A HOT end of the holography A HOT end of the holography meeting .. - PowerPoint PPT Presentation

A HOT end of the holography A HOT end of the holography meeting .. meeting .. Jan Zaanen 1

Holographic subjects. - “Foundations” = mathematical machine building:Higher spin (Fredenhagen, Jottar, Ammon), SUYN integrability (Kazakov, Gromiv), AdS3/CFT2 (Kirsch), blackfolding (Obers) - AdS/QCD : nearly entirely (Bajnok,Young) heavy ion collisions, non equilibrium (Kiritsis, Craps, Vuorinen, Mateos, Heller, Evans, Fiol,Sin) - Non-equilibrium general (Yarom, Craps, Vuorinen,Mateos, Heller, Baseen, Evans,Das,Sin,Rangamani). - AdS/CMT (equilibrium ). (Hartnoll, Tong,Semenoff, Goutereaux,Gauntlett, Hartmann,Surowka,Cremonini,O’Bannon,Meyer, Schalm) - Quantum info (Karch, Goutereaux,Jensen,Takayanagi,Hubeny, Dong) +TI’s (Mc Greevy) 2

Holographic subjects. - “Foundations” = mathematical machine building:Higher spin (Fredenhagen, Jottar, Ammon), SUYN integrability (Kazakov, Gromiv), AdS3/CFT2 (Kirsch), blackfolding (Obers) - AdS/QCD : nearly entirely (Bajnok,Young) heavy ion collisions, non equilibrium (Kiritsis, Craps, Vuorinen, Mateos, Heller, Evans, Fiol,Sin) - Non-equilibrium general (Yarom, Craps, Vuorinen,Mateos, Heller, Baseen, Evans,Das,Sin,Rangamani). - AdS/CMT (equilibrium ). (Hartnoll, Tong,Semenoff, Goutereaux,Gauntlett, Hartmann,Surowka,Cremonini,O’Bannon,Meyer, Schalm) - Quantum info (Karch, Goutereaux,Jensen,Takayanagi,Hubeny, Dong) +TI’s (Mc Greevy) 5

Smashing things. 6

Chesler, Adams,Liu. Holographic Superfluid turbulence (Science, just published) 7

Holographic subjects. - “Foundations” = mathematical machine building:Higher spin (Fredenhagen, Jottar, Ammon), SUYN integrability (Kazakov, Gromiv), AdS3/CFT2 (Kirsch), blackfolding (Obers) - AdS/QCD : nearly entirely (Bajnok,Young) heavy ion collisions, non equilibrium (Kiritsis, Craps, Vuorinen, Mateos, Heller, Evans, Fiol,Sin) - Non-equilibrium general (Yarom, Craps, Vuorinen,Mateos, Heller, Baseen, Evans,Das,Sin,Rangamani). - AdS/CMT (equilibrium ). (Hartnoll, Tong,Semenoff, Goutereaux,Gauntlett, Hartmann,Surowka,Cremonini,O’Bannon,Meyer, Schalm) - Quantum info (Karch, Goutereaux,Jensen,Takayanagi,Hubeny, Dong) +TI’s (Mc Greevy) 8

David’s outlook: strings 2013. “our community has overhyped the application of AdS/CFT to condensed matter physics” “It is understandable that it met resistance in the condensed matter community” David Gross 10

Physics Today (2013). 11

Another Master Phenomenologist. Chandra Varma 12

The DMFT people …. Jarrell Georges Kotliar Cluster DMFT: small QMC clusters in self consistent effective medium “Sign-full numerics”: long time scales need only small lengths. τ ∝ ξ z , z →∞ 13

AdS/CFT as a Femme fatale. Senthil (MIT/Harvard) 14

The higher dimensional ? quantum smectic. Donos Hartnoll “ab-plane” optical conductivity: perfect Drude metal. “c-axis” optical conductivity: turns from “bad metal” ( ) ∝ ω 4 / 3 at T = 0 σ ω to “pseudogap-insulator” when potential increases: 15

Serendipity. 16

Self-organized two dimensionality. ab- vs. c-axis optical ab- vs. c-axis DC resistivity conductivity 17

Anderson’s “central dogmas” Dogma IV: the “normal” metal above Tc is not a Fermi-liquid. Dogma V: this normal state is strictly two- dimensional and coherent transport in the third dimension is blocked. Perhaps the strongest non-Fermi-liquid signal: it is theorem that a Fermi liquid can only localize in all spatial dimensions at the same time! 18

Quantum smectics in 2+1D. SC - 2D superconductor FL - Fermi Liquid CDW - charge density wave insulator SM - smectic metal When the individual Luttinger liquids are sufficiently strongly interacting, while the inter-LL interaction is long range a smectic metal is realized characterized by a continuous irrelevant renormalization flow of the perpendicular transport: ( ) ∝ ω ν ; ν ≥ 0 ( ) ∝ Z δ ω ( ) σ // ω σ ⊥ ω Emery,Fradkin, Kivelson,Lubensky, PRL 85, 2160 (2000); Vishwanath, Carpentier, PRL 86, 676 (2001) 19

Divine resistivity 20

Corrugated horizon versus optical conductivity. Santos Horowitz Tong Similar “corrugated horizon” lattice potential but now currents: photons + gravitons at zero momentum. 21

Optical conductivity: “mid infrared” At “intermediate” frequency: k B T < h ω < µ The conductivity shows an emergent scaling behavior: A ( ) = 2/ 3 + B σ ω ( ) i ω which is quite robust, only a sufficiently strong lattice potential is needed. 22

