The mott transition in f electron systems pu a dynamical mean field perspective
Download
1 / 105

- PowerPoint PPT Presentation


  • 273 Views
  • Updated On :

The Mott transition in f electron systems, Pu, a dynamical mean field perspective Gabriel Kotliar Physics Department and Center for Materials Theory Rutgers University Collaborators: S. Savrasov (NJIT) ASR2002 Tokai Japan November 12-24 2002

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about '' - jaden


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
The mott transition in f electron systems pu a dynamical mean field perspective l.jpg

The Mott transition in f electron systems, Pu, a dynamical mean field perspective

Gabriel Kotliar

Physics Department and

Center for Materials Theory

Rutgers University

Collaborators: S. Savrasov (NJIT)

ASR2002

Tokai Japan November 12-24 2002


Mott transition in the actinide series smith kmetko phase diagram l.jpg
Mott transition in the actinide series (Smith Kmetko phase diagram)

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Small amounts of ga stabilize the d phase a lawson lanl l.jpg
Small amounts of Ga stabilize the phase diagram)d phase (A. Lawson LANL)

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Outline l.jpg

Introduction: some Pu puzzles. phase diagram)

Introduction to DMFT.

Some qualitative insights from model Hamiltonian studies.

Towards and understanding of elemental Pu.

Conclusions

Outline

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Plutonium puzzles l.jpg

DFT in the LDA or GGA is a well established tool for the calculation of ground state properties.

Many studies (Freeman, Koelling 1972)APW methods

ASA and FP-LMTO Soderlind et. Al 1990, Kollar et.al 1997, Boettger et.al 1998, Wills et.al. 1999) give

an equilibrium volume of the d phaseIs 35% lower than experiment

This is the largest discrepancy ever known in DFT based calculations.

Plutonium Puzzles

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Dft studies l.jpg

LSDA predicts magnetic long range (Solovyev et.al.) calculation of ground state properties.

Experimentally d Pu is not magnetic.

If one treats the f electrons as part of the core LDA overestimates the volume by 30%

DFT in GGA predicts correctly the volume of the a phase of Pu, when full potential LMTO (Soderlind Eriksson and Wills) is used. This is usually taken as an indication that a Pu is a weakly correlated system

U/W is not so different in alpha and delta

DFT Studies

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Pu specific heat l.jpg
Pu Specific Heat calculation of ground state properties.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Anomalous resistivity l.jpg
Anomalous Resistivity calculation of ground state properties.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Pu is not magnetic l.jpg
Pu is calculation of ground state properties.NOT MAGNETIC

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Plutonium puzzles10 l.jpg

How to think about the alpha and delta phases and compute their physical properties?

Why does delta have a negative thermal expansion?

Why do minute amount of impurities stablize delta?

Where does epsilon fit? Why is it smaller than delta?

Plutonium puzzles.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Outline11 l.jpg

Introduction: some Pu puzzles. their physical properties?

Introduction to DMFT.

Some qualitative insights from model Hamiltonian studies.

Towards and understanding of elemental Pu.

Conclusions

Outline

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Mean field classical vs quantum l.jpg
Mean-Field : Classical vs Quantum their physical properties?

Classical case

Quantum case

A. Georges, G. Kotliar (1992)

Phys. Rev. B 45, 6497

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Extensions of dmft l.jpg

Renormalizing the quartic term in the local impurity action.

EDMFT.

Taking several sites (clusters) as local entity.

CDMFT

Combining DMFT with other methods.

LDA+DMFT, GWU.

Extensions of DMFT.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Dmft effective action point of view r chitra and g kotliar phys rev b 62 12715 2000 b63 115110 2001 l.jpg

Identify observable, A. Construct an exact functional of <A>=a, G [a] which is stationary at the physical value of a.

Construct approximations to the functional G to perform practical calculations.

Example: Density functional theory (Fukuda et. al.),density, LDA, GGA.

