Towards a first Principles Electronic Structure Method Based on
Dynamical Mean Field Theory Gabriel Kotliar Physics Department and
Center for Materials Theory Rutgers University Montauk Long Island
September 13-17 2009
Slide 2
Outline Dynamical Mean Field Theory: Basic Ideas Dynamical Mean
Field Theory and Electronic Structure, LDA+ DMFT Illustrative
Applications Reviews: G. Kotliar et. al. Reviews of Modern Physics
78, 865-951, (2006). K. Held Advances in Physics 56, 829
(2007)
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Correlated Electron Systems Pose Basic Questions in CMT FROM
ATOMS TO SOLIDS How to describe electron from localized to
itinerant ? How do the physical properties evolve ? Spectra and
Total Energies
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D MFT Local Physics of a solid as atom in a medium10
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Early Review: Georges Kotliar Krauth Rozenberg RMP Early
Review: Georges Kotliar Krauth Rozenberg RMP 68, 13 (1996) 12
Spectra=- Im G(k, ) Self consistency for V and Simple extensions to
phases with LRO Locality: simple extensions to cluster of sites.
Rapid advances in impurity solvers
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But how accurate is it ? Important tests in Cold Atom
Traps
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Cluster DMFT Reviews: T. Maier et. al. Rev. Mod. Phys. 77,
1027, (2005). G. Kotliar et. al. Rev. of Mod. Phys. 78, 865,
(2006). A.M Tremblay B. Kyung D. Senechal JLT Phys. 32, 424-451
(2006).
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Cluster DMFT Difficulties 2x2 cluster DMFT equations are
considerably harder to solve and to interpret than single site
DMFT. Uniqueness: No unique formulation of cluster DMFT.
Reconstruction of k dependence of quantities. Multiplicity of
Solutions.
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CDMFT vs BA in the 1D Hubbard Model density n vs chemical
potential Gap vs U at half filling V. Kancharla C. Bolech and GK
PRB 67, 075110 (2003)][[M.Capone M.Civelli V Kancharla C.Castellani
and GK PR B 69,195105 (2004) ]
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Outline Dynamical Mean Field Theory: Basic Idea Dynamical Mean
Field Theory and Electronic Structure and LDA+ DMFT Applications to
3d Materials Applications to 4f Materials Applications to 5f
Materials Outlook
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THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Functional
formulation. Chitra and Kotliar Phys. Rev. B 63, 115110 (2001)
Ambladah et. al Int. Jour Mod. Phys. B 13, 535 (1999). Ir>=|R,
> Double loop in Gloc and Wloc
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Full implementation in the context of a a one orbital lattice
model. P Sun and G. Kotliar Phys. Rev. B 66, 85120 (2002). After
finishing the loop one can treat the graphs involving Gnonloc
Wnonloc in perturbation theory.. Phys. Rev. Lett. 92, 196402 (2004)
Limiting case (perturbation theory as solvers) Zeyn and Antropov.
N. E. Zein and V. P. Antropov, J. Appl. Phys. 89, 7314 (2001),
Phys. Rev. Lett. 89, 126402 (2002) Application to semiconductors N.
Zeyn S. Savrasov and G. Kotliar PRL 96, 226403, 2006 EDMFT loop
Chitra and Kotliar Phys. Rev. B 63, 115110 (2001). G. Kotliar and
S. Savrasov in New Theoretical Approaches to Strongly Correlated
Systems, A. M. Tsvelik Ed. 2001 Kluwer Academic Publishers.
259-301. cond-mat/0208241 S. Y. Savrasov, G. Kotliar, Phys. Rev. B
69, 245101 (2004)
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Determine energy and and self consistently from extremizing a
functional : the spectral density functional. Chitra and Kotliar
(2001). Determine energy and and self consistently from extremizing
a functional : the spectral density functional. Chitra and Kotliar
(2001). R. Chitra and G. Kotliar, Phys. Rev. B 63, 115110 Savrasov
and Kotliar (2001) Full self consistent implementation. Review:
Kotliar et.al. RMP (2006) (2001). Savrasov and Kotliar (2001) Full
self consistent implementation. Review: Kotliar et.al. RMP (2006)
12 LDA+DMFT. V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and
G. Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997). U is parametrized
in terms of Slater integrals F0 F2 F4 .