Quantum self-similarity: optical conductivity Van der Marel, JZ Nature 2003: ‘ High’ frequency optical conductivity: α σ = e i πα σ / 2 ( ) ( ) = cos πα c /2 + i sin πα σ /2 1 ( ) ∝ σ ω α σ α σ α σ ( ) i ω ω ω ω Exponent α σ ≈ 0.65 Violates single parameter- and hyper scaling: non-Wilsonian RNG !! 23

Holographic quenched disorder. David Vegh Dictionary entry “number one”: Global translational invariance in the boundary (energy-momentum conservation) <==> General covariance in the bulk (Einstein theory) Breaking of Galilean invariance in the boundary = elastic scattering (?) <==> Fix the (spatial) frame in the bulk = “Massive gravity” Couple the metric g ab to a fixed metric f xx =f yy =1 24

Analytical solution for conductivity for RN Metal. Davison Parnachev h ω < k B T Hydrodynamical regime ρ ( T ) ∝ 1 σ 0 η ( ) = σ 1 ω = Drude form: l 2 ρ m 1 − i ωτ rel τ rel l = η = ρ m = viscosity mean free path Electron mass density η = A h Famous “minimal” or “Planckian” viscosity of (temporal) quantum s critical states (A of order 1, s is entropy density): k B h ρ ( T ) ∝ 1 S = A l 2 m e k B τ rel 25

Entropy versus transport: optimal doping Optimally doped Massive gravity: ρ ∝ 1 ∝ S ∝ T C = γ T ⇒ S = T / µ τ rel Loram, Tallon Explicit realization: “Gubser” strange metal ! 26

Magnitude of momentum relaxation. According to the cuprate optical conductivity the momentum relaxation rate is: 1 ≈ k B T h τ exp According to “massive gravity”, the RN strange metal has a momentum relaxation rate: h 2 S = k B T h 1 S k B T assuming = A = A l 2 m e µ l 2 m e k B µ h k B τ exp A ≈ 10 − 9 m l = h It follows for the microscopic mean free path: µ m e 27

“Fermi-liquid like” pseudogap transport vd Marel et al, PNAS Pseudogap regime Massive gravity: 110, 5774 ρ ∝ 1 C ∝ T 2 ⇒ S ∝ T 2 (?) ∝ S ∝ T 2 τ rel Loram, Tallon DC resistivity Energy/temperature scaling collapse 28

Holographic subjects. - “Foundations” = mathematical machine building:Higher spin (Fredenhagen, Jottar, Ammon), SUYN integrability (Kazakov, Gromiv), AdS3/CFT2 (Kirsch), blackfolding (Obers) - AdS/QCD : nearly entirely (Bajnok,Young) heavy ion collisions, non equilibrium (Kiritsis, Craps, Vuorinen, Mateos, Heller, Evans, Fiol,Sin) - Non-equilibrium general (Yarom, Craps, Vuorinen,Mateos, Heller, Baseen, Evans,Das,Sin,Rangamani). - AdS/CMT (equilibrium ). (Hartnoll, Tong,Semenoff, Goutereaux,Gauntlett, Hartmann,Surowka,Cremonini,O’Bannon,Meyer, Schalm) - Quantum info (Karch, Goutereaux,Jensen,Takayanagi,Hubeny, Dong) +TI’s (Mc Greevy) 29

Bell pairs and the “spooky action at a distance”. Classical computers live in tensor product space: | product = 0 A ⊗ 1 B or 1 A ⊗ 0 B Quantum computers exploit entangled states capable of “spooky action at a distance” (EPR paradox). | Bell = 1 ( ) 2 0 A ⊗ |1 B − 1 A ⊗ 0 B 30

“The classical condensates: from crystals to Fermi-liquids.” States of matter that we understand are product! + Ω i } = Π i ˆ { ( ) vac X Ψ 0 Ω i i 0 − r )^2 ( R i + R i σ 2 ψ + r ( ) ∝ e 0 ( ) - Crystals: put atoms in real space wave packets X i - Magnets: put spins in generalized coherent state + r ( ) ∝ e i ϕ i / 2 cos θ i /2 + + e − i ϕ i / 2 sin θ i /2 ( ) c i ↑ ( ) c i ↓ + X i n i - Superconductors/superfluids: put bosons/Cooper pairs in coherent superposition + ∝ u k + v k c k ↑ + c − k ↓ + , u i + v i e i ϕ i b i + X k / i - Fermi gas/liquid special, but only “Fermi-Dirac entanglement” + vac k F c k Ψ FL = Π k 31

Quantum matter. “Macroscopic stuff that can quantum compute all by itself” ∑ A configs configs Ψ = configs - Topological incompressible systems, no low energy excitations but the whole carries quantum information: fractional quantum Hall … - Compressible systems: strongly interacting bosonic quantum critical states have dense long range entanglements (Planckian dissipation) - Compressible systems: are the strange metals of this kind?? Strongly interacting fermions at finite density: the fermion signs as entanglement resource! 32

Holographic strange metal entanglement entropy. ⎛ ⎞ dt 2 ds 2 = 1 r 2 d ( z − 1)/( d − θ ) + r 2 ϑ /( d − θ ) dr 2 + dx i 2 r 2 − ⎜ ⎟ Geometry in Einstein-Maxwell-Dilaton bulk: ⎝ ⎠ t → ζ z t , ds → ζ θ / d ds x i → ζ x i , “ Hyperscaling violation ” in boundary theory: S ∝ T ( d − θ )/ z Thermal entropy: Entanglement entropy (Sachdev, Huijse, Swingle): Looks much like a deconfined S vN ∝ Σ , θ < d − 1 Fermi-liquid, hidden from the S vN ∝ Σ ln Σ , θ = d − 1 gauge singlet UV propagators! S vN ∝ Σ θ /( d − 1) , θ > d − 1 But this is longer ranged !? 33