Example: model DMFT. Observable: Local Greens function Gii (w). Exact functional G [Gii (w) ]. DMFT Approximation the functional keeping 2PI graphs

DMFT: effective action point of view. R. Chitra and G. KotliarPhys. Rev. B 62, 12715 (2000), B63, 115110 (2001)

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Slide15 l.jpg

Effective action construction. <A>=a,

Introduce local orbitals, caR(r-R), and local GF

G(R,R)(i w) =

The exact free energy can be expressed as a functional of the local Greens function and of the density by introducing sources for r(r) and G and performing a Legendre transformation, G[r(r),G(R,R)(iw)]

Spectral Density Functionals for Electronic Structure Calculations, Sergej Savrasov and Gabriel Kotliar,  cond-mat/0106308

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Slide16 l.jpg

The light, SP (or SPD) electrons are extended, well described by LDA

The heavy, D (or F) electrons are localized,treat by DMFT.

LDA already contains an average interaction of the heavy electrons, substract this out by shifting the heavy level (double counting term)

The U matrix can be estimated from first principles (Gunnarson and Anisimov, McMahan et.al. Hybertsen et.al) of viewed as parameters

Construct approximate functional which gives the LDA+DMFT equations.V. Anisimov, A. Poteryaev, M. Korotin, A.  Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, 7359-7367 (1997).

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Outer loop relax l.jpg
Outer loop relax described by LDA

Edc

G0

Impurity Solver

Imp. Solver: Hartree-Fock

G,S

U

SCC

DMFT

LDA+U

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Review l.jpg

A. Georges G. Kotliar W. Krauth M. Rozenberg. Rev Mod Phys 68,1 (1996)

Kotliar, Savrasov, in New Theoretical approaches to strongly correlated systems, Edited by A. Tsvelik, Kluwer Publishers, (2001).

Held Nekrasov Blumer Anisimov and Vollhardt et.al. Int. Jour. of Mod PhysB15, 2611 (2001).

A. Lichtenstein M. Katsnelson and G. Kotliar condmat 0211076(2002)

Review

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Outline19 l.jpg

Introduction: some Pu puzzles. 68,1 (1996)

Introduction to DMFT.

Some qualitative insights from model Hamiltonian studies.

Towards and understanding of elemental Pu.

Conclusions

Outline

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Slide20 l.jpg
Schematic DMFT phase diagram one band Hubbard model (half filling, semicircular DOS, partial frustration) Rozenberg et.al PRL (1995)

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Cerium l.jpg
Cerium filling, semicircular

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Slide22 l.jpg
Spectral Evolution at T=0 , half filling full frustration, Hubbard bands in the metal, transfer of spectral weight.

X.Zhang M. Rozenberg G. Kotliar (PRL 1993) A. Georges, G. Kotliar (1992) Phys. Rev. B 45, 6497

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Qualitative phase diagram in the u t m plane two band kotliar murthy rozenberg prl 2002 l.jpg

Coexistence regions between localized and delocalized spectral functions.

k diverges at generic Mott endpoints

Qualitative phase diagram in the U, T , m plane (two band Kotliar Murthy Rozenberg PRL (2002).

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Minimum in melting curve and divergence of the compressibility at the mott endpoint l.jpg
Minimum in melting curve and divergence of the compressibility at the Mott endpoint

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Cerium25 l.jpg
Cerium compressibility at the Mott endpoint

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Generalized phase diagram l.jpg
Generalized phase diagram compressibility at the Mott endpoint

T

U/W

Structure, bands, orbitals

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Slide27 l.jpg
Case study in f electrons, Mott transition in the actinide series. B. Johanssen 1974 Smith and Kmetko Phase Diagram 1984.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Outline28 l.jpg

Introduction: some Pu puzzles. series. B. Johanssen 1974 Smith and Kmetko Phase Diagram 1984.

DMFT , qualitative aspects of the Mott transition in model Hamiltonians.

DMFT as an electronic structure method.

DMFT results for delta Pu, and some qualitative insights.

Conclusions

Outline

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


What is the dominant atomic configuration local moment l.jpg

Snapshots of the f electron series. B. Johanssen 1974 Smith and Kmetko Phase Diagram 1984.

Dominant configuration:(5f)5

Naïve view Lz=-3,-2,-1,0,1

ML=-5 mB

S=5/2 Ms=5 mB

Mtot=0

What is the dominant atomic configuration? Local moment?

