Holographic duality in condensed matter physics.! Jan Zaanen!!

Transcription

1 Holographic duality in condensed matter physics.! Jan Zaanen!! 1!

2 Book sales! Cambridge University Press! Release: October ! It is 600 pages and only 80!! 2!

3 Plan of course.! 1. Overview of AdS/CMT in pictures (slides).! 2. How the computations actually work: from GR and metrics to free energies and propagators with the GKPW rule (blackboard).! 3. Physics highlights: strange metals, holographic superconductivity and Fermi liquids, transport, entanglement (slides).! 3!

4 String theory! Quantum physics of strings! Beautiful mathematics (Calabi-Yau, )! Quantum space-time (big bang, )!

5 String theory: what is it really good for?! - Quantum matter: heavy fermion systems, high Tc superconductors, Quark-gluon plasma! Polchinski! Kachru! Starinets! Erdmenger! Gubser! Horowitz! Silverstein! Gauntlett! Policastro! Tong! Son! Hartnoll! Herzog! Adams! McGreevy! Liu! Schalm! Karch! Sachdev! Phillips!Zaanen! 5!

6 Photoemission spectrum!?!

7 The cloverleaf of matter.! String theory! Quantum information! AdS/ CFT! Black hole physics! Condensed matter physics! 7!

8 Quantum field theory = Statistical physics.! Z = X e E config k B T configs. Path integral mapping! Thermal QFT, Wick rotate:! Z ~ = X e S history ~ worldhistories But generically: the quantum partition function is not probabilistic: sign problem, no mathematical control!! Z ~ = X worldhistories t! i ( 1) history e S history ~ 8!

9 Fermions at a finite density: the sign problem.! Imaginary time first quantized path-integral formulation Boltzmannons or Bosons:! integrand non-negative! probability of equivalent classical system: (crosslinked) ringpolymers Fermions:! negative Boltzmann weights! non probablistic: NP-hard problem (Troyer, Wiese)!!!

10 Fermions: the tiny repertoire! Fermiology! BCS superconductivity! Ψ BCS = Π ( k u k + v k c + c + ) k vac. k 10!

11 29 years later: the consensus document.! 11!

12 The high Tc enigma.! The clash: the quantum critical metal! which is good for superconductivity!! The quantized traffic jam! The quantum fog (Fermi gas) returns! Exotic orders: stripes, orbital currents, nematics! 12!

13 Divine resistivity! 13!

14 A universal phase diagram! High Tc superconductors! Heavy fermions! Iron superconductors (?)! Quantum critical! 14!

15 Fractal Cauliflower (romanesco)!

16 Quantum Critical Cauliflower!

17 Quantum Critical Cauliflower!

18 Quantum Critical Cauliflower!

19 Quantum Critical Cauliflower!

20 High energy physics: elementary particles.!

21 Particles as string vibrations (1980 s)! String vibration modes" Different particles Morphing strings " Particle interactions up quark down quark electron =>Unified theory: one string = all particles => Vibrations of closed strings describe gravitons (quantum particles carrying gravitational force).

22 The second string revolution (1995)! Dualities! 22!

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25 General relativity = quantum field theory! General relativity! AdS/CFT! Quantum fields! Maldacena 1997! =! 25!

26 Particle-wave duality.! Cat, cold, female! Dog, hot, male! Particle! Heisenberg uncertainty relation:! The exact opposites form an indivisable whole! Δp Δx! Wave! 26!

27 Weak-Strong or Kramers- Wannier duality! Low temperature or weakly coupled! H = J k B T z z S i S j <ij > Kramers! High temperature or strongly coupled! Wannier! = domain wall condensate =! H = k B T J S z i <ij > S j z Self-duality special to 2D: e.g. in 3D global Ising dual to Ising gauge theory.! 27!

28 The Grand Unified holographic duality.! Thermal matter, dissipation! AdS/CFT! the exact opposites form an indivisible whole!! General relativity! Quantum fields- Quantum matter! Kramers/Wannier-, Local-gobal duality.! 28!

29 Einstein! Einstein equations (theory of general relativity):! R µν 1 2 R g µν = 8πG c 4 T µν Space time as fabric! Matter and energy!

30 Hawking radiation: space-time turns into material stuff!

31 Hawking Temperature: g = acceleration at horizon A = area of horizon t Hooft s holographic principle! BH entropy:! Number of degrees of freedom (field theory) scales with the area and not with the volume (gravity)!

