ads/cft and condensed matter talk online: sachdev.physics.harvard.edu talk online:...
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AdS/CFT and AdS/CFT and condensed matter condensed matter
Talk online: sachdev.physics.harvard.edu
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Particle theorists
Sean Hartnoll, KITPChristopher Herzog,
PrincetonPavel Kovtun, VictoriaDam Son, Washington
Sean Hartnoll, KITPChristopher Herzog,
PrincetonPavel Kovtun, VictoriaDam Son, Washington
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Markus MuellerGeneva
Markus MuellerGeneva
Condensed matter theorists
Cenke XuHarvard
Cenke XuHarvard
Yang QiHarvardYang QiHarvard
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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)
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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
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Three foci of modern physics
Quantum phase transitions
Black holes
Hydrodynamics
Canonical problem in condensed matter: transport
properties of a correlated electron system
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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
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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
Hydrodynamics
Many QPTs of correlated electrons in 2+1 dimensions are described by conformal
field theories (CFTs)
![Page 15: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/15.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 16: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/16.jpg)
Ground state has long-range Néel order
Square lattice antiferromagnet
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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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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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S. Wenzel and W. Janke, arXiv:0808.1418M. Troyer, M. Imada, and K. Ueda, J. Phys. Soc. Japan (1997)
Quantum Monte Carlo - critical exponents
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Quantum Monte Carlo - critical exponents
Field-theoretic RG of CFT3
E. Vicari et al.
S. Wenzel and W. Janke, arXiv:0808.1418M. Troyer, M. Imada, and K. Ueda, J. Phys. Soc. Japan (1997)
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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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Half-filled band Mott insulator with spin S = 1/2
Triangular lattice of [Pd(dmit)2]2
frustrated quantum spin system
X[Pd(dmit)X[Pd(dmit)22]]22 Pd SC
X Pd(dmit)Pd(dmit)22
t’tt
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
Neel ground state for small J’/J
Broken spin rotation symmetry
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Anisotropic triangular lattice antiferromagnet
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Magnetic CriticalityMagnetic CriticalityT
N (
K)
Neel orderNeel order
Me4P
Me4As
EtMe3As
Et2Me2As Me4Sb
Et2Me2P
EtMe3Sb
Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, J. Phys.: Condens. Matter 19, 145240 (2007)
X[Pd(dmit)2]2Et2Me2Sb (CO)
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Anisotropic triangular lattice antiferromagnet
Possible ground state for intermediate J’/J
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Anisotropic triangular lattice antiferromagnet
Possible ground state for intermediate J’/J
Valence bond solid (VBS)
Broken lattice space group symmetry
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Anisotropic triangular lattice antiferromagnet
Possible ground state for intermediate J’/J
Valence bond solid (VBS)
Broken lattice space group symmetry
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Anisotropic triangular lattice antiferromagnet
Possible ground state for intermediate J’/J
Valence bond solid (VBS)
Broken lattice space group symmetry
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Anisotropic triangular lattice antiferromagnet
Possible ground state for intermediate J’/J
Valence bond solid (VBS)
Broken lattice space group symmetry
![Page 37: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/37.jpg)
Anisotropic triangular lattice antiferromagnet
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Magnetic CriticalityMagnetic CriticalityT
N (
K)
Neel orderNeel order
Me4P
Me4As
EtMe3As
Et2Me2As Me4Sb
Et2Me2P
EtMe3Sb
Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, J. Phys.: Condens. Matter 19, 145240 (2007)
X[Pd(dmit)2]2Et2Me2Sb (CO)
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Magnetic CriticalityMagnetic CriticalityT
N (
K)
Neel orderNeel order
Me4P
Me4As
EtMe3As
Et2Me2As Me4Sb
Et2Me2P
EtMe3Sb
EtMe3P
Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, J. Phys.: Condens. Matter 19, 145240 (2007)
X[Pd(dmit)2]2Et2Me2Sb (CO)
Spingap
Spingap
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Magnetic CriticalityMagnetic CriticalityT
N (