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Gga u bands savrasov kotliar phys rev lett 84 3670 3673 2000 l.jpg
GGA+U bands. Savrasov Kotliar , series. B. Johanssen 1974 Smith and Kmetko Phase Diagram 1984.Phys. Rev. Lett. 84, 3670-3673, (2000)

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


How is the magnetic moment quenched l.jpg

L=5, S=5/2, J=5/2, Mtot=Ms= series. B. Johanssen 1974 Smith and Kmetko Phase Diagram 1984.mB gJ =.7 mB

Crystal fields G7 +G8

GGA+U estimate (Savrasov and Kotliar 2000) ML=-3.9 Mtot=1.1

This bit is quenched by Kondo effect of spd electrons [ DMFT treatment]

Experimental consequence: neutrons large magnetic field induced form factor (G. Lander).

How is the Magnetic moment quenched.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Pu dmft total energy vs volume s savrasov g kotliar and e abrahams nature 410 793 2001 l.jpg
Pu: DMFT total energy vs Volume series. B. Johanssen 1974 Smith and Kmetko Phase Diagram 1984.S. Savrasov, G. Kotliar, and E. Abrahams, Nature 410, 793 (2001),

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Double well structure and d pu l.jpg

Qualitative explanation of negative thermal expansion

Double well structure and d Pu

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Dynamical mean field view of pu savrasov kotliar and abrahams nature 2001 l.jpg

Delta and Alpha Pu are both strongly correlated, the DMFT mean field free energy has a double well structure, for the same value of U. One where the f electron is a bit more localized (delta) than in the other (alpha).

Is the natural consequence of the model Hamiltonian phase diagram once electronic structure is about to vary.

Dynamical Mean Field View of Pu(Savrasov Kotliar and Abrahams, Nature 2001)

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Comments on the hf static limit for pu l.jpg

Describes only the Hubbard bands. mean field free energy has a double well structure, for the same value of U. One where the f electron is a bit more localized (delta) than in the other (alpha).

No QP states.

Single well structure in the E vs V curve.

(Savrasov and Kotliar PRL). Same if one uses a Hubbard one impurity solver.

Comments on the HF static limit for Pu

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Lda vs exp spectra l.jpg
Lda vs Exp Spectra mean field free energy has a double well structure, for the same value of U. One where the f electron is a bit more localized (delta) than in the other (alpha).

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Pu spectra dmft savrasov exp arko joyce morales wills jashley prb 62 1773 2000 l.jpg
Pu Spectra DMFT(Savrasov) EXP ( mean field free energy has a double well structure, for the same value of U. One where the f electron is a bit more localized (delta) than in the other (alpha).Arko Joyce Morales Wills Jashley PRB 62, 1773 (2000)

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Summary l.jpg

Spectra mean field free energy has a double well structure, for the same value of U. One where the f electron is a bit more localized (delta) than in the other (alpha).

Method

E vs V

Summary

LDA

LDA+U

DMFT


The delta epsilon transition l.jpg

The high temperature phase, (epsilon) is body centered cubic, and has a smaller volume than the (fcc) delta phase.

What drives this phase transition?

A functional, that computes total energies opens the way to the computation of phonon frequencies in correlated materials (S. Savrasov and G. Kotliar 2002)

The delta –epsilon transition

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Effects of structure gga dmft hubbard1 imp solver l.jpg
Effects of structure. GGA+DMFT_Hubbard1 imp.solver cubic, and has a smaller volume than the (fcc) delta phase.

Ee-Ed=350 K

GGA gives

Ee-Ed=

-6000 K

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Phonon freq thz vs q in delta pu s savrasov l.jpg
Phonon freq (THz) vs q in delta Pu (S. Savrasov) cubic, and has a smaller volume than the (fcc) delta phase.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Phonon frequency thz vs q in epsilon pu l.jpg
Phonon frequency (Thz ) vs q in epsilon Pu. cubic, and has a smaller volume than the (fcc) delta phase.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Epsilon plutonium l.jpg

Compute the energy of the most unstable frozen mode. Transverse mode at ( 0,pi, pi) with polarization (0,1,-1).

