoshida and Yamada (1970)
NRG: Wilson (1980)
D (w)
0
m0 = áS0 ñHMF (heff ) IPT: Georges Kotliar (1992). .
†
G
(
i
w
)
=
á
c
os
n
os (iwn )cos (iwn )ñSMF (D )
QMC: M. Jarrell, (1992),
heff =
å
j
Jij m j +
NCA T.Pruschke D. Cox and M. Jarrell
(1993),
1
G
(
i
w
)
=
h ED:Caffarel Krauth nand Rozenberg
(1994) 1
å
Projective method: G Moellerk (1995).
[D (1999)
(iwn ) - t (k ) + m]
NRG: R. Bulla et. al. PRL 83, 136
G
(
i
w
)
[
D
]
n
,……………………………………...
• Pruschke et. al Adv. Phys. (1995)
• Georges et. al RMP
A.(1996)
Georges, G. Kotliar (1992)
DMFT Qualitative Phase diagram of a
frustrated Hubbard model at integer filling
T/W
Synthesis:
Brinkman Rice
Hubbard
Castellani et.al.
Kotliar Ruckenstein
Fujimori
Interaction with Experiments.
V2O3:Anomalous transfer of spectral weight
T=170
T=300
M. Rozenberg G. Kotliar H. Kajueter G Thomas D. Rapkine J Honig and P
Metcalf Phys. Rev. Lett. 75, 105 (1995)
.
V2O3
Mo, Denlinger, Kim,
Park, Allen, Sekiyama,
Yamasaki,
Photoemission
measurements
and Theory
Kadono, NiSxSe
Suga,1-xSaitoh,
Metcalf,
Keller,
Eyert,(1998)
Anisimov,
MatsuuraMuro,
Watanabe
Kim Doniach
ShenHeld,
Thio Bennett
Vollhardt PRL . (2003)
Poteryaev et.al. (to be published)
Spinodals and Ising critical endpoint.
Theory: Castellani et.al
Kotliar et.al.
PRL 43, 1957 (1979);
PRL84, 5180 (2003)
Observation in V2O3 :
P. Limelette et.al. Science 302, 89 (2003)
Electronic Structure Meets DMFT
• LDA+DMFT
t (k )
U
®H
®U
lda
(k ) - Edc
abcd
• Functional formulations, life without U
Gdft[r ] ¾ ¾
® Gsdft[Gloc, r ,U ] ¾ ¾
® Gsdft[Gloc, Wloc]
• Further extensions, clusters, GW+DMFT …
V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat.
35, 7359 (1997). Lichtentsein and Katsnelson. PRB 57,6884 (1998).
Almbladh et.al.(1999), Chitra and Kotliar (2000) (2001).
Savrasov Kotliar and Abrahams (2001)
Large Number of Groups and Many Compounds have been studied.
Localization Delocalization in the
Actinides
The f electrons in Plutonium are close to a localization-delocalization
transition (Johansson, 1974) .
Mott Transition

a
after G. Lander, Science (2003).
Modern understanding of this phenomena using functional
approach toDMFT. Savrasov et.al. (2001-2005)
DMFT Phonons in fcc -Pu
( Dai, Savrasov, Kotliar,Ledbetter, Migliori, Abrahams, Science, 9 May 2003)
Experiments at the European Synchrotron Radiation Facility, (Wong, Krisch, Farber,
Occelli, Schwartz,Chiang,Wall, Boro and Xu et.al, Science, 22 August 2003)
Cluster DMFT: removes limitations of single site DMFT
•No k dependence of the self energy.
•No d-wave superconductivity.
•No Peierls dimerization.
•No (R)valence bonds.
S latt (k , w) = S 11 + S 23 (cos kx + cos ky )
+ S 24 cos kx cos ky
Reviews: Georges et.al. RMP(1996). Th. Maier, M.
Jarrell, Th.Pruschke, M.H. Hettler RMP (2005);
Kotliar Savrasov et. .al. RMP in Press.
Two Site Cellular DMFT (G.. Kotliar et.al. PRL (2001)) in the 1D
Hubbard model M.Capone M.Civelli V. Kancharla C.Castellani and GK PRB
69,195105 (2004)
U/t=4.
Doping Driven Mott transiton at low temperature, in 2d
(U=16 t=1, t’=-.3 ) Hubbard model
Spectral Function A(k,ω→0)= -1/π G(k, ω →0) vs k
K.M. Shen et.al. 2004
Antinodal Region
Nodal Region
2X2 CDMFT
Civelli et.al. PRL 95 (2005)
Conclusion
• Controlled, first principles, many body
studies of correlated materials.
• Finite T Mott transition in 3d . Single site
DMFT worked well!
• Lower T, 2d ? Will CDMFT on a plaquette
help us generate the right concepts?
• New RG methods built around DMFT ?