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

Oct 05, 2022 231 likes •587 views

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,

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A HOT end of the holography A HOT end of the holography meeting .. meeting ..

Jan Zaanen

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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)

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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)

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Smashing things.

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Chesler, Adams,Liu.

Holographic Superfluid turbulence (Science, just published)

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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)

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David’s outlook: strings 2013.

“our community has overhyped the application of AdS/CFT to condensed matter physics”

David Gross

“It is understandable that it met resistance in the condensed matter community”

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Physics Today (2013).

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Another Master Phenomenologist.

Chandra Varma

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The DMFT people ….

Kotliar Jarrell Georges Cluster DMFT: small QMC clusters in self consistent effective medium “Sign-full numerics”: long time scales need only small lengths.

τ ∝ ξz, z →∞

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AdS/CFT as a Femme fatale.

Senthil (MIT/Harvard)

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The higher dimensional quantum smectic.

σ ω

( ) ∝ ω 4 / 3 at T = 0

?

Donos Hartnoll

“ab-plane” optical conductivity: perfect Drude metal. “c-axis” optical conductivity: turns from “bad metal” to “pseudogap-insulator” when potential increases:

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Serendipity.

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Self-organized two dimensionality.

ab- vs. c-axis DC resistivity ab- vs. c-axis optical conductivity

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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!

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Quantum smectics in 2+1D.

Emery,Fradkin, Kivelson,Lubensky, PRL 85, 2160 (2000); Vishwanath, Carpentier, PRL 86, 676 (2001) 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:

σ// ω

( ) ∝ Zδ ω ( )

σ

⊥ ω

( ) ∝ ων;ν ≥ 0

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Divine resistivity

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Corrugated horizon versus

  • ptical conductivity.

Horowitz Tong Santos

Similar “corrugated horizon” lattice potential but now currents: photons + gravitons at zero momentum.

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Optical conductivity: “mid infrared”

σ ω

( ) =

A iω

( )

2/ 3 + B

kBT < hω < µ

At “intermediate” frequency: The conductivity shows an emergent scaling behavior: which is quite robust, only a sufficiently strong lattice potential is needed.

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Quantum self-similarity: optical conductivity

Van der Marel, JZ Nature 2003:

σ ω

( ) ∝

1 iω

( )

ασ = eiπασ / 2

ω

ασ

= cos παc /2

( )

ω

ασ

+ i sin πασ /2

( )

ω

ασ

‘High’ frequency optical conductivity:

Exponent ασ ≈ 0.65 Violates single parameter- and hyper scaling: non-Wilsonian RNG !!

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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 gab to a fixed metric fxx=fyy=1

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Analytical solution for conductivity for RN Metal.

Davison Parnachev

Hydrodynamical regime

hω < kBT

Drude form:

σ1 ω

( ) =

σ0 1− iωτ rel

ρ(T) ∝ 1 τ rel = η l2ρm

η =

l =

ρm =

Famous “minimal” or “Planckian” viscosity of (temporal) quantum critical states (A of order 1, s is entropy density):

η = A h kB s

ρ(T) ∝ 1 τ rel = A h l2me S kB

viscosity

mean free path Electron mass density

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Entropy versus transport:

  • ptimal doping

Loram, Tallon

C = γT ⇒ S = T /µ

Optimally doped Massive gravity:

ρ ∝ 1 τ rel ∝ S ∝ T

Explicit realization: “Gubser” strange metal !

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Magnitude of momentum relaxation.

According to the cuprate optical conductivity the momentum relaxation rate is:

1 τexp ≈ kBT h

According to “massive gravity”, the RN strange metal has a momentum relaxation rate:

1 τexp = A h l2me S kB = A h2 µl2me kBT h S kB = kBT µ l = h A µme ≈10−9m

assuming It follows for the microscopic mean free path:

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“Fermi-liquid like” pseudogap transport

Loram, Tallon

C ∝ T 2 ⇒ S ∝ T 2(?)