Extrapolate the form of the quartic interaction to the whole Brillouin zone.

Carry out a self consistent Born approximation to obtain the restabilize phones. Recompute the entropy difference between delta and epsilon.

Estimate the critical temperatures: 500-700 K , depending on the detials of the extrapolation.

Epsilon plutonium.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Phonon entropy drives the epsilon delta phase transition l.jpg

Epsilon is slightly more metallic than delta, but it has a much larger phonon entropy than delta.

At the phase transition the volume shrinks but the phonon entropy increases.

Phonon entropy drives the epsilon delta phase transition

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Phonons epsilon l.jpg
Phonons epsilon much larger phonon entropy than delta.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Outline46 l.jpg

Introduction: some Pu puzzles. much larger phonon entropy than delta.

DMFT , qualitative aspects of the Mott transition in model Hamiltonians.

DMFT as an electronic structure method.

DMFT results for delta Pu, and some qualitative insights into other phases.

Conclusions

Outline

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Conclusions l.jpg

DMFT produces non magnetic state, around a fluctuating (5f)^5 configuraton with correct volume the qualitative features of the photoemission spectra, and a double minima structure in the E vs V curve.

Correlated view of the alpha and delta phases of Pu. Interplay of correlations and electron phonon interactions (delta-epsilon).

Calculations can be refined.

Conclusions

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Conclusions48 l.jpg

Phonons matter. Role of electronic entropy. (5f)^5 configuraton with correct volume the qualitative features of the photoemission spectra, and a double minima structure in the E vs V curve.

In the making, new generation of DMFT programs, QMC with multiplets, full potential DMFT, frequency dependent U’s, multiplet effects , combination of DMFT with GW

Other materials, Cerium and Yterbium compounds…………

Conclusions

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Acknowledgements development of dmft l.jpg
Acknowledgements: Development of DMFT (5f)^5 configuraton with correct volume the qualitative features of the photoemission spectra, and a double minima structure in the E vs V curve.

Collaborators: V. Anisimov, R. Chitra, V. Dobrosavlevic, D. Fisher, A. Georges, H. Kajueter, W.Krauth, E. Lange, A. Lichtenstein, G. Moeller, Y. Motome, G. Palsson, S. Pankov, M. Rozenberg,S. Murthy , S. Savrasov, Q. Si, V. Udovenko, X.Y. Zhang

Funding: National Science Foundation.

Department of Energy and LANL.

Office of Naval Research.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Slide50 l.jpg

THE STATE UNIVERSITY OF NEW JERSEY (5f)^5 configuraton with correct volume the qualitative features of the photoemission spectra, and a double minima structure in the E vs V curve.

RUTGERS


Slide51 l.jpg

THE STATE UNIVERSITY OF NEW JERSEY (5f)^5 configuraton with correct volume the qualitative features of the photoemission spectra, and a double minima structure in the E vs V curve.

RUTGERS


Slide52 l.jpg

THE STATE UNIVERSITY OF NEW JERSEY (5f)^5 configuraton with correct volume the qualitative features of the photoemission spectra, and a double minima structure in the E vs V curve.

RUTGERS


Technical details l.jpg

Multiorbital situation and several atoms per unit cell considerably increase the size of the space H (of heavy electrons).

QMC scales as [N(N-1)/2]^3 N dimension of H

Fast interpolation schemes (Slave Boson at low frequency, Roth method at high frequency, + 1st mode coupling correction), match at intermediate frequencies. (Savrasov et.al 2001)

Technical details

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Technical details54 l.jpg

Atomic sphere approximation. considerably increase the size of the space H (of heavy electrons).

Ignore crystal field splittings in the self energies.

Fully relativistic non perturbative treatment of the spin orbit interactions.

Technical details

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Slide55 l.jpg

THE STATE UNIVERSITY OF NEW JERSEY considerably increase the size of the space H (of heavy electrons).

RUTGERS


Solving the dmft equations l.jpg
Solving the DMFT equations considerably increase the size of the space H (of heavy electrons).

  • Wide variety of computational tools (QMC,ED….)Analytical Methods

  • Extension to ordered states.

