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Hydrodynamic%20transport%20near%20quantum%20critical%20points%20and%20the%20AdS/CFT%20correspondence

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Nernst effect and a hydrodynamic cyclotron. resonance. 4. The AdS/CFT correspondence ... cyclotron frequency! 0.035 times smaller than the cyclotron frequency ... – PowerPoint PPT presentation

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Title: Hydrodynamic%20transport%20near%20quantum%20critical%20points%20and%20the%20AdS/CFT%20correspondence


1
Hydrodynamic transport near quantum critical
points and the AdS/CFT correspondence
2
Condensed matter theorists
Particle theorists
Sean Hartnoll, KITP Christopher Herzog,
Princeton Pavel Kovtun, Victoria Dam Son,
Washington
Markus Mueller, Harvard Subir Sachdev, Harvard
3
Outline
1. Model systems (i) Superfluid-insulator
transition of lattice bosons,
(ii) graphene 2. Quantum-critical transport at
integer filling, zero magnetic field, and
with no impurities Collisionless-t0-hydrod
ynamic crossover of CFT3s 3. Quantum-critical
transport at integer generic filling,
nonzero magnetic field, and with impurities
Nernst effect and a hydrodynamic cyclotron
resonance 4. The AdS/CFT
correspondence Quantum criticality and dyonic
black holes
4
Outline
1. Model systems (i) Superfluid-insulator
transition of lattice bosons,
(ii) graphene 2. Quantum-critical transport at
integer filling, zero magnetic field, and
with no impurities Collisionless-t0-hydrod
ynamic crossover of CFT3s 3. Quantum-critical
transport at integer generic filling,
nonzero magnetic field, and with impurities
Nernst effect and a hydrodynamic cyclotron
resonance 4. The AdS/CFT
correspondence Quantum criticality and dyonic
black holes
5
M. Greiner, O. Mandel, T. Esslinger, T. W.
Hänsch, and I. Bloch, Nature 415, 39 (2002).
6
The insulator
7
Excitations of the insulator
8
Excitations of the insulator
9
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10
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11
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12
Graphene
13
Outline
1. Model systems (i) Superfluid-insulator
transition of lattice bosons,
(ii) graphene 2. Quantum-critical transport at
integer filling, zero magnetic field, and
with no impurities Collisionless-t0-hydrod
ynamic crossover of CFT3s 3. Quantum-critical
transport at integer generic filling,
nonzero magnetic field, and with impurities
Nernst effect and a hydrodynamic cyclotron
resonance 4. The AdS/CFT
correspondence Quantum criticality and dyonic
black holes
14
Outline
1. Model systems (i) Superfluid-insulator
transition of lattice bosons,
(ii) graphene 2. Quantum-critical transport at
integer filling, zero magnetic field, and
with no impurities Collisionless-t0-hydrod
ynamic crossover of CFT3s 3. Quantum-critical
transport at integer generic filling,
nonzero magnetic field, and with impurities
Nernst effect and a hydrodynamic cyclotron
resonance 4. The AdS/CFT
correspondence Quantum criticality and dyonic
black holes
15
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16
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17
Wave oscillations of the condensate (classical
Gross-Pitaevski equation)
18
Dilute Boltzmann gas of particle and holes
19
CFT at Tgt0
20
Resistivity of Bi films
D. B. Haviland, Y. Liu, and A. M. Goldman, Phys.
Rev. Lett. 62, 2180 (1989)
M. P. A. Fisher, Phys. Rev. Lett. 65, 923 (1990)
21
Density correlations in CFTs at T gt0
22
Density correlations in CFTs at T gt0
23
Density correlations in CFTs at T gt0
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714
(1997).
24
Density correlations in CFTs at T gt0
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714
(1997).
25
Collisionless-hydrodynamic crossover in graphene
L. Fritz, M. Mueller, J. Schmalian and S.
Sachdev, to appear.
26
Outline
1. Model systems (i) Superfluid-insulator
transition of lattice bosons,
(ii) graphene 2. Quantum-critical transport at
integer filling, zero magnetic field, and
with no impurities Collisionless-t0-hydrod
ynamic crossover of CFT3s 3. Quantum-critical
transport at integer generic filling,
nonzero magnetic field, and with impurities
Nernst effect and a hydrodynamic cyclotron
resonance 4. The AdS/CFT
correspondence Quantum criticality and dyonic
black holes
27
Outline
1. Model systems (i) Superfluid-insulator
transition of lattice bosons,
(ii) graphene 2. Quantum-critical transport at
integer filling, zero magnetic field, and
with no impurities Collisionless-t0-hydrod
ynamic crossover of CFT3s 3. Quantum-critical
transport at integer generic filling,
nonzero magnetic field, and with impurities
Nernst effect and a hydrodynamic cyclotron
resonance 4. The AdS/CFT
correspondence Quantum criticality and dyonic
black holes
28
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29
For experimental applications, we must move away
from the ideal CFT
  • A chemical potential µ
  • A magnetic field B

CFT
e.g.
30
Cuprate superconductors
31
Cuprate superconductors
Nernst measurements
32
Nernst experiment
ey
Hm
H
33
Cuprate superconductors
Use coupling g to induce a transition to a VBS
insulator
34
Cuprate superconductors
Nernst measurements
35
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36
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37
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
38
Conservation laws/equations of motion
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
39
Constitutive relations which follow from Lorentz
transformation to moving frame
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
40
Single dissipative term allowed by requirement of
positive entropy production. There is only one
independent transport co-efficient
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
41
For experimental applications, we must move away
from the ideal CFT
  • A chemical potential µ
  • A magnetic field B
  • An impurity scattering rate 1/timp (its T
    dependence follows from scaling arguments)

