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![Page 1: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/1.jpg)
Quantum Criticality Quantum Criticality and and
Black HolesBlack Holes
Talk online: sachdev.physics.harvard.edu
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Markus Mueller, HarvardLars Fritz, Harvard
Subir Sachdev, Harvard
Markus Mueller, HarvardLars Fritz, Harvard
Subir Sachdev, Harvard
Particle theoristsCondensed matter
theorists
Sean Hartnoll, KITPChristopher Herzog,
PrincetonPavel Kovtun, VictoriaDam Son, Washington
Sean Hartnoll, KITPChristopher Herzog,
PrincetonPavel Kovtun, VictoriaDam Son, Washington
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Three foci of modern physics
Quantum phase transitions
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Three foci of modern physics
Quantum phase transitions
Many QPTs of correlated electrons in 2+1 dimensions are described by conformal
field theories (CFTs)
![Page 5: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/5.jpg)
Three foci of modern physics
Quantum phase transitions
Black holes
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Three foci of modern physics
Quantum phase transitions
Black holesBekenstein and Hawking originated the quantum theory, which has found fruition in string theory
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Three foci of modern physics
Quantum phase transitions
Black holes
Hydrodynamics
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Three foci of modern physics
Quantum phase transitions
Black holes
HydrodynamicsUniversal description of fluids
based upon conservation laws and positivity of entropy
production
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Three foci of modern physics
Quantum phase transitions
Black holes
Hydrodynamics
![Page 10: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/10.jpg)
Three foci of modern physics
Quantum phase transitions
Black holes
Hydrodynamics
Canonical problem in condensed matter: transport
properties of a correlated electron system
![Page 11: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/11.jpg)
Three foci of modern physics
Quantum phase transitions
Black holes
Hydrodynamics
Canonical problem in condensed matter: transport
properties of a correlated electron system
New insights and results from detour
unifies disparate fields of physics
![Page 12: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/12.jpg)
Three foci of modern physics
Quantum phase transitions
Black holes
Hydrodynamics
![Page 13: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/13.jpg)
Three foci of modern physics
Quantum phase transitions
Black holes
Hydrodynamics
Many QPTs of correlated electrons in 2+1 dimensions are described by conformal
field theories (CFTs)
![Page 14: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/14.jpg)
Three foci of modern physics
Black holes
HydrodynamicsQuantum phase transitions
Many QPTs of correlated electrons in 2+1 dimensions are described by conformal
field theories (CFTs)
![Page 15: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/15.jpg)
The cuprate superconductors
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Antiferromagnetic (Neel) order in the insulator
No entanglement of spins
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Antiferromagnetic (Neel) order in the insulator
Excitations: 2 spin waves (Goldstone modes)
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Weaken some bonds to induce spin entanglement in a new quantum phase
J
J/
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Ground state is a product of pairs of entangled spins.
J
J/
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Excitations: 3 S=1 triplons
J
J/
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J
J/
Excitations: 3 S=1 triplons
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J
J/
Excitations: 3 S=1 triplons
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J
J/
Excitations: 3 S=1 triplons
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J
J/
Excitations: 3 S=1 triplons
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M. Matsumoto, C. Yasuda, S. Todo, and H. Takayama, Phys. Rev.B 65, 014407 (2002).
Quantum critical point with non-local entanglement in spin wavefunction
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CFT3
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TlCuCl3
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Pressure in TlCuCl3
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N. Cavadini, G. Heigold, W. Henggeler, A. Furrer, H.-U. Güdel, K. Krämer and H. Mutka, Phys. Rev. B 63 172414 (2001).
“triplon”
TlCuCl3 at ambient pressure
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Christian Ruegg, Bruce Normand, Masashige Matsumoto, Albert Furrer, Desmond McMorrow, Karl Kramer, Hans–Ulrich Gudel, Severian Gvasaliya,
Hannu Mutka, and Martin Boehm, Phys. Rev. Lett. 100, 205701 (2008)
TlCuCl3 with varying pressure
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Three foci of modern physics
Quantum phase transitions
Black holes
Hydrodynamics
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Black holes
Three foci of modern physics
Quantum phase transitions
Hydrodynamics
Canonical problem in condensed matter: transport
properties of a correlated electron system
![Page 33: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/33.jpg)
Black holes
Three foci of modern physics
Quantum phase transitions
Hydrodynamics
Canonical problem in condensed matter: transport
properties of a correlated electron system
![Page 34: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/34.jpg)
10000
8000
6000
4000
2000
0
ρ (Ω/q)
86420
B (T)
Ta1/20micT=0.012-0.8 K
SC INS
Indium Oxide films
G. Sambandamurthy, A. Johansson, E. Peled, D. Shahar, P. G. Bjornsson, and K. A. Moler, Europhys. Lett. 75, 611
(2006).