  • Review: A. Georges, G. Kotliar, W. Krauth and M. Rozenberg Rev. Mod. Phys. 68,13 (1996)]

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Temperature stabilizes a very anharmonic phonon mode l.jpg
Temperature stabilizes a very anharmonic phonon mode considerably increase the size of the space H (of heavy electrons).

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Slide58 l.jpg

THE STATE UNIVERSITY OF NEW JERSEY considerably increase the size of the space H (of heavy electrons).

RUTGERS


Lsda dmft functional l.jpg
LSDA+DMFT functional considerably increase the size of the space H (of heavy electrons).

F Sum of local 2PI graphs with local U matrix and local G

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


E dmft references l.jpg

H. Kajueter and G. Kotliar (unpublished and Kajuter’s Ph.D thesis (1995)).

Q. Si and J L Smith PRL 77 (1996)3391 .

R. Chitra and G.Kotliar Phys. Rev. Lett 84, 3678-3681 (2000 )

Y. Motome and G. Kotliar. PRB 62, 12800 (2000)

R. Chitra and G. Kotliar Phys. Rev. B 63, 115110 (2001)

S. Pankov and G. Kotliar PRB 66, 045117 (2002)

E-DMFT references

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Dmft impurity cavity construction l.jpg
DMFT Impurity cavity construction thesis (1995)).

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Cluster extensions of dmft l.jpg

Two impurity method. [A. Georges and G. Kotliar (1995 unpublished ) and RMP 68,13 (1996) , A. Schiller PRL75, 113 (1995)]

M. Jarrell et al Dynamical Cluster Approximation [Phys. Rev. B 7475 1998]

Periodic cluster] M. Katsenelson and A. Lichtenstein PRB 62, 9283 (2000).

G. Kotliar S. Savrasov G. Palsson and G. Biroli Cellular DMFT [PRL87, 186401 2001]

Cluster extensions of DMFT

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


C dmft l.jpg
C-DMFT unpublished ) and RMP 68,13 (1996) , A. Schiller PRL75, 113 (1995)]

C:DMFT The lattice self energy is inferred

from the cluster self energy.

Alternative approaches DCA (Jarrell et.al.) Periodic clusters (Lichtenstein and Katsnelson)

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


C dmft test in one dimension bolech kancharla gk cond mat 2002 l.jpg
C-DMFT: test in one dimension. unpublished ) and RMP 68,13 (1996) , A. Schiller PRL75, 113 (1995)](Bolech, Kancharla GK cond-mat 2002)

Gap vs U, Exact solution Lieb and Wu, Ovshinikov

Nc=2 CDMFT

vs Nc=1

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Slide65 l.jpg

THE STATE UNIVERSITY OF NEW JERSEY unpublished ) and RMP 68,13 (1996) , A. Schiller PRL75, 113 (1995)]

RUTGERS


Dmft models l.jpg
DMFT MODELS. unpublished ) and RMP 68,13 (1996) , A. Schiller PRL75, 113 (1995)]

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Mean field classical vs quantum67 l.jpg
Mean-Field : Classical vs Quantum unpublished ) and RMP 68,13 (1996) , A. Schiller PRL75, 113 (1995)]

Classical case

Quantum case

A. Georges, G. Kotliar (1992)

Phys. Rev. B 45, 6497

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Example single site dmft functional formulation l.jpg

Express in terms of Weiss field unpublished ) and RMP 68,13 (1996) , A. Schiller PRL75, 113 (1995)](G. Kotliar EPJB 99)

Example: Single site DMFT, functional formulation

Local self energy (Muller Hartman 89)

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Dmft impurity cavity construction69 l.jpg
DMFT Impurity cavity construction unpublished ) and RMP 68,13 (1996) , A. Schiller PRL75, 113 (1995)]

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Dmft review a georges g kotliar w krauth and m rozenberg rev mod phys 68 13 1996 l.jpg
DMFT Review: unpublished ) and RMP 68,13 (1996) , A. Schiller PRL75, 113 (1995)]A. Georges, G. Kotliar, W. Krauth and M. Rozenberg Rev. Mod. Phys. 68,13 (1996)]

