LDA+DMFT study for LiV2O4 at T 0corpes07/BEITRAEGE/arita.pdfLiV2O4: 3d heavy Fermionsystem I n c o h...

Ryotaro ARITA (RIKEN)

LDA+DMFT study for LiV2O4 at T→0

Phys. Rev. Lett. 98 166402 (2007)

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K. Held(Max Planck Institute, Stuttgart)

A.V. Lukoyanov(Ural State Technical Univ.)

V.I. Anisimov(Institute of Metal Physics)

Collaborators

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Outline

Introduction LiV2O4: 3d heavy Fermion system

heavy (sharp) quasi-peak in A(w) for low T

Development of PQMC QMC for T→0 Application to DMFT calculation

Results LDA+DMFT(PQMC) for LiV2O4

Discussion Origin of HF behaviors

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Crossover at T*~20K

・ resistivity: r =r0+AT2 with an enhanced A

・ specific heat coefficient: anomalously largeg(T→0)~190mJ/V mol・K2

(Kadowaki-Woods relation satisfied)

・ c: broad maximum (Wilson ratio～1.8)

cf) CeRu2Si2 ~350mJ/Ce mol・K2

UPt3 ~420mJ/U mol・K2

T*・・ onset of the formation of the heavy mass quasiparticles(m*～25mLDA)

T*

(Urano et al. PRL85, 1052(2000))

LiV2O4: 3d heavy Fermion system

Incoherenet metal

FL(T2 law)

g(T→0)~190mJ/Vmol・K2

CW law at HT S=1/2 per V ion

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(Shimoyamada et al. PRL 96 026403(2006))

PhotoEmission Spectroscopy Magnetization curves(Niitaka et al. ‘06)

A sharp peak appearsfor T<26K

w=4meV, D~10meV

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

M (m

B/f.u

.)

6050403020100H (T)

H//110 1.3K 4.2K 10K 20K 30K

LiV2O4: 3d heavy Fermion system

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Kondo scenario

• Anisimov et al, 99• Eyert et al, 99• Matsuno et al, 99• Kusunose et al, 00• Lacroix, 01

• Shannon, 01 • Fulde et al, 01• Burdin et al, 02• Hopkinson et al, 02• Fujimoto, 02

Geometrical Frustration

hybridization→Kondo?

Hund

• Tsunetsugu, 02• Yamashita et al, 03• Laad et al, 03• Nekrasov et al, 03• Yushankhai et al, 07

Anisimov et al, PRL 83 364(1999)

a1g(localized)

eg(itinerant)

Theoretical studies so far

Short range (local) correlationsbecome dominant⇒ DMFT expected to be a good approx.

T=750K

LDA+DMFT by Nekrasov et al, PRB 67 085111 (2003)

Calculation forT→0

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LDA+DMFT Successful beyond-LDA method

Applications to various strongly correlated materials

Solver for the effective impurity model QMC (Hirsch-Fye)

Numerically exact Restricted to high T

(Numerically expensive for Low Teffort ~ 1/T3)

Development of Projective QMC for T→0 and its application to LDA+DMFT calculations for LiV2O4

S(w)

Impurity model

Lattice model

LDA+DMFT(QMC)

DMFT

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Purpose

Reproduce the sharp (heavy) quasi-particle peak in A(w) at T→0 by LDA+DMFT(PQMC)

Clarify the origin of HF behaviors

(Shimoyamada et al. PRL 96 026403(2006))

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1 2

1 2

1 2

..., ...

... : arbitrary operator L

L

L

s s ss s s

s s sA

ZA A

Zá ñ = á ñå

Suzuki-Trotter decomposition

Hubbard-Stratonovich transformation for Hint

Many-particle system = (free one-particle system + auxiliary field)

1 2

1 2

......