32 Holography with lasers! Three dimensional image! Encoded on a two dimensional photographic plate!

33 Holographic gauge-gravity duality! Einstein Universe AdS! Quantum field world CFT! t Hooft-Susskind holographic principle! Classical general relativity! Uniqueness of GR solutions! Extremely strongly coupled (quantum) matter! Generating functional of matter emergence principle!

34 Holography and scale invariance.! Einstein universe AdS = Anti de Sitter universe! Quantum field theory CFT = quantum critical!

35 GeneralRelativity = RenormalizationGroup! IR! UV! Extra radial dimension of the bulk <=> scaling dimension in the field theory! Bulk AdS geometry = scale invariance of the field theory!

36 r

37 r z J. McGreevy, arxiv !

38 GKPW rule: propagators in QFT are classical waves in AdS! Z CFT (N) = he R Z d d+1 xj(x)o(x) i QFT = D Z D e in 2 S AdS ( ) e is bulk( (x,r)) (x,r=1)=j(x) g 2 YMN = R4 g 2 YM = g s Only in the large N limit the strongly coupled boundary field theory becomes dual to classical gravity!! 38!

39 SUSY Einstein-Maxwell in AdS <==> SUSY Yang-Mills CFT! AdS/CFT dictionary: E-field D transverse E-field <=> D-1 electric field D radial E-field <=> D-1 charge density B-field D radial B-field <=> D-1 magnetic field D transverse B-field <=> D-1 current density spatial metric perturb. D transverse gradient <=> D-1 distortion D radial gradient <=> D-1 stress tensor temporal metric perturb. D transverse gradient <=> D-1 temperature gradient D radial gradient <=> D-1 heat flow

40 Matrix large N! 40!

41 UV independence.! 41!

42 Blackboard break.! - GKPW rule (i): computing CFT propagators using GR.! - GKPW rule (ii): Schwarzschild black holes and finite temperature.! - The mysterious matrix large N mean field limit! 42!

43 The triumph: gravitational encoding of all thermal physics!! Schwarzschild black hole in the bulk! Boundary: the emergence theories of finite temperature matter.! - All of thermodynamics! Caveat: phase transitions are mean field (large N limit).! - Precise encoding of Navier-Stokes hydrodynamics! Right now used to debug complicated hydrodynamics (e.g. superfluids).! - For special Planckian dissipation values of parameters (quantum criticality):!! τ! = const. k B T, const.= O(1)

44 Turbulence and fractal black hole horizons.! Holography and numerical GR! Chesler! Yaffe! Vorticity in the liquid (Kolmagorov scaling)! Near horizon geometry (fractal)! 44!

45 Plan of course.! 1. Overview of AdS/CMT in pictures (slides).! 2. How the computations actually work: from GR and metrics to free energies and propagators with the GKPW rule (blackboard).! 3. Physics highlights: strange metals, holographic superconductivity and Fermi liquids, transport, entanglement (slides).! 45!

46 Finite density: Reissner- Nordstrom Black Hole.! Dirac waves, photons, scalar fields! E! µ µ k! Electrical monopole! 46!

47 The charged back hole encoding for finite density (2008 -????)! Anti de Sitter universe.! Finite density quantum matter:! Holographic strange metals! Charged black hole in the middle! Stripy pseudogap orders! High Tc superconductors! Emergent Fermi liquids!

48 Finite density: the Reissner- Nordstrom strange metals (Liu et al.).! Near-horizon geometry of the extremal RN black hole:! - Space directions: flat, codes for simple Galilean invariance in the boundary.! - Time-radial(=scaling) direction: emergent AdS 2, codes for emergent temporal scale invariance!! Fermion spectral functions:! A(k,ω) G" AdS2 ( k,ω) ω 2ν k ν k = 1 6 k ξ 2 Un-particle physics!! 48!

49 Scaling atlas of holographic quantum critical phases.! Deep interior geometry sets the scaling behavior in the emergent deep infrared of the field theory. Uniqueness of GR solutions:! 1. Cap-off geometry = confinement: conventional superconductors, Fermi liquids.! 2. Geometry survives: hyperscaling violating geometries (Einstein Maxwell- Dilaton Scalar fields Fermions).! ds 2 = 1 % ' r 2 & dt 2 r + 2d (z 1)/(d θ ) r2ϑ /(d θ ) dr dx i x i ζ x i, t ζ z t, ds ζ θ / d ds S T (d θ )/z ( * ) Quantum critical phases with unusual values of:! z = = Dynamical critical exponent! Hyperscaling violation exponent! 49!