Weissfield

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Case study ipt half filled hubbard one band l.jpg

(Uc1) unpublished ) and RMP 68,13 (1996) , A. Schiller PRL75, 113 (1995)]exact = 2.2+_.2 (Exact diag, Rozenberg, Kajueter, Kotliar PRB 1996) , confirmed by Noack and Gebhardt (1999) (Uc1)IPT =2.6

(Uc2)exact =2.97+_.05(Projective self consistent method, Moeller Si Rozenberg Kotliar Fisher PRL 1995 ), (Confirmed by R. Bulla 1999) (Uc2)IPT =3.3

(TMIT ) exact =.026+_ .004 (QMC Rozenberg Chitra and Kotliar PRL 1999), (TMIT )IPT =.045

(UMIT )exact =2.38 +- .03 (QMC Rozenberg Chitra and Kotliar PRL 1999), (UMIT )IPT =2.5 (Confirmed by Bulla 2001)

For realistic studies errors due to other sources (for example the value of U, are at least of the same order of magnitude).

Case study: IPT half filled Hubbard one band

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Spectral density functional l.jpg

The exact functional can be built in perturbation theory in the interaction (well defined diagrammatic rules )The functional can also be constructed from the atomic limit, but no explicit expression exists.

DFT is useful because good approximations to the exact density functional GDFT[r(r)] exist, e.g. LDA, GGA

A useful approximation to the exact functional can be constructed, the DMFT +LDA functional.

Spectral Density Functional

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Interfacing dmft in calculations of the electronic structure of correlated materials l.jpg
Interfacing DMFT in calculations of the electronic structure of correlated materials

Crystal Structure

+atomic positions

Model

Hamiltonian

Correlation functions

Total energies etc.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


E dmft gw effective action l.jpg
E-DMFT+GW effective action of correlated materials

G=

D=

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


E dmft gw p sun and g kotliar phys rev b 2002 l.jpg
E-DMFT +GW P. Sun and G. Kotliar Phys. Rev. B 2002 of correlated materials

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Lda dmft and lda u l.jpg

Static limit of the LDA+DMFT functional , of correlated materials

with FatomFHF reduces to the LDA+U functional

of Anisimov Andersen and Zaanen.

Crude approximation. Reasonable in ordered Mott insulators. Short time picture of the systems.

Total energy in DMFT can be approximated by LDA+U with an effective U . Extra screening processes in DMFT produce smaller Ueff.

ULDA+U < UDMFT

LDA+DMFT and LDA+U

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Minimum in melting curve and divergence of the compressibility at the mott endpoint77 l.jpg
Minimum in melting curve and divergence of the compressibility at the Mott endpoint

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Interface dmft with electronic structure l.jpg

Derive model Hamiltonians, solve by DMFT compressibility at the Mott endpoint

(or cluster extensions). Total energy?

Full many body aproach, treat light electrons by GW or screened HF, heavy electrons by DMFT [E-DMFT frequency dependent interactionsGK and S. Savrasov, P.Sun and GK cond-matt 0205522]

Treat correlated electrons with DMFT and light electrons with DFT (LDA, GGA +DMFT)

Interface DMFT with electronic structure.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Lda dmft outer loop relax l.jpg
LDA+DMFT-outer loop relax compressibility at the Mott endpoint

Edc

U

DMFT

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Outer loop relax80 l.jpg
Outer loop relax compressibility at the Mott endpoint

Edc

G0

Impurity Solver

Imp. Solver: Hartree-Fock

G,S

U

SCC

DMFT

LDA+U

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Lda dmft and lda u81 l.jpg

Static limit of the LDA+DMFT functional , compressibility at the Mott endpoint

with FatomFHF reduces to the LDA+U functional

of Anisimov Andersen and Zaanen.

Crude approximation. Reasonable in ordered Mott insulators. Short time picture of the systems.

Total energy in DMFT can be approximated by LDA+U with an effective U .

