LDA+DMFT study for LiV 2 O 4 at T 0

Transcription

1 LDA+DMFT study for LiV 2 O 4 at T 0 Phys. Rev. Lett (2007) Ryotaro ARITA (RIKEN)

2 Collaborators K. Held (Max Plack Istitute, Stuttgart) A.V. Lukoyaov (Ural State Techical Uiv.) V.I. Aisimov (Istitute of Metal Physics)

3 Outlie Itroductio LiV 2 O 4 : 3d heavy Fermio system heavy (shar) quasi-eak i A(w) for low T Develomet of PQMC QMC for T 0 Alicatio to DMFT calculatio Results LDA+DMFT(PQMC) for LiV 2 O 4 Discussio Origi of HF behaviors

4 LiV 2 O 4 : 3d heavy Fermio system Icohereet metal FL(T 2 law) g(t 0)~190mJ/Vmol K 2 Crossover at T*~20K resistivity: r =r 0 +AT 2 with a ehaced A secific heat coefficiet: aomalously large g(t 0)~190mJ/V mol K 2 cf) CeRu 2 Si 2 ~350mJ/Ce mol K 2 UPt 3 ~420mJ/U mol K 2 T* CW law at HT S=1/2 er V io (Urao et al. PRL85, 1052(2000)) (Kadowaki-Woods relatio satisfied) c: broad maximum (Wilso ratio~1.8) T* oset of the formatio of the heavy mass quasiarticles (m*~25m LDA )

5 LiV 2 O 4 : 3d heavy Fermio system PhotoEmissio Sectroscoy (Shimoyamada et al. PRL (2006)) Magetizatio curves (Niitaka et al. 06) M (m B /f.u.) H// K 4.2K 10K 20K 30K H (T) A shar eak aears for T<26K w=4mev, D~10meV

6 Theoretical studies so far Aisimov et al, 99 Eyert et al, 99 Matsuo et al, 99 Kusuose et al, 00 Lacroix, 01 Shao, 01 Fulde et al, 01 Burdi et al, 02 Hokiso et al, 02 Fujimoto, 02 Tsuetsugu, 02 Yamashita et al, 03 Laad et al, 03 Nekrasov et al, 03 Yushakhai et al, 07 Kodo sceario Aisimov et al, PRL (1999) e g (itierat) Geometrical Frustratio Short rage (local) correlatios become domiat DMFT exected to be a good arox. Hud a 1g (localized) hybridizatio Kodo? T=750K LDA+DMFT by Nekrasov et al, PRB (2003) Calculatio for T 0

7 LDA+DMFT(QMC) LDA+DMFT Successful beyod-lda method Alicatios to various strogly correlated materials DMFT Solver for the effective imurity model QMC (Hirsch-Fye) Lattice model Numerically exact Restricted to high T (Numerically exesive for Low T effort ~ 1/T 3 ) S(w) Imurity model Develomet of Projective QMC for T 0 ad its alicatio to LDA+DMFT calculatios for LiV 2 O 4

8 Purose Reroduce the shar (heavy) quasi-article eak i A(w) at T 0 by LDA+DMFT(PQMC) Clarify the origi of HF behaviors (Shimoyamada et al. PRL (2006))

9 Auxiliary-field QMC Suzuki-Trotter decomositio L - H H H Z Tr e b -D Tr e t -D = Õ e t b t 0 it = ( = 1/ T = LD ) l= 1 Hubbard-Stratoovich trasformatio for H it e -Dt U [ ( + )] l s ( - ) May-article system = (free oe-article system + auxiliary field) å = å e (cosh( l) = ex[ DtU/2]) 1 2 s =± 1 = å 0 Z= åz 1 - Dt H sl Z Tr [ e s ls s e ] ss... s 1 2 L ss... s L á Añ = á Añ s s å 1 2 L... s L Z s s Z... s s1s2... s L L 2 s l = 1 s s s L, L º Õ Õ A : arbitrary oerator Mote Carlo samlig

10 Projective QMC Fiite-T QMC for the Aderso imurity model (Hirsch-Fye 86) Itegrate out the coductio bads ad calculate G of the imurity Projective QMC for T=0 Feldbacher, KH, Assaad, PRL (2004) Calculate G {s} (t 1,t 2 ) from G 0 (t 1,t 2 ) G( t, t ) = - T c ( t ) c ( t ) 1 2 t s 1 s 2 = å w G { s} ( t, t ) { s} { s} 1 2 0<t 1,t 2 <b=1/t, b=ldt Size of G =L 2 Effort ~L 3 (calculatio for low T is umerically exesive)