K)
Neel orderNeel order
Me4P
Me4As
EtMe3As
Et2Me2As Me4Sb
Et2Me2P
EtMe3Sb
EtMe3P
Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, J. Phys.: Condens. Matter 19, 145240 (2007)
X[Pd(dmit)2]2Et2Me2Sb (CO)
VBS order
Spingap
Spingap
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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)
Observation of a valence bond solid (VBS) in ETMe3P[Pd(dmit)2]2
Spin gap ~ 40 K J ~ 250 K
X-ray scattering
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Magnetic CriticalityMagnetic CriticalityT
N (
K)
Neel orderNeel order
Me4P
Me4As
EtMe3As
Et2Me2As Me4Sb
Et2Me2P
EtMe3Sb
EtMe3P
Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, J. Phys.: Condens. Matter 19, 145240 (2007)
X[Pd(dmit)2]2Et2Me2Sb (CO)
VBS order
Spingap
Spingap
![Page 43: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/43.jpg)
Anisotropic triangular lattice antiferromagnet
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Anisotropic triangular lattice antiferromagnet
Classical ground state for large J’/JFound in Cs2CuCl4
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Anisotropic triangular lattice antiferromagnet
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Anisotropic triangular lattice antiferromagnet
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Spin liquid obtained in a generalized spin model with S=1/2 per unit cell =
P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974).
Triangular lattice antiferromagnet
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P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974).
Spin liquid obtained in a generalized spin model with S=1/2 per unit cell =
Triangular lattice antiferromagnet
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P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974).
Spin liquid obtained in a generalized spin model with S=1/2 per unit cell =
Triangular lattice antiferromagnet
![Page 50: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/50.jpg)
P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974).
Spin liquid obtained in a generalized spin model with S=1/2 per unit cell =
Triangular lattice antiferromagnet
![Page 51: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/51.jpg)
P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974).
Spin liquid obtained in a generalized spin model with S=1/2 per unit cell =
Triangular lattice antiferromagnet
![Page 52: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/52.jpg)
P. Fazekas and P. W. Anderson, Philos. Mag. 30, 23 (1974).
Spin liquid obtained in a generalized spin model with S=1/2 per unit cell =
Triangular lattice antiferromagnet
![Page 53: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/53.jpg)
Excitations of the Z2 Spin liquid
=A spinon
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Excitations of the Z2 Spin liquid
=A spinon
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Excitations of the Z2 Spin liquid
=A spinon
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Excitations of the Z2 Spin liquid
=A spinon
![Page 57: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/57.jpg)
Excitations of the Z2 Spin liquid
A spinon
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Excitations of the Z2 Spin liquid
A spinon
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Excitations of the Z2 Spin liquid
A vison
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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=
-1-1
Excitations of the Z2 Spin liquid
A vison
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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=
-1-1
Excitations of the Z2 Spin liquid
A vison
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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=
-1-1
Excitations of the Z2 Spin liquid
A vison
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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=
-1-1
Excitations of the Z2 Spin liquid
A vison
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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=
-1-1
-1-1
Excitations of the Z2 Spin liquid
A vison
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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=
-1-1
-1-1
Excitations of the Z2 Spin liquid
A vison
N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991)
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A Simple Toy Model (A. Kitaev, 1997)
Spins Sα living on the links of a square lattice:
Hence, Fp's and Ai's form a set of conserved quantities.
![Page 67: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/67.jpg)
A Simple Toy Model (A. Kitaev, 1997)
Spins Sα living on the links of a square lattice:
Hence, Fp's and Ai's form a set of conserved quantities.
![Page 68: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/68.jpg)
A Simple Toy Model (A. Kitaev, 1997)
Spins Sα living on the links of a square lattice:
Hence, Fp's and Ai's form a set of conserved quantities.