LDA+DMFT and LDA+U

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Very partial list of application of realistic dmft to materials l.jpg

QP bands in ruthenides: A. Liebsch et al (PRL 2000) compressibility at the Mott endpoint

N phase of Pu: S. Savrasov G. Kotliar and E. Abrahams (Nature 2001)

MIT in V2O3: K. Held et al (PRL 2001)

Magnetism of Fe, Ni: A. Lichtenstein M. Katsenelson and G. Kotliar et al PRL (2001)

J-G transition in Ce: K. Held A. Mc Mahan R. Scalettar (PRL 2000); M. Zolfl T. et al PRL (2000).

3d doped Mott insulator La1-xSrxTiO3 Anisimov et.al 1997, Nekrasov et.al. 1999, Udovenko et.al 2002)

………………..

Very Partial list of application of realistic DMFT to materials

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Lda dmft references l.jpg

Anisimov Poteryaev Korotin Anhokin and Kotliar J. Phys. Cond. Mat. 35, 7359 (1997).

Lichtenstein and Katsenelson PRB (1998).

Reviews:Kotliar, Savrasov, in New Theoretical approaches to strongly correlated systems, Edited by A. Tsvelik, Kluwer Publishers, (2001).

Held Nekrasov Blumer Anisimov and Vollhardt et.al. Int. Jour. of Mod PhysB15, 2611 (2001).

A. Lichtenstein M. Katsnelson and G. Kotliar (2002)

LDA+DMFT References

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Lda dmft self consistency loop l.jpg
LDA+DMFT Self-Consistency loop Cond. Mat. 35, 7359 (1997).

E

U

DMFT

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Lda dmft functional l.jpg
LDA+DMFT functional Cond. Mat. 35, 7359 (1997).

F Sum of local 2PI graphs with local U matrix and local G

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Comments on lda dmft l.jpg

Static limit of the LDA+DMFT functional , with Cond. Mat. 35, 7359 (1997).F= FHF reduces to LDA+U

Gives the local spectra and the total energy simultaneously, treating QP and H bands on the same footing.

Luttinger theorem is obeyed.

Functional formulation is essential for computations of total energies, opens the way to phonon calculations.

Comments on LDA+DMFT

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


References l.jpg

LDA+DMFT: Cond. Mat. 35, 7359 (1997).

V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, 7359-7367 (1997).

A Lichtenstein and M. Katsenelson Phys. Rev. B 57, 6884 (1988).

S. Savrasov G.Kotliar funcional formulation for full self consistent implementation of a spectral density functional.

Application to Pu S. Savrasov G. Kotliar and E. Abrahams (Nature 2001).

References

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Debye temperatures l.jpg
Debye temperatures Cond. Mat. 35, 7359 (1997).

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


References89 l.jpg

Long range Coulomb interactios, E-DMFT. R. Chitra and G. Kotliar

Combining E-DMFT and GW, GW-U , G. Kotliar and S. Savrasov

Implementation of E-DMFT , GW at the model level. P Sun and G. Kotliar.

Also S. Biermann et. al.

References

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Wilson and kadowaki woods ratio l.jpg
Wilson and Kadowaki Woods Ratio Kotliar

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Dependence on structure l.jpg
Dependence on structure Kotliar

Expt: Ve-Vd=.54 A

Theory: Ve-Vd=.35 A

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Slide92 l.jpg

Local approximation (Treglia and Ducastelle PRB 21,3729), local self energy, as in CPA.

Exact the limit defined by Metzner and Vollhardt prl 62,324(1989) inifinite.

Mean field approach to many body systems, maps lattice model onto a quantum impurity model (e.g. Anderson impurity model )in a self consistent medium for which powerful theoretical methods exist. (A. Georges and G. Kotliar prb45,6479 (1992)). See also M. Jarrell (PRL 1992) .Connect local spectra and lattice total energy.

Dynamical Mean Field Theory(DMFT)Review: A. Georges G. Kotliar W. Krauth M. Rozenberg. Rev Mod Phys 68,1 (1996)

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Correlation betwee the minimum of the melting point and the mott transition endpoint l.jpg

Divergence of the compressibility at the Mott transition endpoint.

Rapid variation of the density of the solid as a function of pressure, in the localization delocalization crossover region.

Slow variation of the volume as a function of pressure in the liquid phase

Elastic anomalies, more pronounced with orbital degeneracy.