Superfluid-insulator transition
![Page 35: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/35.jpg)
M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
Superfluid-insulator transition
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Classical vortices and wave oscillations of the condensate
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10000
8000
6000
4000
2000
0
ρ (Ω/q)
86420
B (T)
Ta1/20micT=0.012-0.8 K
SC INS
Indium Oxide films
G. Sambandamurthy, A. Johansson, E. Peled, D. Shahar, P. G. Bjornsson, and K. A. Moler, Europhys. Lett. 75, 611
(2006).
Superfluid-insulator transition
![Page 40: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/40.jpg)
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Dilute Boltzmann/Landau gas of particle and holes
![Page 42: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/42.jpg)
10000
8000
6000
4000
2000
0
ρ (Ω/q)
86420
B (T)
Ta1/20micT=0.012-0.8 K
SC INS
Indium Oxide films
G. Sambandamurthy, A. Johansson, E. Peled, D. Shahar, P. G. Bjornsson, and K. A. Moler, Europhys. Lett. 75, 611
(2006).
Superfluid-insulator transition
![Page 43: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/43.jpg)
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CFT at T>0
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Quantum critical transport
S. Sachdev, Quantum Phase Transitions, Cambridge (1999).
![Page 46: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/46.jpg)
Quantum critical transport
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).
![Page 47: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/47.jpg)
Quantum critical transport
P. Kovtun, D. T. Son, and A. Starinets, Phys. Rev. Lett. 94, 11601 (2005)
, 8714 (1997).
![Page 48: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/48.jpg)
10000
8000
6000
4000
2000
0
ρ (Ω/q)
86420
B (T)
Ta1/20micT=0.012-0.8 K
SC INS
Indium Oxide films
G. Sambandamurthy, A. Johansson, E. Peled, D. Shahar, P. G. Bjornsson, and K. A. Moler, Europhys. Lett. 75, 611
(2006).
Superfluid-insulator transition
![Page 49: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/49.jpg)
Three foci of modern physics
Quantum phase transitions
Black holes
Hydrodynamics
![Page 50: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/50.jpg)
HydrodynamicsQuantum phase transitions
Three foci of modern physics
Black holes
New insights and results from detour
unifies disparate fields of physics
Canonical problem in condensed matter: transport
properties of a correlated electron system
![Page 51: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/51.jpg)
HydrodynamicsQuantum phase transitions
Canonical problem in condensed matter: transport
properties of a correlated electron system
Three foci of modern physics
Black holes
New insights and results from detour
unifies disparate fields of physics
![Page 52: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/52.jpg)
Objects so massive that light is gravitationally bound to them.
Black Holes
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Objects so massive that light is gravitationally bound to them.
Black Holes
The region inside the black hole horizon is causally
disconnected from the rest of the universe.
![Page 54: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/54.jpg)
Black Hole ThermodynamicsBekenstein and Hawking discovered astonishing connections between the Einstein theory of black
holes and the laws of thermodynamics
![Page 55: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/55.jpg)
Black Hole ThermodynamicsBekenstein and Hawking discovered astonishing connections between the Einstein theory of black
holes and the laws of thermodynamics
![Page 56: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/56.jpg)
AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
Maldacena, Gubser, Klebanov, Polyakov, Witten
3+1 dimensional AdS space
![Page 57: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/57.jpg)
AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
Maldacena, Gubser, Klebanov, Polyakov, Witten
3+1 dimensional AdS space A 2+1
dimensional system at its
quantum critical point
![Page 58: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/58.jpg)
AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
Maldacena, Gubser, Klebanov, Polyakov, Witten
3+1 dimensional AdS space Quantum
criticality in 2+1
dimensions
![Page 59: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/59.jpg)
AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
Maldacena, Gubser, Klebanov, Polyakov, Witten
3+1 dimensional AdS space Quantum
criticality in 2+1
dimensionsBlack hole temperatur
e = temperatur
e of quantum criticality
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AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
Strominger, Vafa
3+1 dimensional AdS space Quantum
criticality in 2+1
dimensionsBlack hole entropy = entropy of quantum criticality
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AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
3+1 dimensional AdS space Quantum
criticality in 2+1
dimensionsQuantum critical
dynamics = waves in
curved space
Maldacena, Gubser, Klebanov, Polyakov, Witten
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AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
3+1 dimensional AdS space Quantum
criticality in 2+1
dimensionsFriction of quantum criticality = waves
falling into black hole
Kovtun, Policastro, Son
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HydrodynamicsQuantum phase transitions
Three foci of modern physics
Black holes
New insights and results from detour
unifies disparate fields of physics
Canonical problem in condensed matter: transport
properties of a correlated electron system
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HydrodynamicsQuantum phase transitions
Three foci of modern physics
Black holes
New insights and results from detour
unifies disparate fields of physics
Canonical problem in condensed matter: transport
properties of a correlated electron system
1
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Hydrodynamics of quantum critical systems1. Use quantum field theory + quantum transport
equations + classical hydrodynamics Uses physical model but strong-coupling makes explicit solution difficult
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HydrodynamicsQuantum phase transitions
Three foci of modern physics
Black holes
New insights and results from detour
unifies disparate fields of physics
Canonical problem in condensed matter: transport
properties of a correlated electron system
1
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HydrodynamicsQuantum phase transitions
Three foci of modern physics
Black holes
New insights and results from detour
unifies disparate fields of physics
Canonical problem in condensed matter: transport
properties of a correlated electron system
1
2
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Hydrodynamics of quantum critical systems1. Use quantum field theory + quantum transport
equations + classical hydrodynamics Uses physical model but strong-coupling makes explicit solution difficult2. Solve Einstein-Maxwell equations in the
background of a black hole in AdS space
Yields hydrodynamic relations which apply to general classes of quantum critical systems. First exact numerical results for transport co-efficients (for supersymmetric systems).