11 Projective QMC Fiite-T QMC for the Aderso imurity model (Hirsch-Fye 86) Itegrate out the coductio bads ad calculate G of the imurity Projective QMC for T=0 Feldbacher, KH, Assaad, PRL (2004) Calculate G {s} (t 1,t 2 ) from G 0 (t 1,t 2 ) G( t, t ) = - T c ( t ) c ( t ) 1 2 t s 1 s 2 = å w G { s} ( t, t ) { s} { s} 1 2 0<t 1,t 2 <b=1/t, b=ldt Size of G =L 2 Effort ~L 3 (calculatio for low T is umerically exesive)

12 Projective QMC Fiite-T QMC for the Aderso imurity model (Hirsch-Fye 86) Itegrate out the coductio bads ad calculate G of the imurity Projective QMC for T=0 Feldbacher, KH, Assaad, PRL (2004) Calculate G {s} (t 1,t 2 ) from G 0 (t 1,t 2 ) G( t, t ) = - T c ( t ) c ( t ) 1 2 t s 1 s 2 = å w G { s} ( t, t ) { s} { s} 1 2 0<t 1,t 2 <b=1/t, b=ldt Size of G =L 2 Effort ~L 3 (calculatio for low T is umerically exesive) 0 Iteractio Isig fields q o iteractio q + b t

13 Projective QMC Iteractio U oly i red art for sufficietly large P: Accurate iformatio o G for light red art

14 DMFT(PQMC) DMFT self-cosistet loo PQMC G0 ( t1, t 2) (T=0) G( t, t ) (T=0) S (iw) = G ( iw) - G iw) ( D( ) G( i w e ) = ò d e i w + m - S( i w ) - e -1 ( w) -1 ( w) ( w) 0 = + S G i G i i Problem G(t) FT G(iw)? No oly G(t),t<q obtaied by PQMC Maximum Etroy Method 1 G( t ) = A( w) ex( -wt ) dw ò 1 A( w) G( iw ) = d w ò iw -w

15 DMFT(PQMC) DMFT self-cosistet loo PQMC G0 ( t1, t 2) (T=0) G( t, t ) (T=0) S (iw) = G ( iw) - G iw) ( D( ) G( i w e ) = ò d e i w + m - S( i w ) - e -1 ( w) -1 ( w) ( w) 0 = + S G i G i i 1/T Problem G(t) FT G(iw)? No oly G(t),t<q obtaied by PQMC Maximum Etroy Method 1 G( t ) = A( w) ex( -wt ) dw ò 1 A( w) G( iw ) = d w ò iw -w

16 DMFT(PQMC) DMFT self-cosistet loo PQMC G0 ( t1, t 2) (T=0) G( t, t ) (T=0) S (iw) = G ( iw) - G iw) ( D( ) G( i w e ) = ò d e i w + m - S( i w ) - e -1 ( w) -1 ( w) ( w) 0 = + S G i G i i 1/T Problem G(t) FT G(iw)? No oly G(t),t<q P obtaied by PQMC Maximum Etroy Method 1 G( t ) = A( w) ex( -wt ) dw ò 1 A( w) G( iw ) = d w ò iw -w

17 DMFT(PQMC) DMFT self-cosistet loo PQMC G0 ( t1, t 2) (T=0) G( t, t ) (T=0) S (iw) = G ( iw) - G iw) ( D( ) G( i w e ) = ò d e i w + m - S( i w ) - e -1 ( w) -1 ( w) ( w) 0 = + S G i G i i q P 1/T-q P Problem G(t) FT G(iw)? No oly G(t),t<q obtaied by PQMC Calculate G oly for t<q P Large t: Extraolatio by Maximum Etroy Method 1/T Maximum Etroy Method 1 G( t ) = A( w) ex( -wt ) dw ò 1 A( w) G( iw ) = d w ò iw -w

18 DMFT(PQMC) DMFT self-cosistet loo PQMC G0 ( t1, t 2) (T=0) G( t, t ) (T=0) S (iw) = G ( iw) - G iw) ( D( ) G( i w e ) = ò d e i w + m - S( i w ) - e -1 ( w) -1 ( w) ( w) 0 = + S G i G i i q P 1/T-q P 1/T Problem G(t) FT G(iw)? No oly G(t),t<q obtaied by PQMC Maximum Etroy Method 1 G( t ) = A( w) ex( -wt ) dw ò 1 A( w) G( iw ) = d w ò iw -w Calculate G oly for t<q P Large t: Extraolatio by Maximum Etroy Method FAQ: Why ca we discuss A(w 0) eve if we do ot calculate G(t ) exlicitly?