50 Plan of course.! 1. Overview of AdS/CMT in pictures (slides).! 2. How the computations actually work: from GR and metrics to free energies and propagators with the GKPW rule (blackboard).! 3. Physics highlights: strange metals, holographic superconductivity and Fermi liquids, transport, entanglement (slides).! 50!

51 The holographic Fermi-liquid: uncollapsing in the electron star.! (Reissner-Nordstrom) Black hole like object! star like object! uncollapse! Phase transition! fractionalized, unstable : strange metal! Cohesive state :! Symmetry breaking: superconductor, crystal ( scalar hair )! Fermi-liquid ( electron star )! 51!

52 The holographic superconductor" Hartnoll, Herzog, Horowitz, arxiv: "! Condensate (superconductor, ) on the boundary!! AdS-CFT! (Scalar) matter atmosphere! Super radiance : in the presence of matter the extremal BH is unstable => zero T entropy always avoided by low T order!!!! 52!

53 The hairy black hole! ( ) = 2ψ 2 V ψ Minimal model:, the dual operator can have conformal dimensions! Δ =1, 2 The Reissner-Nordstrom BH describes the normal state, but it goes 2 unstable at a because m eff m 2 q 2 2 T<T c ' p A 0 turns negative, violation of the BF bound.! Below T c the black hole gets hair in the form of a scalar atmosphere : via the dictionary, a VEV emerges in the field theory in the absence of a source.! The global U(1) symmetry of the CFT is spontaneously broken into a superfluid!! Ψ 53!

54 The Bose-Einstein Black hole hair! Hartnoll! Herzog! Horowitz Scalar hair accumulates at the horizon Mean field thermal transition.

55 The top-down holographic superconductors! Erdmenger et al.:! D3/D7 brane intersections, (arxiv: )! Gubser et al.:! type II sugra (arxiv: )! Gauntlett et al.:! M-theory, Sasaki-Einstein (arxiv: ).! 55!

56 The holographic Fermi-liquid: uncollapsing in the electron star.! (Reissner-Nordstrom) Black hole like object! star like object! uncollapse! Phase transition! fractionalized, unstable : strange metal! Cohesive state :! Symmetry breaking: superconductor, crystal ( scalar hair )! Fermi-liquid ( electron star )! 56!

57 The holographic Fermi-liquid: uncollapsing in the electron star.! Reissner-Nordstrom BH! Photoemission in the boundary! Strange metal! uncollapse! charged neutron star! Relaxational Fermi surface! Fermi-surface (Fermi liquid)! Hartnoll et al., Schalm et al.! 57!

58 Holographic superconductivity: stabilizing the fermions.! Fermion spectrum for scalar-hair black hole (Faulkner et al., ):! BCS Gap in fermion spectrum!!! Pseudogap Temperature dependence! 58!

59 Plan of course.! 1. Overview of AdS/CMT in pictures (slides).! 2. How the computations actually work: from GR and metrics to free energies and propagators with the GKPW rule (blackboard).! 3. Physics highlights: strange metals, holographic superconductivity and Fermi liquids, transport, entanglement (slides).! 59!

60 Dissipation = absorption of classical waves by Black hole!! Hartnoll-Son-Starinets (2002):! Viscosity: absorption cross section of gravitons by black hole! ( ) η = σ 0 abs 16πG = area of horizon (GR theorems)! Entropy density s: Bekenstein-Hawking BH entropy = area of horizon! Universal viscosity-entropy ratio for CFT s with gravitational dual limited in large N by:! s = ! ~ k B

61 Planckian dissipation! Universal entropy production time in QC system:! τ = τ!! k B T Observed in Quark gluon plasma (heavy ion colliders RIHC, LHC) and cold atom unitary fermi gas :! s = T ~ = 1 4 ~ k B Since early 1990 s recognized as responsible for strange metal properties, also linear resistivity high Tc metals??:! ρ 1 τ! k B T 61!

62 Holographic optical conductivity (2+1D).! Optical conductivity in finite density systems:! Strange metal.! 1.2 Holographic superconductor.! ReHsL Momentum conservation in Galilean continuum: everything is a perfect conductor!! w T 62!