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Effective interaction among electrons. Constrained RPA (cRPA)
Ferdi Ariasetiwan,A, M Imada, A Georges, G Kotliar, S Biermann, AI
Lichtenstein, PRB 70, 195104 (2004) energy-dependent effective
interaction between the 3d electrons Can be used to extract a
screened U Identity:
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THE STATE UNIVERSITY OF NEW JERSEY RUTGERS LDA+DMFT functional
Sum of local 2PI graphs with local U matrix and local G
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LDA+DMFT Self-Consistency loop DMFT U E dc
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Practical Matters Choice of the projector, in the simplest case
choice of orbital. (i.e. Projective LMTOs ) Basis in which to
truncate the Kohn Sham Hamiltonian. Implementation of charge self
consistency Impurity Solvers: slave bosons, NCA, OCA, CTQMC,
Hubbard I, etc. tradeoff between speed and accuracy. Choice of U
and double counting.
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Total Energy as a function of volume for Pu. Wrest( ) Total
Energy as a function of volume for Pu. Wrest( ) (ev) vs (a.u. 27.2
ev) (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)
Pu
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DMFT Phonons in fcc -Pu C 11 (GPa) C 44 (GPa) C 12 (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)
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Main DMFT Concepts Valence Histograms. Describes the history of
the atom in the solid, multiplets! Weiss Weiss field, collective
hybridizationfunction, quantifies the degree of localization
Functionals of density and spectra give total energies Local Self
Energies and Correlated Bands
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Qualitative Phase diagram :frustrated Hubbard model, integer
filling M. Rozenberg et.al. 75, 105 (1995) T/W 10 CONCEPT:
(orbitally resolved) spectral function. Transfer of spectral
weight. CONCEPT: Mott transition. DMFT view of Pu: adding orbitals
and coupling to strucure to this bare bones phase diagram
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What is the valence in the late actinides ? Plutonium has an
unusual form of MIXED VALENCE
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LDA results Finding the f occupancyTobin et. al. PRB 72, 085109
2005 K. Moore and G. VanDerLaan RMP (2009). Shim et. al.
Europhysics Lett (2009)
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Looking for moments. Pu under (negative ) pressure. C
Marianetti, K Haule GK and M. Fluss Phys. Rev. Lett. 101, 056403
(2008)
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Application to Electron and Hole Doped Cuprates : Review:
Armitage Fournier Green (arXiv:0906.2931 )
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Single Site vs 2 site CDMFT Phase Diagram
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Doping NCCO.2 ev.03 ev N. L. Wang, G. Li, D. Wu, X. H. Chen, C.
H. Wang, and H. Ding, Phys. Rev. B 73, 184502 (2006). Y. Onose et
al., Phys. Rev. B, 69, 024504 (2004)
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Optical Spectral Weights. C. Weber et. al. Not a very sensitive
probe of the strength of correlations around the intermediate
correlation regime. Expt points : Y. Onose et al., Phys. Rev. B,
69, 024504 (2004). S. Uchida et al., Phys. Rev. B 43, 7942
(1991).
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Underdoped vs Overdoped T=0 M. Civelli PRB 79,195113
(2009)arXiv:cond-mat/0508302arXiv:cond-mat/0508302T. Stanescu and
G. Kotliar Phys. Rev. B 74, 125110 (2006) F. F. Balakirev et. al.
arXiv.org:0710.4612 (2007). Phys. Rev. B 74, 125110 (2006)
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Avoided Quantum Criticality : QCP under the dome.
arXiv:cond-mat/0605149K. Haule and GK Phys. Rev. B 76, 092503
(2007)Avoided Quantum Criticality : QCP under the dome.
arXiv:cond-mat/0605149K. Haule and GK Phys. Rev. B 76, 092503
(2007). Coherence vanishes underdoped overdoped optimally
scattering at Tc
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Real Space Picture Momentum Space Picture: High T Singlet
formation. S,T N=2 singlet, triplet E N=0 1+ states with 1 electron
in + orb Underdoped region: arcs shrink as T is reduced. Overdoped
region FS sharpens as T is reduced.
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Conclusion Dynamical Mean Field Theory: Locality as a Basic
Idea Dynamical Mean Field Theory and Electronic Structure. Some
Interesting Applications Many others taking place, many groups
working in this area all over the world.