19 DMFT(PQMC) DMFT self-cosistet loo PQMC G0 ( t1, t 2) (T=0) G( t, t ) (T=0) S (iw) = G ( iw) - G iw) ( D( ) G( i w e ) = ò d e i w + m - S( i w ) - e -1 ( w) -1 ( w) ( w) 0 = + S G i G i i q P 1/T-q P 1/T Problem G(t) FT G(iw)? No oly G(t),t<q obtaied by PQMC Maximum Etroy Method 1 G( t ) = A( w) ex( -wt ) dw ò 1 A( w) G( iw ) = d w ò iw -w Calculate G oly for t<q P Large t: Extraolatio by Maximum Etroy Method FAQ: Why ca we discuss A(w 0) eve if we do ot calculate G(t ) exlicitly? Sufficietly large q P eeded

20 DMFT(PQMC) T>0 A(w) A(w) T 0 0 w 0 0 w 0

21 DMFT(PQMC) T>0 A(w) A(w) T 0 w w 0 G(t) ~ex(-wt 0 ) G(t) Slow decay comoet 0 t 0 t

22 DMFT(PQMC) Sigle-bad Hubbard model HF-QMC vs. PQMC M I HF-QMC b=16 b=40 isulatig metallic

23 DMFT(PQMC) Sigle-bad Hubbard model HF-QMC vs. PQMC M I PQMC q=16 q=40 Covergece w.r.t q is much better tha b

24 DMFT(PQMC) Sigle-bad Hubbard model HF-QMC vs. PQMC Orbital selective Mott trasitio i the two-orbital Hubbard model M I RA ad KH, PRB (2005) PQMC q=16 q=40 DCA(PQMC) study for aisotroic airig i the t-t Hubbard model Covergece w.r.t q is much better tha b RA ad KH, PRB (2006)

25 Effective low eergy Hamiltoia 12 (=4x3) bad Hamiltoia e g a 1g H ij (k)= e /V=1.5 8 (=4x2) bad model e g a 1g H ij (k)= DMFT self-cosistet eq. hybridizatio (H ij, i j) take ito accout exlicitly

26 LDA+DMFT Result (T=1200K, HF-QMC) U U U -J Hud coulig = Isig U=3.6, U =2.4, J=0.6 a 1g e g

27 LDA+DMFT Result (T=300K, HF-QMC) U U U -J Hud coulig = Isig U=3.6, U =2.4, J=0.6 a 1g e g

28 LDA+DMFT Result (T=0, PQMC) U U U -J Hud coulig = Isig U=3.6, U =2.4, J=0.6 a 1g e g

29 LDA+DMFT Result (T=0, PQMC)

30 Theoretical studies so far Aisimov et al, 99 Eyert et al, 99 Matsuo et al, 99 Kusuose et al, 00 Lacroix, 01 Shao, 01 Fulde et al, 01 Burdi et al, 02 Hokiso et al, 02 Fujimoto, 02 Tsuetsugu, 02 Yamashita et al, 03 Laad et al, 03 Nekrasov et al, 03 Yushakhai et al, 07 Kodo sceario Aisimov et al, PRL (1999) e g (itierat) Geometrical Frustratio Short rage (local) correlatios become domiat DMFT exected to be a good arox. Hud a 1g (localized) hybridizatio Kodo? T=750K LDA+DMFT by Nekrasov et al, PRB (2003) Calculatio for T 0

31 Effect of a 1g -e g hybridizatio hybridizatio Kodo? DMFT self-cosistet eq. a 1g -e g hybridizatio ot cosidered exlicitly Kodo coulig betwee a 1g ad e g ot reaso for eak above E F

32 Origi of the eak: a 1g =slightly doed Mott isulator? LDA a1g ~ eg LDA+DMFT a1g ~ 0.95 DMFT for the sigle bad Hubbard =0.97 (U=4) Th. Pruschke et al, PRB (1993)

33 Origi of the eak: a 1g =slightly doed Mott isulator? LDA a1g ~ eg LDA+DMFT a1g ~ 0.95 DMFT for the sigle bad Hubbard =0.97 (U=4) Questio: Strog reormalizatio ca survive the resece of short-rage correlatio beyod DMFT? cf) A.Toschi, A. Katai, K. Held (PRB (2007)) DGA study for cubic lattice Th. Pruschke et al, PRB (1993) Damig of the eak: Irrelevat for 3D frustrated lattice(?)

34 Coclusios Develomet of PQMC ad its alicatio to LDA+DMFT calculatios for LiV 2 O 4 Origi of the shar eak just above E F a 1g = slightly doed Mott Isulator Future roblems beyod-dmft