Role of Hund Coupling in Two-Orbital Systems

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1 Role of Hund Coupling in Two-Orbital Systems Gun Sang Jeon Ewha Womans University NCTS Workshop on Quantum Condensation (QC13) collaboration with A. J. Kim, M.Y. Choi (SNU)

2 Mott-Hubbard Transition Weakly correlated Intermediate regime : hard to describe quantitatively Strongly correlated U W C Kotliar, Vollhardt (2004)

3 Quasiparticle Weight (DMFT+NRG) U W C Bulla, PRL (1999)

4 Two-Orbital System DOS Degenerate bands with different bandwidths Z 1 W 1 W 2 2 energy different U c for Mott transition Orbital-Selective Mott Phase (OSMP) coexistence of localized and itinerant electrons Ca 2-x Sr x RuO 4 (0.2<x<0.5) completely decoupled case U Anisimov, Nekrasov, Kondakov, Rice, Sigrist Bulla, (2002)

5 Multiband System inter-orbital Coulomb interaction U, Hund coupling J from Sakai (2006) Renormalization by the inter-orbital coupling may affect the transition behaviors.

6 Single Transition? large deviation of Z 1 and Z 2 from bare values claim for single Mott transition W1 = 2eV, W2 = 4eV J = 0.2eV, U ' = U 2J T = 0.125meV DMFT+QMC Liebsch (2003)

7 Orbital-Selective Transition? single transition for J=0 orbital-selective transition for finite J DMFT+ED OSMP Koga, Kawakami, Rice, Sigrist (2004)

8 Hamiltonian for Two-Orbital Systems Hamiltonian J ' J : Ising type Hund coupling J : including spin-flip and pairwise hopping

9 Resolution to this issue Isotropic Hund coupling ( J =J ) Two successive first-order transition near 2.0 ev, narrow band : complete MIT wide band : incomplete transition to new more correlated phase near 3.0 ev wide band : complete MIT Liebsch (2005)

10 Resolution to this issue Ising-type Hund coupling only ( J =0 ) lower transition: first-order for both bands upper transition: change of slope Liebsch (2005)

11 NFL for Ising-type Hund Coupling In intermediate phase ImΣ 2 (i0 + ) 0: finite life time at Fermi level non-fermi liquid Fermi liquid non-fermi liquid Mott insulator Biermann, de Medici, Georges (2005); Liebsch, Costi (2006)

12 Motivation Aim to investigate the dependence of transition nature on Ising-type Hund coupling strength J intra-orbital hopping, t α Intra- and inter-orbital Coulomb interaction, (U, U ) Ising-type Hund s coupling, J U = U 2J ; W 1 =2, W 2 =4 Bethe lattice in infinite dimensions half-filled case paramagnetic phase

13 Dynamical Mean-Field Theory + Continuous Time QMC Mapping of lattice model onto two-impurity model two-impurity problem Bethe lattice Impurity solver impurity model impurity solver: continuous-time QMC hybridization expansion Inverse Fourier transform G 0 ( τ ) G ( iω ) 0 n DMFT Selfconsistent Loop G (τ ) G ( i ω Σ ( i ω Self-consistency relation n n ) ) Fourier transform

14 ORBITAL-SELECTIVE MOTT TRANSITION FOR J=U/4

15 Quasiparticle Weight Monotonic decrease as U increases. First-order transition with hysteresis for both around U c1 2.0 Long tail in Z 2 above U c2 Change in slope around U c2 2.5

16 Double Occupancy Monotonic decrease as U increases. First-order transition with hysteresis for both around U c1 2.0 Change in the slope of d 2 around U c2 2.5 d 1 and d 2 are insensitive to temperature above U c1 For U c1 <U<U c2 d 1 far suppressed narrow band is MI d 2 is rather high and decreases gradually wide band is not MI

17 Local Magnetic Moment Monotonic increase as U increases. First-order transition with hysteresis for both around U c1 2.0 Change in the slope for wide band around U c2 2.5 Both are insensitive to temperature above U c1 For U c1 <U<U c2 narrow band: high moment MI wide band: comparatively low and gradually increasing not MI

18 Self-Energy for Wide Band For U<U c1 ImΣ 2 (iω n ) 0 linearly as ω n 0 Fermi liquid (FL) For U >U c2 ImΣ 2 (iω n ) - as ω n 0 Mott insulator (MI) For U c1 <U<U c2 ImΣ 2 (iω n ) finite as ω n 0 finite lifetime at Fermi level non-fermi liquid (NFL)

19 Determination of U c2 imaginary part of selfenergy in wide band fitting low frequency part ImΣ Σ ω 2 c ω a ( iω ) = + b n + n a=0: divergence to - at, MI a<0: convergence to finite negative value at NFL ω = 0 ω = 0

20 Phase Diagram DMFT+CT-QMC (,, ): this work DMFT+ED (,---) DMFT+ED (T=0) ( ) DMFT+HF-QMC ( ) FL NFL MI FL-NFL: first-order transition with negative slope, conventional Mott transition NFL-MI: continuous transition with positive slope

21 EFFECTS OF HUND COUPLING ON ORBITAL-SELECTIVE MOTT TRANSITION

22 Phase diagram in U-U Ising-type Hund coupling isotropic Hund coupling Koga, Kawakami, Rice, Sigrist (2004) generally similar to that with isotropic Hund coupling U c s are slightly lower than isotropic case second transition change from continuous to firstorder

23 VARIATION OF BANDWIDTH RATIO

24 Variation of bandwidth ratio DMFT + ED Gutzwiller J=0 When bandwidth ratio is far from unity, OSMP shows up even for J=0 de Medici,Georges,Biermann (2005); Ferrero,Becca,Fabrizio,Capone (2005)

25 Double Occupancy and Quasiparticle Weights A single first-order transition for small W 2 /W 1 Two separate transitions for large W 2 /W 1 (W 2 /W 1 ) c = 1.5 ± 0.1

26 Phase diagram OSMT appears above finite (W 2 /W 1 ) c slightly smaller NFL region for lower T Ising-type Hund J=U/4 J=0 de Medici,Georges,Biermann (2005)

27 Summary We have investigated metal-insulator transitions in two-orbital system with Isingtype Hund coupling J. For large J/U, FL NFL MI as U. Transition from FL to NFL is first-order Transition from NFL to MI is continuous for large J/U first-order for small J/U We anticipate richer physics by the interplay of Hund coupling and bandwidth ratio.

28 Thank You! Acknowledgement National Research Foundation of Korea Basic Science Research, No Quantum Metamaterials Research Center, No