![Page 69: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/69.jpg)
A Simple Toy Model (A. Kitaev, 1997)
Spins Sα living on the links of a square lattice:
Hence, Fp's and Ai's form a set of conserved quantities.
![Page 70: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/70.jpg)
A Simple Toy Model (A. Kitaev, 1997)
Spins Sα living on the links of a square lattice:
Hence, Fp's and Ai's form a set of conserved quantities.
![Page 71: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/71.jpg)
A Simple Toy Model (A. Kitaev, 1997)
Spins Sα living on the links of a square lattice:
Hence, Fp's and Ai's form a set of conserved quantities.
![Page 72: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/72.jpg)
A Simple Toy Model (A. Kitaev, 1997)
Spins Sα living on the links of a square lattice:
Hence, Fp's and Ai's form a set of conserved quantities.
![Page 73: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/73.jpg)
A Simple Toy Model (A. Kitaev, 1997)
Spins Sα living on the links of a square lattice:
Hence, Fp's and Ai's form a set of conserved quantities.
![Page 74: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/74.jpg)
A Simple Toy Model (A. Kitaev, 1997)
Spins Sα living on the links of a square lattice:
Hence, Fp's and Ai's form a set of conserved quantities.
![Page 75: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/75.jpg)
A Simple Toy Model (A. Kitaev, 1997)
Spins Sα living on the links of a square lattice:
Hence, Fp's and Ai's form a set of conserved quantities.
![Page 76: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/76.jpg)
A Simple Toy Model (A. Kitaev, 1997)
Spins Sα living on the links of a square lattice:
Hence, Fp's and Ai's form a set of conserved quantities.
![Page 77: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/77.jpg)
Properties of the Ground State
Ground state: all Ai=1, Fp=1 Pictorial representation: color each link with an up-spin. Ai=1 : closed loops. Fp=1 : every plaquette is an equal-amplitude superposition of
inverse images.
The GS wavefunction takes the same value on configurationsconnected by these operations. It does not depend on the geometry of the configurations, only on their topology.
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Properties of Excitations
“Electric” particle, or Ai = –1 – endpoint of a line “Magnetic particle”, or vortex: Fp= –1 – a “flip” of this plaquette
changes the sign of a given term in the superposition. Charges and vortices interact via topological Aharonov-Bohm
interactions.
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Properties of Excitations
“Electric” particle, or Ai = –1 – endpoint of a line (a “spinon”) “Magnetic particle”, or vortex: Fp= –1 – a “flip” of this plaquette
changes the sign of a given term in the superposition. Charges and vortices interact via topological Aharonov-Bohm
interactions.
![Page 80: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/80.jpg)
Properties of Excitations
“Electric” particle, or Ai = –1 – endpoint of a line (a “spinon”) “Magnetic particle”, or vortex: Fp= –1 – a “flip” of this plaquette
changes the sign of a given term in the superposition (a “vison”).
Charges and vortices interact via topological Aharonov-Bohm interactions.
![Page 81: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/81.jpg)
Properties of Excitations
“Electric” particle, or Ai = –1 – endpoint of a line (a “spinon”) “Magnetic particle”, or vortex: Fp= –1 – a “flip” of this plaquette
changes the sign of a given term in the superposition (a “vison”).
Charges and vortices interact via topological Aharonov-Bohm interactions.