63 Quasiparticle versus Unparticle transport.! Hydrodynamics is based on momentum conservation: how about the broken translational symmetry in metals?! Fermi liquid: the charge carriers are quantum-mechanical waves diffracting against the lattice while the Fermi-momentum is of order of the Umklapp momentum,! 1 1 ' (k BT ) 2 = C 1 ' (ne F ) coll 1 coll ~E F K coll T 2 Quantum critical metals:! - QC fluctuations are not waves, these do not diffract against the periodic lattice!! - Planckian dissipation : extremely rapid equilibration, only after hydrodynamics is established momentum relaxes!?! 63!

64 Black holes with a corrugated horizon! Charged Black Hole: describes finite density strange metal.! Breaking translational symmetry in the boundary:! Corrugate the black hole horizon.! Not a favorite thing of general relativity -- hard work, still in progress!!

65 Holographic quenched disorder.! Dictionary entry number one :! David Vegh! 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! 65!

66 Holographic linear resistivity.! Steve Gubser! Richard Davison! Champion strange metal: Einstein-Maxwell-dilaton (consistent truncation), local quantum critical, marginal Fermi-liquid (3+1D), susceptible to holo. superconductivity, healthy thermodynamics: unique ground state, Sommerfeld thermal entropy.! Breaking of Galilean invariance (finite conductivities) due to quenched disorder: massive gravity = fixing space-like diffeomorphisms in the bulk.! David Vegh! Explicit holographic construction explaining linear resistivity!! 66!

67 The secret of the linear resistivity! Davison! Planckian dissipation = very rapid local equilibration: a hydrodynamical fluid is established before it realizes that momentum is non conserved due to the lattice potential (not true in Fermi-gas: Umklapp time is of order collision time).! Hartnoll! Stokes! Resistivity in hydrodynamics! ρ(t) 1 = D τ rel l 2 Einstein! Einstein relation:! D = η m e n η = A! e Sachdev! Son! Planckian viscosity! k B s ρ(t) = 1 = A! S ω p 2 τ rel ω p 2 l 2 m e k B 67!

68 Entropy versus transport: optimal doping! Optimally doped! C = γt S = T /µ ρ 1 τ rel S T Loram, Tallon! Plugging in numbers: mean-free path! l 10 9 m Quite dirty but no residual resistivity since the fluid becomes perfect at T =0!! 68!

69 Plan of course.! 1. Overview of AdS/CMT in pictures (slides).! 2. How the computations actually work: from GR and metrics to free energies and propagators with the GKPW rule (blackboard).! 3. Physics highlights: strange metals, holographic superconductivity and Fermi liquids, transport, entanglement (slides).! 69!

70 Quantum matter.! Macroscopic stuff that can quantum compute all by itself! Ψ = configs A configs configs - Topological incompressible systems, no low energy excitations but the whole carries quantum information: fractional quantum Hall, top. Superconductors/insulators (Majorana s, theta vacuum,..)! - Compressible systems: are the strange metals of this kind??! Strongly interacting fermions at finite density: the fermion signs as entanglement resource!! 70!

71 Entanglement entropy! Bipartite von Neumann entropy: measures entanglement = quantum information of Bell pairs.! Trace the full density matrix over B:! ρ A = Tr B ρ Compute the entropy associated with the reduced density matrix:! S vn,a = Tr[ ρ A ln ρ ] A Universal measure of two bit entanglement:! Bell = 1 ( ) A B A B Prod = 1 ( ) A ( ) B S vn,a = 2 S vn,a = 0 71!

72 Bipartite entanglement entropy and quantum field theory.! A = Tr B [ ] S vn = Tr[ A ln A ] A! B! Wilczek! Measure of entanglement of degrees of freedom in spatial volume B with those in A.! Generic energy eigenstates: S vn scales with volume of B.! Ground states of bosonic systems: S vn scales with the area of B.! Fermi gas: longer ranged signful entangled! L d L d 1 S vn L d 1 ln(l d 1 ) 72!

73 Entanglement entropy ρ A = Tr B versus AdS/CFT.! [ ρ] S vn = Tr[ ρ A lnρ ] A Takayanagi! Ryu! The spatial bipartite entanglement entropy in the boundary is dual to the area of the minimal surface in the bulk, bounded by the cut in the space of the boundary! 73!

