Quantum Criticality and

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Quantum Criticality and Black Holes
Talk online sachdev.physics.harvard.edu
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Particle theorists
Sean Hartnoll, KITP Christopher Herzog,
Princeton Pavel Kovtun, Victoria Dam Son,
Washington
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Condensed matter theorists
Yang Qi Harvard
Cenke Xu Harvard
Markus Mueller Geneva
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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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Square lattice antiferromagnet
Ground state has long-range Néel order
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Square lattice antiferromagnet
J
J/
Weaken some bonds to induce spin entanglement in
a new quantum phase
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TlCuCl3
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Pressure in TlCuCl3
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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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Prediction of quantum field theory
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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XPd(dmit)22
S
C
Pd
X
Pd(dmit)2
t
t
t
Half-filled band ? Mott insulator with spin S
1/2 Triangular lattice of Pd(dmit)22 ?
frustrated quantum spin system
Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and
R. Kato, J. Phys. Condens. Matter 19, 145240
(2007)
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Anisotropic triangular lattice antiferromagnet
Broken spin rotation symmetry
Neel ground state for small J/J
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Anisotropic triangular lattice antiferromagnet
Possible ground state for intermediate J/J
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694
(1989)
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Anisotropic triangular lattice antiferromagnet
Broken lattice space group symmetry
Valence bond solid (VBS)
Possible ground state for intermediate J/J
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694
(1989)
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Anisotropic triangular lattice antiferromagnet
Broken lattice space group symmetry
Valence bond solid (VBS)
Possible ground state for intermediate J/J
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694
(1989)
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Anisotropic triangular lattice antiferromagnet
Broken lattice space group symmetry
Valence bond solid (VBS)
Possible ground state for intermediate J/J
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694
(1989)
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Anisotropic triangular lattice antiferromagnet
Broken lattice space group symmetry
Valence bond solid (VBS)
Possible ground state for intermediate J/J
N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694
(1989)
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Magnetic Criticality
XPd(dmit)22
Et2Me2Sb (CO)
Me4P
Me4As
TN (K)
EtMe3As
Et2Me2P
Et2Me2As
Me4Sb
Neel order
EtMe3Sb
Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and
R. Kato, J. Phys. Condens. Matter 19, 145240
(2007)
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Magnetic Criticality
XPd(dmit)22
Et2Me2Sb (CO)
Me4P
Me4As
EtMe3P
TN (K)
EtMe3As
Et2Me2P
Et2Me2As
Me4Sb
Spin gap
Neel order
EtMe3Sb
Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and
R. Kato, J. Phys. Condens. Matter 19, 145240
(2007)
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Magnetic Criticality
XPd(dmit)22
Et2Me2Sb (CO)
Me4P
Me4As
EtMe3P
TN (K)
EtMe3As
VBS order
Et2Me2P
Et2Me2As
Me4Sb
Spin gap
Neel order
EtMe3Sb
Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and
R. Kato, J. Phys. Condens. Matter 19, 145240
(2007)
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Observation of a valence bond solid (VBS) in
ETMe3PPd(dmit)22
X-ray scattering
Spin gap 40 K J 250 K
M. Tamura, A. Nakao and R. Kato, J. Phys. Soc.
Japan 75, 093701 (2006) Y. Shimizu, H. Akimoto,
H. Tsujii, A. Tajima, and R. Kato, Phys. Rev.
Lett. 99, 256403 (2007)
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Magnetic Criticality
XPd(dmit)22
Et2Me2Sb (CO)
Me4P
Me4As
EtMe3P
TN (K)
EtMe3As
VBS order
Et2Me2P
Et2Me2As
Me4Sb
Spin gap
Neel order
EtMe3Sb
Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and
R. Kato, J. Phys. Condens. Matter 19, 145240
(2007)
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Theoretical global phase diagram
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773
(1991) T. Senthil, A. Vishwanath, L. Balents, S.
Sachdev and M.P.A. Fisher, Science 303, 1490
(2004). Cenke Xu and S. Sachdev, arXiv0811.1220
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Theoretical global phase diagram
CFTs
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773
(1991) T. Senthil, A. Vishwanath, L. Balents, S.
Sachdev and M.P.A. Fisher, Science 303, 1490
(2004). Cenke Xu and S. Sachdev, arXiv0811.1220
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Theoretical global phase diagram
CFTs
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773
(1991) T. Senthil, A. Vishwanath, L. Balents, S.
Sachdev and M.P.A. Fisher, Science 303, 1490
(2004). Cenke Xu and S. Sachdev, arXiv0811.1220
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Magnetic Criticality
XPd(dmit)22
Et2Me2Sb (CO)
Me4P
Me4As
EtMe3P
TN (K)
EtMe3As
VBS order
Et2Me2P
Et2Me2As
Me4Sb
Spin gap
Neel order
EtMe3Sb
Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and
R. Kato, J. Phys. Condens. Matter 19, 145240
(2007)
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Magnetic Criticality
XPd(dmit)22
Et2Me2Sb (CO)
Me4P
Me4As
Quantum criticality described by CFT
EtMe3P
TN (K)
EtMe3As
VBS order
Et2Me2P
Et2Me2As
Me4Sb
Spin gap
Neel order
EtMe3Sb
Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and
R. Kato, J. Phys. Condens. Matter 19, 145240
(2007)
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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
Dilute Boltzmann/Landau gas of particle and holes
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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
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
1
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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
1
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Three foci of modern physics
1
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 near
the superconductor-insulator transition
and in graphene 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 near
the superconductor-insulator transition
and in graphene 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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Cuprates
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Cuprates
STM observations of VBS modulations by Y.
Kohsaka et al., Nature 454, 1072 (2008)
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Cuprates
CFT?
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Cuprates
Thermoelectric measurements
CFT?
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Cuprates
Thermoelectric measurements
CFT?
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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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Nernst experiment
ey
Hm
H
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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).
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
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Applications
1. Magneto-thermo-electric transport near
the superconductor-insulator transition
and in graphene 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 near
the superconductor-insulator transition
and in graphene 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.