L

L

ss sss s

Z Z= å 0

1 2 ...1

12

Tr [ ]l

L

LH s n

s s sl

LZ e es

st ls

s

- D

=

º Õ Õ

0 intL

l 1= ( 1/ )Tr Tr HHH T LZ e e e ttb b t-D-D-

== = D= Õ

12( )

1

( )[ ] 12s

U s n nn n n ne et l ¯- +

=±

¯ ¯-D -= å (cosh( ) exp[ /2])Ul t= D

Monte Carlo sampling

å

= å

Auxiliary-field QMC

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0<t1,t2<b=1/T, b=LDt

Projective QMC

Finite-T QMC for the Anderson impurity model (Hirsch-Fye 86)

Projective QMC for T=0

Size of G =L2

Effort ~L3

(calculation for low T is numerically expensive)

†1 2 1 2

{ } { } 1 2{ }

( , ) ( ) ( )

( , )p p

s ss

G T c c

w Gt s st t t t

t t

= -

= å

Integrate out the conduction bandsand calculate G of the impurity

Calculate G{s}(t1,t2) from G0(t1,t2)

Feldbacher, KH, Assaad, PRL 93 136405(2004)

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0<t1,t2<b=1/T, b=LDt

Projective QMC

Finite-T QMC for the Anderson impurity model (Hirsch-Fye 86)

Projective QMC for T=0

Size of G =L2

Effort ~L3

(calculation for low T is numerically expensive)

†1 2 1 2

{ } { } 1 2{ }

( , ) ( ) ( )

( , )p p

s ss

G T c c

w Gt s st t t t

t t

= -

= å

Integrate out the conduction bandsand calculate G of the impurity

Calculate G{s}(t1,t2) from G0(t1,t2)

Feldbacher, KH, Assaad, PRL 93 136405(2004)

q b+ 0

InteractionIsing fields no interaction

tq

→∞ →∞

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Projective QMC

Interaction U only in red part

for sufficiently large P:Accurate information onG for light red part

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DMFT(PQMC)

PQMC

1 2( )G t t,1

01() ( ) )(i G i G iw w w- -S = -

( )( )( )n n

DG i di i

ew e

w m w e=

+ - S -ò1 1

0 ( ) ( ) ( )G i G i iw w w- -= + S

0 1 2( )G t t,

1 ex( p( ))) (A dG t w wt wp

= -ò(( ) 1 )

nn d

iAG i w w

p ww

w=

-ò

Maximum Entropy Method

ProblemG(t)→FT→G(iw)? No

only G(t),t<q obtained by PQMC

(T=0)(T=0)

DMFT self-consistent loop

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DMFT(PQMC)

PQMC

1 2( )G t t,1

01() ( ) )(i G i G iw w w- -S = -

( )( )( )n n

DG i di i

ew e

w m w e=

+ - S -ò1 1

0 ( ) ( ) ( )G i G i iw w w- -= + S

0 1 2( )G t t,


= -ò(( ) 1 )

nn d

iAG i w w

p ww

w=

-ò




(T=0)(T=0)


1/T

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DMFT(PQMC)

PQMC

1 2( )G t t,1

01() ( ) )(i G i G iw w w- -S = -

( )( )( )n n

DG i di i

ew e

w m w e=

+ - S -ò1 1

0 ( ) ( ) ( )G i G i iw w w- -= + S

0 1 2( )G t t,


= -ò(( ) 1 )

nn d

iAG i w w

p ww

w=

-ò



only G(t),t<qP obtained by PQMC

(T=0)(T=0)


1/T

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DMFT(PQMC)

PQMC

1 2( )G t t,1

01() ( ) )(i G i G iw w w- -S = -

( )( )( )n n

DG i di i

ew e

w m w e=

+ - S -ò1 1

0 ( ) ( ) ( )G i G i iw w w- -= + S

0 1 2( )G t t,


= -ò(( ) 1 )

nn d

iAG i w w

p ww

w=

-ò




(T=0)(T=0)


1/TqP 1/T-qP

Calculate G only for t<qPLarge t: Extrapolation byMaximum Entropy Method

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DMFT(PQMC)

PQMC

1 2( )G t t,1

01() ( ) )(i G i G iw w w- -S = -

( )( )( )n n

DG i di i

ew e

w m w e=

+ - S -ò1 1

0 ( ) ( ) ( )G i G i iw w w- -= + S

0 1 2( )G t t,


= -ò(( ) 1 )

nn d

iAG i w w

p ww

w=

-ò




(T=0)(T=0)


1/TqP 1/T-qP


FAQ:Why can we discuss A(w→0)even if we do not calculateG(t→∞) explicitly?