Correlation betwee the Minimum of the melting point and the Mott transition endpoint.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Localization delocalization transition and f electrons l.jpg

Mott phenomena. Evolution of the electronic structure between the atomic limit and the band limit in an open shell situation.

The “”in between regime” is ubiquitous central them in strongly correlated systems, gives rise to interesting physics. Example Mott transition across the actinide series [ B. Johansson Phil Mag. 30,469 (1974)]

Connection between local spectra and cohesive energy using Anderson impurity models foreshadowed by J. Allen and R. Martin PRL 49, 1106 (1982) in the context of KVC for cerium.

Localization delocalization transition and f electrons.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Dmft and f electrons l.jpg

These views of the localization delocalization transition are not orthogonal and were incorporated into a more complete Dynamical Mean Field picture of the Mott transition.

G. Kotliar, EPJ-B, 11, (1999), 27 . A. Georges G. Kotliar W. Krauth M. Rozenberg. Rev Mod Phys 68,1 (1996) . Moeller Q. Si G. Kotliar M. Rozenberg and D. S Fisher, PRL 74 (1995) 2082.

DMFT: Powerful new tool for studying f electrons.

Qualitative insights into complex materials.

Turn technology developed to solve models into practical quantitative electronic structure method , to study eg. PU.

DMFT and f electrons.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Evolution of the spectral function with temperature near mott endpoint l.jpg
Evolution of the Spectral Function with Temperature near Mott endpoint.

Anomalous transfer of spectral weight connected to the proximity to the Ising Mott endpoint (Kotliar Lange and Rozenberg Phys. Rev. Lett. 84, 5180 (2000)

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Dmft effective action point of view r chitra and g kotliar phys rev b 2000 2001 l.jpg
DMFT: Effective Action point of view. Mott endpoint.R. Chitra and G. Kotliar Phys Rev. B.(2000), (2001).

  • Identify observable, A. Construct an exact functional of <A>=a, G [a] which is stationary at the physical value of a.

  • Example, density in DFT theory. (Fukuda et. al.)

  • When a is local, it gives an exact mapping onto a local problem, defines a Weiss field.

  • The method is useful when practical and accurate approximations to the exact functional exist. Example: LDA, GGA, in DFT.

  • It is useful to introduce a Lagrange multiplier l conjugate to a, G [a, l ].

  • It gives as a byproduct a additional lattice information.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Slide98 l.jpg
Schematic DMFT phase diagram one band Hubbard model (half filling, semicircular DOS, partial frustration) Rozenberg et.al PRL (1995)

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Slide99 l.jpg
Mott transition in layered organic conductors filling, semicircular S Lefebvre et al. Ito et.al, Kanoda’s talk Bourbonnais talk

Magnetic Frustration

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Ultrasound study of l.jpg
Ultrasound study of filling, semicircular

Fournier et. al. (2002)

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Comparaison with lda u l.jpg
Comparaison with LDA+U filling, semicircular

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Slide102 l.jpg
DMFT: Effective Action point of view. filling, semicircular R. Chitra and G. Kotliar Phys Rev. B.(2000), Phys. Rev. B 63, 115110 (2001)

  • Identify observable, A. Construct an exact functional of <A>=a, G [a] which is stationary at the physical value of a.

  • Example, density in DFT theory. (Fukuda et. al.)

  • When a is local, it gives an exact mapping onto a local problem, defines a Weiss field.

  • The method is useful when practical and accurate approximations to the exact functional exist. Example: LDA, GGA, in DFT.

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Example dmft for lattice model e g single band hubbard l.jpg

Observable: Local Greens function G filling, semicircular ii (w).

Exact functional G [Gii (w) ].

DMFT Approximation to the functional.

Example: DMFT for lattice model (e.g. single band Hubbard).

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Wilson and kadowaki woods ratio104 l.jpg
Wilson and Kadowaki Woods Ratio filling, semicircular

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


Comparaison with the hartree fock static limit gga u l.jpg
Comparaison with the Hartree Fock static limit: GGA+U. filling, semicircular

Volume, total energies are OK much better than LDA, but no double minima

Ee-Ed=350 K

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS


ad