74 Holographic strange metal entanglement entropy.! Huijse! Swingle! Sachdev! Einstein-Maxwell-Dilaton bulk => hyperscaling violating geometry (Kiritsis et al.):! ds 2 = 1 % dt 2 r 2 r + ( 2d (z 1)/(d θ ) r2ϑ /(d θ ) dr 2 2 ' + dx i * & ) Boundary: interpolating between normal and RN strange metals.! x i ζ x i, t ζ z t, ds ζ θ / d (d θ )/ z ds S T Entanglement entropy:! S vn L d 1,θ < d 1 S vn L d 1 ln L d 1,θ = d 1 S vn L θ, d 1<θ < d Bosonic fields! Fermi liquid-like! But this is longer ranged!! 74!

75 Hyperscaling violation.! Bosonic field theories: single point of masslessness in momentum space.! =0 Fermi gas: surface of masslessness with dimension d-1 in momentum space (Fermi-surface).! = d 1 momentum space! Very exotic in Ginzburg-Landau-Wilson classical/bosonic physics. For Fermi gas rooted in poor man s antisymmetrization entanglement!! k 1 k 2 k n i = 1 p N X P P k 1 (P)1i k 2 (P2)i k N (PN)i 75!

76 Fermion signs and dense entanglement! Grover! Fisher! arxiv: ! S vn area law: ground states of sign-free systems (bosons, tensor product states..)! Energy eigenstates:! ii = P conf ( 1)i,conf A i conf confi ( 1) i,conf = - Antisymmetrization => area log area S vn (Fermi gas)! - Random => Volume S vn (typical excited states)! The quantum critical metallic phases of holography are characterized by dense sign driven entanglement as characterized by the hyperscaling violation exponent!! 76!

77 Quantum statistics and path integrals! Feynman! Bose condensation: Partition sum dominated by infinitely long cycles! Fermions: infinite cycles set in at T F, but cycles with length w and w +1 cancel each other approximately. Free energy pushed to E F!! Cycle decomposition! 77!

78 The nodal hypersurface! Antisymmetry of the wave function Free Fermions Pauli hypersurface d=2! Nodal hypersurface Test particle!

79 Constrained path integrals! Formally we can solve the sign problem!! Ceperley, J. Stat. Phys. (1991) Self-consistency problem: Path restrictions depend on!

80 Reading the worldline picture! Fermi-energy: confinement energy imposed by local geometry Average node to node spacing Fermi surface encoded globally: Change in coordinate of one particle changes the nodes everywhere Finite T: Non-locality length: ρ F = Det e ik i r j ( ) = 0. ( ρ F = (4πλβ) dn / 2 Det exp (r r + 1 i j 0 0 * )2-3 / 0 ) 4λτ, 23 $ E λ nl = v F τ inel = v F ' $ F & )& % k B T (% λ =! 2 /(2M)! k B T ' ) (

81 Key to fermionic quantum criticality! Phys. Rev. B 78, (2008)! Kruger! JZ! At the QCP scale invariance, no E F Nodal surface has to become fractal!!!

82 Turning on the backflow! Nodal surface has to become fractal!!! Try backflow wave functions Collective (hydrodynamic) regime:

83 MC calculation of n(k)! m m # 1 a * $ % a c & ' ( 3 Divergence of effective mass as a a c!

84 Fractal nodes and entanglement entropy.! Grover! Kaplis! Second Renyi entropy: leading contribution scales like vn entropy.! S q (z) = ln(tr q A ) 1 q, q =2 (R, R 0 )= (R) (R 0 ) Kruger! Backflow range exponent eta (=3 for hydro backflow) :! (r) = a r + r 0 84!

85 Fractal nodes and entanglement entropy.! Grover! Kaplis! S q (z) = ln(tr q A Second Renyi entropy:! ), q =2 1 q Hydrodynamical backflow, for increasing backflow length a (a c =0.5):! Kruger! z a=0. a=0.2 S2/z 15 z log z a=0.25 a= a=0.35 a=0.4 a= log z 85!

86 Fractal nodes and entanglement entropy.! Grover! (r) = Kaplis! a r + r 0 Kruger! Tentative result: by varying the backflow range exponent eta the Haussdorff dimension of the nodal surface is changing, and thereby the range of the entanglement entropy, as for the holographic strange metals!! S (2) (z) S vn (z) z !

