Quantum Criticality and

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Quantum Criticality and Black Holes
Talk online sachdev.physics.harvard.edu
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Condensed matter theorists
Particle theorists
Sean Hartnoll, KITP Christopher Herzog,
Princeton Pavel Kovtun, Victoria Dam Son,
Washington
Markus Mueller, Harvard Lars Fritz, Harvard Subir
Sachdev, Harvard
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Three foci of modern physics
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Three foci of modern physics
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Three foci of modern physics
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Three foci of modern physics
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Three foci of modern physics
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Three foci of modern physics
Universal description of fluids based upon
conservation laws and positivity of entropy
production
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Three foci of modern physics
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Three foci of modern physics
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Three foci of modern physics
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Three foci of modern physics
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Three foci of modern physics
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Three foci of modern physics
Black holes
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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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Quantum critical point with non-local
entanglement in spin wavefunction
M. Matsumoto, C. Yasuda, S. Todo, and H.
Takayama, Phys. Rev.B 65, 014407 (2002).
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CFT3
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TlCuCl3
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Pressure in TlCuCl3
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TlCuCl3 at ambient pressure
triplon
N. Cavadini, G. Heigold, W. Henggeler, A. Furrer,
H.-U. Güdel, K. Krämer and H. Mutka, Phys. Rev.
B 63 172414 (2001).
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TlCuCl3 with varying pressure
Christian Ruegg, Bruce Normand, Masashige
Matsumoto, Albert Furrer, Desmond McMorrow, Karl
Kramer, HansUlrich Gudel, Severian Gvasaliya,
Hannu Mutka, and Martin Boehm, Phys. Rev. Lett.
100, 205701 (2008)
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S1/2 insulator on the square lattice
A.W. Sandvik, Phys. Rev. Lett. 98, 227202
(2007). R.G. Melko and R.K. Kaul, Phys. Rev.
Lett. 100, 017203 (2008).
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S1/2 insulator on the square lattice
Phase diagram
A.W. Sandvik, Phys. Rev. Lett. 98, 227202
(2007). R.G. Melko and R.K. Kaul, Phys. Rev.
Lett. 100, 017203 (2008).
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694
(1989). T. Senthil, A. Vishwanath, L. Balents, S.
Sachdev and M.P.A. Fisher, Science 303, 1490
(2004).
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Theory for loss of Neel order
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S1/2 insulator on the square lattice
Phase diagram
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S1/2 insulator on the square lattice
CFT3
RG flow of gauge coupling
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d-wave superconductor on the square lattice
CFT3
R. K. Kaul, Y. B. Kim, S. Sachdev, and T.
Senthil, Nature Physics 4, 28 (2008) R. K. Kaul,
M.A. Metlitski, S. Sachdev, and C. Xu,
arXiv0804.1794
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U(1) gauge theory with N 4 supersymmetry
CFT3
N. Seiberg and E. Witten, hep-th/9607163 K.A.
Intriligator and N. Seiberg, hep-th/9607207 A.
Kapustin and M. J. Strassler, hep-th/9902033
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SU(N) gauge theory with N 8 supersymmetry (SYM3)
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Graphene
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Three foci of modern physics
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Three foci of modern physics
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Three foci of modern physics
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Superfluid-insulator transition
Indium Oxide films
G. Sambandamurthy, A. Johansson, E. Peled, D.
Shahar, P. G. Bjornsson, and K. A. Moler,
Europhys. Lett. 75, 611 (2006).
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Superfluid-insulator transition
M. Greiner, O. Mandel, T. Esslinger, T. W.
Hänsch, and I. Bloch, Nature 415, 39 (2002).
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Classical vortices and wave oscillations of the
condensate
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Superfluid-insulator transition
Indium Oxide films
G. Sambandamurthy, A. Johansson, E. Peled, D.
Shahar, P. G. Bjornsson, and K. A. Moler,
Europhys. Lett. 75, 611 (2006).
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Dilute Boltzmann/Landau gas of particle and holes
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Superfluid-insulator transition
Indium Oxide films
G. Sambandamurthy, A. Johansson, E. Peled, D.
Shahar, P. G. Bjornsson, and K. A. Moler,
Europhys. Lett. 75, 611 (2006).
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CFT at Tgt0
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Quantum critical transport
S. Sachdev, Quantum Phase Transitions, Cambridge
(1999).
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Quantum critical transport
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714
(1997).
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Quantum critical transport
P. Kovtun, D. T. Son, and A. Starinets, Phys.
Rev. Lett. 94, 11601 (2005) , 8714 (1997).
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Superfluid-insulator transition
Indium Oxide films
G. Sambandamurthy, A. Johansson, E. Peled, D.
Shahar, P. G. Bjornsson, and K. A. Moler,
Europhys. Lett. 75, 611 (2006).
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Three foci of modern physics
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Three foci of modern physics
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Three foci of modern physics
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Black Holes
Objects so massive that light is gravitationally
bound to them.
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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.
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Black Hole Thermodynamics
Bekenstein and Hawking discovered astonishing
connections between the Einstein theory of black
holes and the laws of thermodynamics
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Black Hole Thermodynamics
Bekenstein and Hawking discovered astonishing
connections between the Einstein theory of black
holes and the laws of thermodynamics
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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
31 dimensional AdS space
Maldacena, Gubser, Klebanov, Polyakov, Witten
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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
31 dimensional AdS space
A 21 dimensional system at its quantum critical
point
Maldacena, Gubser, Klebanov, Polyakov, Witten
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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
31 dimensional AdS space
Quantum criticality in 21 dimensions
Maldacena, Gubser, Klebanov, Polyakov, Witten
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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
31 dimensional AdS space
Quantum criticality in 21 dimensions
Black hole temperature temperature of quantum
criticality
Maldacena, Gubser, Klebanov, Polyakov, Witten
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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
31 dimensional AdS space
Quantum criticality in 21 dimensions
Black hole entropy entropy of quantum
criticality
Strominger, Vafa
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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
31 dimensional AdS space
Quantum criticality in 21 dimensions
Quantum critical dynamics waves in curved space
Maldacena, Gubser, Klebanov, Polyakov, Witten
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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
31 dimensional AdS space
Quantum criticality in 21 dimensions
Friction of quantum criticality waves falling
into black hole
Kovtun, Policastro, Son
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Three foci of modern physics
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Three foci of modern physics
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Hydrodynamics of quantum critical systems
1. Use quantum field theory quantum transport
equations classical hydrodynamics Uses
physical model but strong-coupling makes
explicit solution difficult
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Three foci of modern physics
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Three foci of modern physics
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2
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Hydrodynamics of quantum critical systems
1. Use quantum field theory quantum transport
equations classical hydrodynamics Uses
physical model but strong-coupling makes
explicit solution difficult
2. 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 systems
1. Use quantum field theory quantum transport
equations classical hydrodynamics Uses
physical model but strong-coupling makes
explicit solution difficult
2. 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
Quantum critical
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Cuprates
Thermoelectric measurements
CFT3?
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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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LSCO Experiments
Theory for
Y. Wang, L. Li, and N. P. Ong, Phys. Rev. B 73,
024510 (2006).
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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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AuAu 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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S1/2 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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Conclusions

• 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.