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Non-Ohmic dissipation in metallic Griffiths phases

Non-Ohmic dissipation in metallic Griffiths phases. Vladimir Dobrosavljevic Department of Physics and National High Magnetic Field Laboratory Florida State University,USA. Funding: NSF grants: DMR-9974311 DMR- 0234215 DMR- 0542026. Collaborators : Matthew Case (FSU)

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Non-Ohmic dissipation in metallic Griffiths phases

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  1. Non-Ohmic dissipation in metallic Griffiths phases Vladimir Dobrosavljevic Department of Physics and National High Magnetic Field Laboratory Florida State University,USA Funding: NSF grants: DMR-9974311 DMR-0234215 DMR-0542026 Collaborators: Matthew Case (FSU) Darko Tanaskovic (FSU) Eduardo Miranda (Campinas) REVIEW: Reports on Progress in Physics 68, 2337–2408 (2005)

  2. Summary: • Historical outlook: important degrees of freedom? • Quantum Griffiths phases (QGPs) and IRFP • Classification of QGPs: symmetry and dissipation • Magnetic vs. Electronic (Kondo) QGPs • RKKY interactions and non-Ohmic dissipation

  3. Criticality and Collectivization There is not, nor should there be, an irreconcilable contrast between the individual and the collective, between the interests of an individual person and the interests of the collective.” (Joseph Stalin) Collectivization: Theory Ken Wilson’s RG Disorder and QCP: The Cold War Era (1960-1990) Long wavelength modes rule! GRIFFITHS singularities, Harris criterion: “Weak” disorder corrections

  4. Trouble Starts (circa 1990) Dissidents run away over the Berlin Wall Weak coupling RG finds run away flows for QCPs with disorder (Sachdev,...,Vojta,...)

  5. T clean phase boundary ordered phase Griffiths phase g Quantum Griffiths phases and IRFP (1990s) • D. Fisher (1991): new scenario for (insulating) QCPs with disorder (Ising) Griffiths phase (Till + Huse): Rare, dilute magnetically ordered cluster tunnels with rate Δ(L) ~ exp{-ALd} P(L) ~ exp{-ρLd} P(Δ) ~ Δα-1 ; χ ~ Tα-1 α→ 0 at QCP (IRFP)

  6. τ • LGW action (L > ξ) Classical spin chain (Kosrerlitz, 1976) Droplet dynamics (all symmetry classes) 2 General classification for single-droplet dynamics (Vojta) • Large droplets: SEMICLASSICAL! L

  7. Symmetry and dissipation (SINGLE DROPLET) • Insulating magnets (z=1) – short-range interaction (in time) • Ising: at “LCD” – tunneling rate Δ(L) ~ τξ -1~ exp{-π|r|Ld} • Heisenberg: below LCD – powerlaw only no QGP! • Metallic magnets (z=2) – long-range 1/τ2 interaction (dissipation) • Ising: above “LCD” – dissipative phase transition • Large droplets (L > Lc) freeze!! (Caldeira-Leggett, i.e. K-T) • “ROUNDING” of QCP (Vojta) • Heisenberg: at “LCD” • Δ(L) ~ τξ -1~ exp{-π|r|Ld} • QGP??? (single-droplet theory) • (Vojta-Schmalian)

  8. Localization-induced electronic Griffiths phase (Miranda & Dobrosavljevic) The physical picture

  9. W W* Wc Electronic Griffiths Phase & metal-insulator transition (MIT) (Tanaskovic, Dobrosavljevic, Miranda) EGP sets in for W > W* = (pt2ravJK)1/2 EGP always comes BEFORE the MIT MIT at W = Wc ~ EF

  10. 2 3 R12 JRKKY 1 4 J14 L1 RKKY-interacting droplets? (Dobrosavljevic, Miranda) • How RKKY affect the droplet dynamics?? random sign • NOTE: Droplet-QGP – all dimensions! • Strategy: integrate-out “other” droplets additional dissipation due to spin fluctuations δSRKKY=J2 ∑∫dτ ∫dτ’φ(τ) χav(τ-τ’) φ(τ’) χav(ωn) = ∫dΔP(Δ) χ(Δ; ωn) = ~ ∫dΔΔα-1 [iωn+ Δ]-1 = χ(0) - |ω|α-1 non-Ohmic (strong)dissipation forα < 2!!

  11. T clean phase boundary cluster glass ordered phase g Griffiths a= a=0 a=1 a=2 eo>0 (non-Ohmic dissipation) Cluster-glass phase (“foot”): generic case of QGP in metals fluctuation-driven first-order glass transition Matthew Case & V.D.

  12. EGP +RKKY interactions: beyond semi-classical spins! (Tanaskovic, Dobrosavljevic, Miranda)! • Similar non-Ohmic (strong)dissipation • Quantum (S=1/2) spin dynamics (Berry phase) • Local action: “Bose-Fermi (BF) Kondo model” • (“E-DMFT”; A. Sengupta, Q. Si,..)

  13. Kondo screened rcJK (Kondo coupling) ~ e spin fluid g (RKKY coupling) NFL - spin fluid Fermi liquid insulator disorder W e > 0 MIT “bare EGP” W* W1 Destruction of the Kondo effect and two-fluid behavior • BF model has a (local) phase transition for a sub-Ohmic dissipative bath (e > 0 ) • EGP model: distribution of Kondo • couplings all the way to zero! • A finite fraction of spins fall on each • side of the critical line • Kondo effect destroyed by dissipation • on a finite fraction of spins • Decoupled spins JKflows to zero; they • form a spin fluid (Sachdev-Ye) • (frustrated insulating magnet)

  14. - disorder Spin-glass (SG) instability of the EGP • χ(T) ~ ln(To/T) for spin fluid (decoupled spins) • Finite (very low!!) temperature SG instability as soon as spins decouple • Quantitative (numerical) results: large N

  15. Conclusions: • In metals dissipation destroys QGP at lowest T • → (quantum) glassy ordering • Magnetic (QCP) QGP: → semi-classical dynamics at T > TG • Fluctuation–driven first-order QCP of the “cluster glass” • Spin liquid in EGP at T > TG

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