87 Conclusions.! - Non-Fermi-liquids as densely entangled states of quantum matter: signs are a blessing!! - Holographic principle: non-fl quantum liquids at finite density are quantum critical phases characterized by non-wilsonian scaling properties (space vs. time, hyperscaling violation, ).! - Conjecture 1: the nodal surface (zero s of the full density matrix) forms the universal measure of signful infinite party entanglement.! - Conjecture 2: the nodal surface is either smooth or fractal and the vacuum is therefore either a Fermi-liquid or a quantum critical strange metal phase.! 87!

88 The tip of the iceberg.! - Electron systems in solids: black holes teach us to think differently High quality Smoking gun predictions are lying ready to be tested in the laboratory (strange metals, holographic SC).! - Decoding the holographic answers in the field theoretical language: Wick-rotation, quantum information, generalized quantum statistics!?! - A wealth of more involved correspondences are lying ready to be explored ( top-downs : Dp/Dq branes, etc.)! - Time dependent AdS/CFT: non-equilibrium physics of field theoretical systems.! - What does this all mean for the greater quantum-gravity agenda?! 88!

89 Book sales! Cambridge University Press! Release: October ! It is 600 pages and only 80!! 89!

90 Its from quantum bits?! Classical space time in bulk! Van Raamsdonk! Encoded by quantum info (entanglement spectrum) in boundary! also!..! Hubeny! Myers! Swingle! 90!

91 Magnitude of momentum relaxation.! According to the cuprate optical conductivity the momentum relaxation rate is:! 1 k BT τ exp! According to massive gravity, the RN strange metal has a momentum relaxation rate:! 1 = A! τ exp l 2 m e S = A!2 k B T k B µl 2 m e! assuming! S k B = k B T µ It follows for the microscopic mean free path:! l =! A µm e 10 9 m 91!

92 Holography s Predictive power! Pseudogap regime! C T 2 S T 2 (?) Loram, Tallon! Massive gravity:! ρ 1 τ rel S T 2 DC resistivity! In addition:! Richard Davison! - Violation of Wiedemann - Franz at low T.! - absence of anomalous skin effect at low T.! This would imply that the pseudogap phase is an order induced CFT (=> holography)!! 92!

93 Observing the origin of the pairing mechanism! 2 nd order Josephson effect! Ferrell Scalapino

94 Standard BCS! Critical glue! T Δ χ p '' (!ω k B T ) T T c Holographic SC (AdS4)! Holographic SC (AdS2)! QC-BCS!!ω /(k B T)

95 Skin effect in metals! Measure impedance of sample in microwave cavity:! AC currents penetrate over a skin depth! ' Z 0 (!) Z(!) =Z 0 (!)+iz 00 (!) Fermi-liquid at high temperature: classical skin effect! ' r (T ) Collision-less regime at low temperature: anomalous skin effect!! ' 1! 1/3 95!

96 Skin effect and viscosity! Forcella, JZ, Valentinis, van der Marel, arxiv: ! Reformulation skin effect in magneto-hydrodynamical language: set by propagation of transversal sound, sensitive to viscosity!! 10-3! 10-8!!! Classical skin effect! Anomalous skin effect! Set by the very small absolute magnitude of the viscosity!! 96!

97 Empty.! 97!

98 Empty.! 98!

99 Empty.! 99!

100 Bulk geometry: AdS Reissner- Nordstrom black hole! Finite temperature and finite charge density: AdS RN black hole! Scalar potential:! ds 2 = g( r)dt 2 + dr2 g(r) + ( r2 dx 2 + dy 2 ) where! g(r) = r 2 1 $ r r ρ 2 ' & ) + ρ 2 % 4r + ( 4r A 0 = r + r Hawking temperature:! T = 12r 4 + ρ πr + 100!

101 Finite density: the Reissner- Nordstrom strange metals (Liu et al.).! Near-horizon geometry of the extremal RN black hole:! - Space directions: flat, codes for simple Galilean invariance in the boundary.! - Time-radial(=scaling) direction: emergent AdS 2, codes for emergent temporal scale invariance!! Fermion spectral functions:! A(k,ω) G" AdS2 ( k,ω) ω 2ν k ν k = 1 6 k ξ 2 Un-particle physics!! 101!

102 AdS/ARPES for the Reissner- Nordstrom non-fermi liquids! Fermi surfaces but no quasiparticles!! Critical FL! Marginal FL! Non Landau FL! Cubrovic, Schalm, JZ; Liu, McGreevy et al.! 102!