Non-Ohmic%20dissipation%20in%20metallic%20Griffiths%20phases

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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,
23372408 (2005)
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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

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Disorder and QCP The Cold War Era (1960-1990)
Long wavelength modes rule! GRIFFITHS
singularities, Harris criterion Weak disorder
corrections
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Trouble Starts (circa 1990)
Dissidents run away over the Berlin Wall
Weak coupling RG finds run away flows for QCPs
with disorder (Sachdev,...,Vojta,...)
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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 ?(L) exp-ALd
P(L) exp-?Ld P(?) ?a-1 ? Ta-1 a ?
0 at QCP (IRFP)
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General classification for single-droplet
dynamics (Vojta)

• Large droplets SEMICLASSICAL!

L
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Symmetry and dissipation (SINGLE DROPLET)

• Insulating magnets (z1) short-range
  interaction (in time)
• Ising at LCD tunneling rate ?(L) t? -1
  exp-prLd
• Heisenberg below LCD powerlaw only no QGP!
• Metallic magnets (z2) long-range 1/t2
  interaction (dissipation)
• Ising above LCD dissipative phase transition
  
• Large droplets (L gt Lc) freeze!!
  (Caldeira-Leggett, i.e. K-T)
• ROUNDING of QCP (Vojta)
• Heisenberg at LCD
• ?(L) t? -1 exp-prLd
• QGP ??? (single-droplet theory)
• (Vojta-Schmalian)

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Localization-induced electronic Griffiths
phase (Miranda Dobrosavljevic)
The physical picture
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Electronic Griffiths Phase metal-insulator
transition (MIT) (Tanaskovic, Dobrosavljevic,
Miranda)
EGP sets in for W gt W (pt2ravJK)1/2
EGP always comes BEFORE the MIT
MIT at W Wc EF
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RKKY-interacting droplets? (Dobrosavljevic,
Miranda)

• How RKKY affect the droplet dynamics??

random sign

• NOTE Droplet-QGP all dimensions!
• Strategy integrate-out other droplets

dSRKKYJ2 ? ?dt ?dt f(t) ?av(t-t)
f(t) ?av(?n) ?d? P(?) ?(? ?n)
?d? ?a-1 i?n ?-1 ?(0) - ?a-1
additional dissipation due to spin fluctuations
non-Ohmic (strong) dissipation for a lt 2!!
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Cluster-glass phase (foot) generic case of QGP
in metals
fluctuation-driven first-order glass
transition Matthew Case V.D.
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EGP RKKY interactions beyond semi-classical
spins! (Tanaskovic, Dobrosavljevic, Miranda)!

• Similar non-Ohmic (strong) dissipation
• Quantum (S1/2) spin dynamics (Berry phase)
• Local action Bose-Fermi (BF) Kondo model
• (E-DMFT A. Sengupta, Q. Si,..)

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Destruction of the Kondo effect and two-fluid
behavior

• BF model has a (local) phase transition for a
  sub-Ohmic dissipative bath (e gt 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 JK flows to zero they
• form a spin fluid (Sachdev-Ye)
• (frustrated insulating magnet)

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Spin-glass (SG) instability of the EGP

• ?(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

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Conclusions

• In metals dissipation destroys QGP at lowest T
• ? (quantum) glassy ordering
• Magnetic (QCP) QGP ? semi-classical dynamics
  at T gt TG
• Fluctuationdriven first-order QCP of the
  cluster glass
• Spin liquid in EGP at T gt TG