1.%20Coupled%20dimer%20antiferromagnets

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Outline
1. Coupled dimer antiferromagnets
Order parameters and Landau-Ginzburg
criticality 2. Graphene Topological
Fermi surface transitions 3. Quantum
criticality and black holes AdS4 theory of
compressible quantum liquids 4. Quantum
criticality in the cuprates Global phase
diagram and the spin density wave transition in
metals
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Outline
1. Coupled dimer antiferromagnets
Order parameters and Landau-Ginzburg
criticality 2. Graphene Topological
Fermi surface transitions 3. Quantum
criticality and black holes AdS4 theory of
compressible quantum liquids 4. Quantum
criticality in the cuprates Global phase
diagram and the spin density wave transition in
metals
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TlCuCl3
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TlCuCl3
An insulator whose spin susceptibility vanishes
exponentially as the temperature T tends to zero.
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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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Square lattice antiferromagnet
J
J/
Ground state is a quantum paramagnet with spins
locked in valence bond singlets
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Pressure in TlCuCl3
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Quantum critical point with non-local
entanglement in spin wavefunction
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TlCuCl3 at ambient pressure
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 at ambient pressure
Sharp spin 1 particle excitation above an energy
gap (spin gap)
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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Spin waves
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Spin waves
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CFT3
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Spin waves
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Spin waves
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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
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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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Classical dynamics of spin waves
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Classical Boltzmann equation for S1 particles
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CFT3 at Tgt0
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Outline
1. Coupled dimer antiferromagnets
Order parameters and Landau-Ginzburg
criticality 2. Graphene Topological
Fermi surface transitions 3. Quantum
criticality and black holes AdS4 theory of
compressible quantum liquids 4. Quantum
criticality in the cuprates Global phase
diagram and the spin density wave transition in
metals
42
Outline
1. Coupled dimer antiferromagnets
Order parameters and Landau-Ginzburg
criticality 2. Graphene Topological
Fermi surface transitions 3. Quantum
criticality and black holes AdS4 theory of
compressible quantum liquids 4. Quantum
criticality in the cuprates Global phase
diagram and the spin density wave transition in
metals
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Graphene
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Quantum phase transition in graphene tuned by a
bias voltage
Electron Fermi surface
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Quantum phase transition in graphene tuned by a
bias voltage
Electron Fermi surface
Hole Fermi surface
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Quantum phase transition in graphene tuned by a
bias voltage
There must be an intermediate quantum critical
point where the Fermi surfaces reduce to a Dirac
point
Electron Fermi surface
Hole Fermi surface
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Quantum critical graphene
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Quantum phase transition in graphene
Quantum critical
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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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Quantum critical transport in graphene
L. Fritz, J. Schmalian, M. Müller and S. Sachdev,
Physical Review B 78, 085416 (2008) M.
Müller, J. Schmalian, and L. Fritz, Physical
Review Letters 103, 025301 (2009)
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Outline
1. Coupled dimer antiferromagnets
Order parameters and Landau-Ginzburg
criticality 2. Graphene Topological
Fermi surface transitions 3. Quantum
criticality and black holes AdS4 theory of
compressible quantum liquids 4. Quantum
criticality in the cuprates Global phase
diagram and the spin density wave transition in
metals
55
Outline
1. Coupled dimer antiferromagnets
Order parameters and Landau-Ginzburg
criticality 2. Graphene Topological
Fermi surface transitions 3. Quantum
criticality and black holes AdS4 theory of
quantum compressible liquids 4. Quantum
criticality in the cuprates Global phase
diagram and the spin density wave transition in
metals
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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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Magnetohydrodynamics of quantum criticality
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
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Magnetohydrodynamics of quantum criticality
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
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Magnetohydrodynamics of quantum criticality
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
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Magnetohydrodynamics of quantum criticality
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S.
Sachdev, Phys. Rev. B 76 144502 (2007)
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Greens function of a fermion
Sung-Sik Lee, arXiv0809.3402 M. Cubrovic, J.
Zaanen, and K. Schalm, arXiv0904.1993
T. Faulkner, H. Liu, J. McGreevy, and D. Vegh,
arXiv0907.2694
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Greens function of a fermion
T. Faulkner, H. Liu, J. McGreevy, and D. Vegh,
arXiv0907.2694
Similar to non-Fermi liquid theories of Fermi
surfaces coupled to gauge fields, and at quantum
critical points
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Free energy from gravity theory
F. Denef, S. Hartnoll, and S. Sachdev,
arXiv0908.1788
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Outline
1. Coupled dimer antiferromagnets
Order parameters and Landau-Ginzburg
criticality 2. Graphene Topological
Fermi surface transitions 3. Quantum
criticality and black holes AdS4 theory of
compressible quantum liquids 4. Quantum
criticality in the cuprates Global phase
diagram and the spin density wave transition in
metals
81
Outline
1. Coupled dimer antiferromagnets
Order parameters and Landau-Ginzburg
criticality 2. Graphene Topological
Fermi surface transitions 3. Quantum
criticality and black holes AdS4 theory of
compressible quantum liquids 4. Quantum
criticality in the cuprates Global phase
diagram and the spin density wave transition in
metals
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The cuprate superconductors
Multiple quantum phase transitions involving at
least two order parameters (antiferromagnetism
and superconductivity) and a topological change
in the Fermi surface
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Crossovers in transport properties of hole-doped
cuprates
N. E. Hussey, J. Phys Condens. Matter 20,
123201 (2008)
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Only candidate quantum critical point observed at
low T
Strange metal
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Theory of quantum criticality in the cuprates
R. Daou et al., Nature Physics 5, 31 - 34 (2009)
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Spin density wave theory in hole-doped cuprates
Hole pockets
S. Sachdev, A. V. Chubukov, and A. Sokol, Phys.
Rev. B 51, 14874 (1995). A. V. Chubukov and D.
K. Morr, Physics Reports 288, 355 (1997).
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Theory of quantum criticality in the cuprates
R. Daou et al., Nature Physics 5, 31 - 34 (2009)
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Theory of quantum criticality in the cuprates
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E. M. Motoyama, G. Yu, I. M. Vishik, O. P. Vajk,
P. K. Mang, and M. Greven,Nature 445, 186 (2007).
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Conclusions
General theory of finite temperature dynamics
and transport near quantum critical points, with
applications to antiferromagnets, graphene, and
superconductors
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Conclusions
The AdS/CFT offers promise in providing a new
understanding of strongly interacting quantum
matter at non-zero density
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Conclusions
Identified quantum criticality in cuprate
superconductors with a critical point at optimal
doping associated with onset of spin density wave
order in a metal
Elusive optimal doping quantum critical point has
been hiding in plain sight. It is shifted to
lower doping by the onset of superconductivity