CFT
CFT
e.g.
42
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
43
Solve initial value problem and relate results to
response functions (KadanoffMartin)
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
44
From these relations, we obtained results for the
transport co-efficients, expressed in terms of a
cyclotron frequency and damping
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
45
From these relations, we obtained results for the
transport co-efficients, expressed in terms of a
cyclotron frequency and damping
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
46
From these relations, we obtained results for the
transport co-efficients, expressed in terms of a
cyclotron frequency and damping
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
47
From these relations, we obtained results for the
transport co-efficients, expressed in terms of a
cyclotron frequency and damping
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
48
From these relations, we obtained results for the
transport co-efficients, expressed in terms of a
cyclotron frequency and damping
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
49
From these relations, we obtained results for the
transport co-efficients, expressed in terms of a
cyclotron frequency and damping
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
50
From these relations, we obtained results for the
transport co-efficients, expressed in terms of a
cyclotron frequency and damping
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
51
From these relations, we obtained results for the
transport co-efficients, expressed in terms of a
cyclotron frequency and damping
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
52
From these relations, we obtained results for the
transport co-efficients, expressed in terms of a
cyclotron frequency and damping
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
53
From these relations, we obtained results for the
transport co-efficients, expressed in terms of a
cyclotron frequency and damping
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
54
LSCO Experiments
Measurement of
(T small)
Y. Wang et al., Phys. Rev. B 73, 024510 (2006).
55
LSCO Experiments
Measurement of
(T small)
Y. Wang et al., Phys. Rev. B 73, 024510 (2006).
56
LSCO Experiments
Measurement of
(T small)
Y. Wang et al., Phys. Rev. B 73, 024510 (2006).
  • T-dependent cyclotron frequency!
  • 0.035 times smaller than the cyclotron frequency
    of free electrons (at T35 K)
  • Only observable in ultra-pure samples where
    .

? Prediction for ?c
56
57
LSCO Experiments
-dependence
Theory for
Y. Wang, L. Li, and N. P. Ong, Phys. Rev. B 73,
024510 (2006).
58
LSCO Experiments
Theory for
Y. Wang, L. Li, and N. P. Ong, Phys. Rev. B 73,
024510 (2006).
59
Outline
1. Model systems (i) Superfluid-insulator
transition of lattice bosons,
(ii) graphene 2. Quantum-critical transport at
integer filling, zero magnetic field, and
with no impurities Collisionless-t0-hydrod
ynamic crossover of CFT3s 3. Quantum-critical
transport at integer generic filling,
nonzero magnetic field, and with impurities
Nernst effect and a hydrodynamic cyclotron
resonance 4. The AdS/CFT
correspondence Quantum criticality and dyonic
black holes
60
Outline
1. Model systems (i) Superfluid-insulator
transition of lattice bosons,
(ii) graphene 2. Quantum-critical transport at
integer filling, zero magnetic field, and
with no impurities Collisionless-t0-hydrod
ynamic crossover of CFT3s 3. Quantum-critical
transport at integer generic filling,
nonzero magnetic field, and with impurities
Nernst effect and a hydrodynamic cyclotron
resonance 4. The AdS/CFT
correspondence Quantum criticality and dyonic
black holes
61
Black Holes
Objects so massive that light is gravitationally
bound to them.
62
Black Holes
Objects so massive that light is gravitationally
bound to them.
The region inside the black hole horizon is
causally disconnected from the rest of the
universe.
63
Black Hole Thermodynamics
Bekenstein and Hawking discovered astonishing
connections between the Einstein theory of black
holes and the laws of thermodynamics
64
Black Hole Thermodynamics
Bekenstein and Hawking discovered astonishing
connections between the Einstein theory of black
holes and the laws of thermodynamics
65
AdS/CFT correspondence
The quantum theory of a black hole in a
31-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory
of a quantum critical point) in 21 dimensions
A 21 dimensional system at its quantum critical
point
31 dimensional AdS space
Maldacena
Black hole
66
AdS/CFT correspondence
The quantum theory of a black hole in a
31-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory
of a quantum critical point) in 21 dimensions
Black hole temperature temperature of quantum
criticality
31 dimensional AdS space
Quantum criticality in 21 D
Strominger, Vafa
Black hole
67
AdS/CFT correspondence
The quantum theory of a black hole in a
31-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory
of a quantum critical point) in 21 dimensions
Dynamics of quantum criticality waves in curved
gravitational background
31 dimensional AdS space
Quantum criticality in 21 D
Maldacena
Black hole
68
AdS/CFT correspondence
The quantum theory of a black hole in a
31-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory
of a quantum critical point) in 21 dimensions
Friction of quantum critical dynamics black
hole absorption rates
31 dimensional AdS space
Quantum criticality in 21 D
Son
Black hole
69
Application of the AdS/CFT correspondence
70
Application of the AdS/CFT correspondence
71
Application of the AdS/CFT correspondence
72
Application of the AdS/CFT correspondence
73
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74
Conclusions
  • Hydrodynamic theory for thermoelectric response
    functions of quantum critical systems
  • Applications to the cuprates and graphene.
  • Exact solutions via black hole mapping have
    yielded first exact results for transport
    co-efficients in interacting many-body systems,
    and were valuable in determining general
    structure of hydrodynamics.

75
Collisionless to hydrodynamic crossover of SYM3
P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son,
Phys. Rev. D 75, 085020 (2007)
76
Collisionless to hydrodynamic crossover of SYM3
P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son,
Phys. Rev. D 75, 085020 (2007)
77
Universal constants of SYM3
C. Herzog, JHEP 0212, 026 (2002)
P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son,
Phys. Rev. D 75, 085020 (2007)
78
Electromagnetic self-duality
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