Title: Hydrodynamic%20transport%20near%20quantum%20critical%20points%20and%20the%20AdS/CFT%20correspondence
1Hydrodynamic transport near quantum critical
points and the AdS/CFT correspondence
2Condensed matter theorists
Particle theorists
Sean Hartnoll, KITP Christopher Herzog,
Princeton Pavel Kovtun, Victoria Dam Son,
Washington
Markus Mueller, Harvard Subir Sachdev, Harvard
3Outline
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
4Outline
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
5M. Greiner, O. Mandel, T. Esslinger, T. W.
Hänsch, and I. Bloch, Nature 415, 39 (2002).
6The insulator
7Excitations of the insulator
8Excitations of the insulator
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12 Graphene
13Outline
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
14Outline
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
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17Wave oscillations of the condensate (classical
Gross-Pitaevski equation)
18Dilute Boltzmann gas of particle and holes
19CFT at Tgt0
20Resistivity 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)
21Density correlations in CFTs at T gt0
22Density correlations in CFTs at T gt0
23Density correlations in CFTs at T gt0
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714
(1997).
24Density 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.
26Outline
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
27Outline
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(No Transcript)
29For experimental applications, we must move away
from the ideal CFT
- A chemical potential µ
- A magnetic field B
CFT
e.g.
30Cuprate superconductors
31Cuprate superconductors
Nernst measurements
32Nernst experiment
ey
Hm
H
33Cuprate superconductors
Use coupling g to induce a transition to a VBS
insulator
34Cuprate superconductors
Nernst measurements
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37S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
38Conservation laws/equations of motion
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
39Constitutive 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)
40Single 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)
41For 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.
42S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
43Solve 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)
44From 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)
45From 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)
46From 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)
47From 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)
48From 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)
49From 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)
50From 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)
51From 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)
52From 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)
53From 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)
54LSCO Experiments
Measurement of
(T small)
Y. Wang et al., Phys. Rev. B 73, 024510 (2006).
55LSCO Experiments
Measurement of
(T small)
Y. Wang et al., Phys. Rev. B 73, 024510 (2006).
56LSCO 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
57LSCO Experiments
-dependence
Theory for
Y. Wang, L. Li, and N. P. Ong, Phys. Rev. B 73,
024510 (2006).
58LSCO Experiments
Theory for
Y. Wang, L. Li, and N. P. Ong, Phys. Rev. B 73,
024510 (2006).
59Outline
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
60Outline
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
61Black Holes
Objects so massive that light is gravitationally
bound to them.
62Black 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.
63Black Hole Thermodynamics
Bekenstein and Hawking discovered astonishing
connections between the Einstein theory of black
holes and the laws of thermodynamics
64Black Hole Thermodynamics
Bekenstein and Hawking discovered astonishing
connections between the Einstein theory of black
holes and the laws of thermodynamics
65AdS/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
66AdS/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
67AdS/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
68AdS/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
69Application of the AdS/CFT correspondence
70Application of the AdS/CFT correspondence
71Application of the AdS/CFT correspondence
72Application of the AdS/CFT correspondence
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74Conclusions
- 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.
75Collisionless to hydrodynamic crossover of SYM3
P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son,
Phys. Rev. D 75, 085020 (2007)
76Collisionless to hydrodynamic crossover of SYM3
P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son,
Phys. Rev. D 75, 085020 (2007)
77Universal 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)
78Electromagnetic self-duality