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DMFT(PQMC)

PQMC

1 2( )G t t,1

01() ( ) )(i G i G iw w w- -S = -

( )( )( )n n

DG i di i

ew e

w m w e=

+ - S -ò1 1

0 ( ) ( ) ( )G i G i iw w w- -= + S

0 1 2( )G t t,


= -ò(( ) 1 )

nn d

iAG i w w

p ww

w=

-ò




(T=0)(T=0)


1/TqP 1/T-qP


Sufficiently large qP needed

FAQ:Why can we discuss A(w→0)even if we do not calculateG(t→∞) explicitly?

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0 0

DMFT(PQMC)A

(w)

A(w

)

T→0

w0 w0

T>0

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0 0

DMFT(PQMC)A

(w)

A(w

)

T→0

w0

G(t

)

0 t

～exp(-wt0) G(t

)

0 t

Slow decay component

w0

T>0

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Single-band Hubbard modelHF-QMC vs. PQMC

DMFT(PQMC)

M I

HF-QMC

insulating metallic

b=16 b=40

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Convergence w.r.t q is much better than b

M I

PQMC

q=16 q=40

DMFT(PQMC)

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Convergence w.r.t q is much better than b

M I

PQMC

q=16 q=40

DMFT(PQMC)Orbital selective Mott transition in the two-orbital Hubbard model

DCA(PQMC) study for anisotropicpairing in the t-t’ Hubbard model

RA and KH, PRB 73 064515(2006)

RA and KH, PRB 72 201102(2005)

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12 (=4x3) band Hamiltonian

egp

a1g

egp

a1g

Hij(k)=

8 (=4x2) band model

Hij(k)=

DMFT self-consistent eq.

hybridization (Hij, i≠j) taken into account explicitly

ne/V=1.5

Effective low energy Hamiltonian

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LDA+DMFT Result (T=1200K, HF-QMC)

U=3.6, U’=2.4, J=0.6

U U’ U’-J Hund coupling = Ising

a1g

egp

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U=3.6, U’=2.4, J=0.6


LDA+DMFT Result (T=300K, HF-QMC)

a1g

egp

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U=3.6, U’=2.4, J=0.6


LDA+DMFT Result (T=0, PQMC)

a1g

egp

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LDA+DMFT Result (T=0, PQMC)

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Kondo scenario

• Anisimov et al, 99• Eyert et al, 99• Matsuno et al, 99• Kusunose et al, 00• Lacroix, 01

• Shannon, 01 • Fulde et al, 01• Burdin et al, 02• Hopkinson et al, 02• Fujimoto, 02

Geometrical Frustration


Hund

• Tsunetsugu, 02• Yamashita et al, 03• Laad et al, 03• Nekrasov et al, 03• Yushankhai et al, 07

Anisimov et al, PRL 83 364(1999)

a1g(localized)

eg(itinerant)

Theoretical studies so far

Short range (local) correlationsbecome dominant⇒ DMFT expected to be a good approx.

T=750K

LDA+DMFT by Nekrasov et al, PRB 67 085111 (2003)

Calculation forT→0

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DMFT self-consistent eq.

a1g-egp hybridization not considered explicitly

Kondo coupling between a1g and egp

not reason for peak above EF

Effect of a1g-egp hybridization

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Origin of the peak: a1g =slightly doped Mott insulator ?

Th. Pruschke et al, PRB 47 3553 (1993)

DMFT for the single band Hubbardn=0.97 (U=4)

na1g ~ 0.95na1g~ neg

LDA LDA+DMFT

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Origin of the peak: a1g =slightly doped Mott insulator ?

Th. Pruschke et al, PRB 47 3553 (1993)

DMFT for the single band Hubbardn=0.97 (U=4)

na1g ~ 0.95na1g~ neg

LDA LDA+DMFT

Question:Strong renormalization can survivethe presence of short-range correlationbeyond DMFT?

cf) A.Toschi, A. Katanin, K. Held (PRB 75 045118 (2007))DGA study for cubic lattice

Damping of the peak:Irrelevant for 3D frustrated lattice(?)

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Development of PQMC and its application to LDA+DMFT calculations for LiV2O4

Origin of the sharp peak just above EF

a1g = slightly doped Mott Insulator

Future problems beyond-DMFT

Conclusions

LDA+DMFT study for LiV2O4 at T 0corpes07/BEITRAEGE/arita.pdfLiV2O4: 3d heavy Fermionsystem I n c o h...

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