Pseudogap regime Massive gravity:

ρ ∝ 1 τ rel ∝ S ∝ T 2

Energy/temperature scaling collapse vd Marel et al, PNAS 110, 5774 DC resistivity

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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)

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Bell pairs and the “spooky action at a distance”.

| Bell = 1 2 0 A⊗ |1

B − 1 A ⊗ 0 B

( )

| product = 0 A ⊗ 1 B or 1 A ⊗ 0 B

Classical computers live in tensor product space: Quantum computers exploit entangled states capable of “spooky action at a distance” (EPR paradox).

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“The classical condensates: from crystals to Fermi-liquids.”

States of matter that we understand are product! Ψ

0 Ωi

{ } = Πi ˆ

X

i + Ωi

( ) vac

  • Crystals: put atoms in real space wave packets
  • Magnets: put spins in generalized coherent state
  • Superconductors/superfluids: put bosons/Cooper pairs in coherent

superposition

Xi

+ Ri

( ) ∝ e

(Ri

0 −r)^2

σ 2ψ + r

( )

Xi

+ r

n

i

( ) ∝ eiϕ i / 2 cos θi /2 ( )ci↑

+ + e−iϕ i / 2 sin θi /2

( )ci↓

+

Xk / i

+ ∝ uk + vkck↑ + c−k↓ + ,

ui + vieiϕ ibi

+

  • Fermi gas/liquid special, but only “Fermi-Dirac entanglement”

Ψ

FL = Πk kF ck + vac

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Quantum matter.

“Macroscopic stuff that can quantum compute all by itself”

Ψ = Aconfigs

configs

∑

configs

  • Topological incompressible systems, no low energy excitations but the

whole carries quantum information: fractional quantum Hall …

  • Compressible systems: are the strange metals of this kind??

Strongly interacting fermions at finite density: the fermion signs as entanglement resource!

  • Compressible systems: strongly interacting bosonic quantum critical

states have dense long range entanglements (Planckian dissipation)

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Holographic strange metal entanglement entropy.

ds2 = 1 r2 − dt 2 r2d(z−1)/(d −θ ) + r2ϑ /(d −θ )dr2 + dxi

2

⎛ ⎝ ⎜ ⎞ ⎠ ⎟

xi →ζ xi, t →ζzt, ds →ζθ / dds

S ∝ T(d −θ )/ z

SvN ∝ Σ ,θ < d −1 SvN ∝ ΣlnΣ ,θ = d −1 SvN ∝ Σθ /(d −1) ,θ > d −1

Geometry in Einstein-Maxwell-Dilaton bulk: “Hyperscaling violation” in boundary theory: Thermal entropy: Entanglement entropy (Sachdev, Huijse, Swingle):

Looks much like a deconfined Fermi-liquid, hidden from the gauge singlet UV propagators!

But this is longer ranged !?

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Holographic very strange metal entanglement entropy

Ground state entropy: S(T = 0) ∝ µN 2 Needs both finite density and large N. RN metal holographic entanglement entropy:

SvN ∝ ld

For infinite l this turns into the T=0 entropy: (Sachdev)

ST =0 = Tr ρlnρ]

[ ]

Counting excitations: Massless point in momentum space = bosonic CFT’s: Massless surface in momentum space = Fermi liquid: SvN = (# points on FS) (CFT2 SvN)

SvN ∝ ld −1

SvN ∝ ld −1

( ) lnl

( )

Massless volume in momentum space = RN metal: SvN = (#points in k space)(CFT1 SvN)

SvN ∝ ld

θ = d 1− 1 z ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ , z →∞

Volume scaling!

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Is the RN ground state entropy classical?

vN entropy is “drunk”: for a finite T unentangled classical state it also scales with volume … For the (eternal) RN back hole the vN entropy of area A is different from its compliment: it is a mixed state.

The RN metal is the most extreme state with its volume vN entropy.

Objection (Hong Liu): but this is ill defined for the eternal BH! Depart from a pure state “infalling matter shell” collapsing in the RN black hole. Causality forbids the minimal surface associated with the vN entropy to wrap around the black hole. Thereby the area and its compliment give the same entropy.

The RN metal is therefore a pure state and the volume entropy means ‘maximal’ entanglement.

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The cloverleaf of matter ….

Condensed matter physics Quantum information Black hole physics String theory Quantum matter Including QCD

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Special thanks to …

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Empty.