1Lecture3Electronic Griffiths Phases and Disordered Quantum MagnetismVladimir DobrosavljevicFlorida State Universityhttp://badmetals.magnet.fsu.edug (RKKY coupling) !cJK (Kondo coupling) ~ " Kondo screened spin fluid1Lecture3Electronic Griffiths Phases and Disordered Quantum MagnetismVladimir DobrosavljevicFlorida State Universityhttp://badmetals.magnet.fsu.edug (RKKY coupling) !cJK (Kondo coupling) ~ " Kondo screened spin fluid2Beyond (standard) DMFT?• How robust (universal) is EGP for different models of disorder?• NFL in non-Kondo systems (MIT)?• Effects of spatial fluctuations of “cavity” fields - Anderson localization?• Large vs small “Griffiths exponents”?• Effect of EGP on magnetic ordering, interactions, spin glass?• Can one destroy local Fermi liquid (Kondo) even within the metallic phase?Short&range+magne-c+correla-ons:+random+RVBMIT(Mott-like?) insulatorNon-Fermi liquidFermi liquidχ(T=0)=χo χ(T=0)= ∞ χ(T=0)= ∞DisorderIRFPDoped(SemiconductorsPaalanen(et#al,(Physica(B(169,(223((1991)Uncompensated(Si:PCompensated(Si:P,(B2HFluid(Phenomenology:(signatures(of(MoE(physics•Strongly(localized(states(dominate(the(spin(response(even(in(the(metallic(state.(MoE(physics(dominates(the(insulator.M.(J.(Hirsch(et#al.((1992)insulatormetalExplained (quantitatively) byBhatt-Lee SDRG theory (1982)6Bha:&Lee+theory+of+the +insula-ng+stateR.+N.+Bha:+and+P.+A.+Lee,+J.+Appl.+Phys.+52,+1703+(1981);+PRL+48,+344+(1982Disordered Heisenberg model:3ʼ 4ʼ Jʼ34 5 Jʼ45 Jʼ35 1 2 3 4 5 !"#$%&'(")*$%+),)-%'#")(-%&.'")Strong disorder RG (Ma-Dasgupta-Hu, 1979)LargeHN(theory:(analyPcal(soluPon[Zhou,(Jose+Hoyos,(Dobrosavljević,(Miranda.,(Europhys.+Le:+(2009)]RVB(decoupling:VB(singlet:Single(occupancy(constraint2314(no renormalization at large N)Potential to extend to metallic side (RVB+slave bosons)8RKKY+interac-ons+in+Electronic+Griffiths+Phases+(EGP)?Physical picture: importance of RKKY for TK < JRKKYEGP: finite density of low-TK spinsSpin-Glass ordering of Kondo-unscreened spins? [experiments by D. MacLaughlin, PRL 2001; quantum spin-glass dynamics at T < 1K]9α ≈ 1 − 0.7 Experiments showing NFL (Kondo alloys)10“Effective” DMFT model of the Electronic Griffiths PhaseLattice of Kondo spins embedded in a disordered metal(U = ∞)11DMFT formulation (exact for d=inf.)Interactions only on f-sites; integrate-out c-electronsSelf-consistency condition:12Electronic Griffiths Phase (EGP)Site-dependent Kondo temperatures:13Disorder-driven non-Fermi (NFL) liquid behaviorLocal spin susceptibilitySingular part from small TKRegular behavior at small WNFL behavior at W > Wnfl14Adding RKKY interaction: spin glass instability• RKKY interactions between (distant) low-TK (unscreened) spins: oscillatory with distance random in magnitude and sign• Expect quantum spin-glass (SG) dynamics at low T EDMFT theory for RKKY interactions: Self-consistency:Bosonic bath:Bose-Fermi (BF) Kondo model: additional dissipation from bosonic bath!15EGP: Sub-Ohmic dissipationHow RKKY affect the Kondo effect for low TK spins (stability of the EGP)?Examine small g-limit:[examine BF model in bath of the “bare” (toy model) theory]Exponent ε =2 – α > 0 for W > W1 = (πt2ρavJK/2)1/2 < W*NOTE: ε > 0 leads to sub-Ohmic (strong) dissipation, phase transition in BF modeldisorder W MIT W* W1 insulator Fermi liquid NFL - spin fluid ! > 0 “bare EGP”16Fractionalization and Two-Fluid Behaviorg (RKKY coupling) !cJK (Kondo coupling) ~ " Kondo screened spin fluid BF model has a phase transition for a sub-Ohmic dissipative bath (ε > 0) EGP model: distribution of KondoCouplings 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)17Self-consistent marginal FL solution Impose self-consistency condition Self-consistent solution ε=1 (RG and large N results) Leading contribution from decoupled spins (spin-fluid) χ(Τ) ~ ln(To/T) Corresponds to renormalized Griffiths exponent αR = 1 for any W > W1 (marginal Fermi liquid) Renormalized, universal distribution of Kondo temperatures (for the spins that remain Kondo-screened) PR(TK) ~ (TK)-1/2 (one loop RG result) Spin-fluid as quantum critical dynamics as precursor of the SG phase18Spin-glass instability of the EGPSG instability criterion: χ(Τ) JRKKY = 1 χ(Τ) ~ ln(To/T) for spin fluid (decoupled spins) Finite (very low!!) temperature SG instability as soon as spins decoupleQuantitative (numerical) results: large N- disorder19Thank You!For further reading see:1. Vlad’s research website: http://badmetals.magnet.fsu.edu/index.html2. Review article: Disorder-Driven Non-Fermi Liquid Behavior of Correlated Electrons, by E. Miranda and V. Dobrosavljevic, Reports on Progress in Physics, 68, 2337–2408 (2005).3. Upcoming book: Conductor-Insulator Quantum Phase Transitions, Edited by V. Dobrosavljevic, N. Trivedi, and J. Valles (Oxford Univ. Press,