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Hydrodynamics of quantum critical systems1. Use quantum field theory + quantum transport
equations + classical hydrodynamics Uses physical model but strong-coupling makes explicit solution difficult2. Solve Einstein-Maxwell equations in the
background of a black hole in AdS space
Yields hydrodynamic relations which apply to general classes of quantum critical systems. First exact numerical results for transport co-efficients (for supersymmetric systems).Find perfect agreement between 1. and 2.
In some cases, results were obtained by 2. earlier !!
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Applications:1. Magneto-thermo-electric transport in graphene and near the superconductor-insulator transition
Hydrodynamic cyclotron resonance Nernst effect
2. Quark-gluon plasma Low viscosity fluid
3. Fermi gas at unitarity Non-relativistic AdS/CFT
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Applications:1. Magneto-thermo-electric transport in graphene and near the superconductor-insulator transition
Hydrodynamic cyclotron resonance Nernst effect
2. Quark-gluon plasma Low viscosity fluid
3. Fermi gas at unitarity Non-relativistic AdS/CFT
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Graphene
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Graphene
Quantum critical
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The cuprate superconductors
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The cuprate superconductors
CFT?CFT?
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Thermoelectric measurements
CFT3?
CFT3?
Cuprates
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S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007)
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S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007)
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S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007)
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Y. Wang, L. Li, and N. P. Ong, Phys. Rev. B 73, 024510 (2006).
Theory for
LSCO Experiments
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Applications:1. Magneto-thermo-electric transport in graphene and near the superconductor-insulator transition
Hydrodynamic cyclotron resonance Nernst effect
2. Quark-gluon plasma Low viscosity fluid
3. Fermi gas at unitarity Non-relativistic AdS/CFT
![Page 83: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/83.jpg)
Applications:1. Magneto-thermo-electric transport in graphene and near the superconductor-insulator transition
Hydrodynamic cyclotron resonance Nernst effect
2. Quark-gluon plasma Low viscosity fluid
3. Fermi gas at unitarity Non-relativistic AdS/CFT
![Page 84: Quantum Criticality and Black Holes Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu.](https://reader035.fdocuments.us/reader035/viewer/2022062805/5697bfe01a28abf838cb33ea/html5/thumbnails/84.jpg)
Au+Au collisions at RHIC
Quark-gluon plasma can be described as “quantum critical QCD”
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Phases of nuclear matter
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S=1/2 Fermi gas at a
Feshbach resonance
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T. Schafer, Phys. Rev. A 76, 063618 (2007).A. Turlapov, J. Kinast, B. Clancy, Le Luo, J. Joseph, J. E. Thomas, J. Low Temp. Physics 150, 567 (2008)
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T. Schafer, Phys. Rev. A 76, 063618 (2007).A. Turlapov, J. Kinast, B. Clancy, Le Luo, J. Joseph, J. E. Thomas, J. Low Temp. Physics 150, 567 (2008)
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T. Schafer, Phys. Rev. A 76, 063618 (2007).A. Turlapov, J. Kinast, B. Clancy, Le Luo, J. Joseph, J. E. Thomas, J. Low Temp. Physics 150, 567 (2008)
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T. Schafer, Phys. Rev. A 76, 063618 (2007).A. Turlapov, J. Kinast, B. Clancy, Le Luo, J. Joseph, J. E. Thomas, J. Low Temp. Physics 150, 567 (2008)
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• Theory for transport near quantum phase transitions in superfluids and antiferromagnets
• 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.
• Theory of Nernst effect near the superfluid-insulator transition, and connection to cuprates.
• Quantum-critical magnetotransport in graphene.
• Theory for transport near quantum phase transitions in superfluids and antiferromagnets
• 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.
• Theory of Nernst effect near the superfluid-insulator transition, and connection to cuprates.
• Quantum-critical magnetotransport in graphene.
ConclusionsConclusions