Spinons and visons are mutual semions
![Page 82: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/82.jpg)
Mutual Chern-Simons Theory
Cenke Xu and S. Sachdev, arXiv:0811.1220
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Cenke Xu and S. Sachdev, arXiv:0811.1220
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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, arXiv:0811.1220
Theoretical global phase diagram
![Page 85: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/85.jpg)
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, arXiv:0811.1220
Theoretical global phase diagram
CFTsCFTs
![Page 86: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/86.jpg)
Magnetic CriticalityMagnetic CriticalityT
N (
K)
Neel orderNeel order
Me4P
Me4As
EtMe3As
Et2Me2As Me4Sb
Et2Me2P
EtMe3Sb
EtMe3P
Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, J. Phys.: Condens. Matter 19, 145240 (2007)
X[Pd(dmit)2]2Et2Me2Sb (CO)
Spingap
Spingap
VBS order
![Page 87: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/87.jpg)
Magnetic CriticalityMagnetic CriticalityT
N (
K)
Neel orderNeel order
Me4P
Me4As
EtMe3As
Et2Me2As Me4Sb
Et2Me2P
EtMe3Sb
EtMe3P
Y. Shimizu, H. Akimoto, H. Tsujii, A. Tajima, and R. Kato, J. Phys.: Condens. Matter 19, 145240 (2007)
X[Pd(dmit)2]2Et2Me2Sb (CO)
VBS order
Spingap
Spingap
Quantumcriticalitydescribed
by CFT
Quantumcriticalitydescribed
by CFT
![Page 88: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/88.jpg)
From quantum antiferromagnets to string theory
![Page 89: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/89.jpg)
Three foci of modern physics
Quantum phase transitions
Black holes
Hydrodynamics
![Page 90: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/90.jpg)
Black holes
Three foci of modern physics
Quantum phase transitions
Hydrodynamics
Canonical problem in condensed matter: transport
properties of a correlated electron system
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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 92: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/92.jpg)
M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
Superfluid-insulator transition
![Page 93: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/93.jpg)
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CFT3
![Page 95: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/95.jpg)
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Classical vortices and wave oscillations of the condensate
Dilute Boltzmann/Landau gas of particle and holes
![Page 97: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/97.jpg)
CFT at T>0
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D. B. Haviland, Y. Liu, and A. M. Goldman, Phys. Rev. Lett. 62, 2180 (1989)
Resistivity of Bi films
M. P. A. Fisher, Phys. Rev. Lett. 65, 923 (1990)
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Density correlations in CFTs at T >0
![Page 100: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/100.jpg)
Density correlations in CFTs at T >0
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).
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Density correlations in CFTs at T >0
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).
![Page 102: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/102.jpg)
Quantum critical transport
S. Sachdev, Quantum Phase Transitions, Cambridge (1999).
![Page 103: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/103.jpg)
Quantum critical transport
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).
![Page 104: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/104.jpg)
Quantum critical transport
P. Kovtun, D. T. Son, and A. Starinets, Phys. Rev. Lett. 94, 11601 (2005)
, 8714 (1997).
![Page 105: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/105.jpg)
Three foci of modern physics
Quantum phase transitions
Black holes
Hydrodynamics
![Page 106: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/106.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
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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
![Page 108: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/108.jpg)
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).
![Page 109: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/109.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
1
![Page 110: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/110.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
1
2
![Page 111: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/111.jpg)
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).
![Page 112: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/112.jpg)
P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son, Phys. Rev. D 75, 085020 (2007)
Collisionless to hydrodynamic crossover of SYM3
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P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son, Phys. Rev. D 75, 085020 (2007)
Collisionless to hydrodynamic crossover of SYM3
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The cuprate superconductors
![Page 115: AdS/CFT and condensed matter Talk online: sachdev.physics.harvard.edu Talk online: sachdev.physics.harvard.edu](https://reader037.vdocument.in/reader037/viewer/2022103123/56649d235503460f949f9a77/html5/thumbnails/115.jpg)
The cuprate superconductors
Proximity to an insulator at 12.5%hole concentration
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Thermoelectric measurements
CFT3?
CFT3?
Cuprates
STM image of Y. Kohsaka et al., Science 315, 1380 (2007).
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For experimental applications, we must move away from the ideal CFT
e.g.
• A chemical potential μ
A magnetic field BCFT
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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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Conservation laws/equations of motion
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007)
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Constitutive 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)
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Single 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)
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For experimental applications, we must move away from the ideal CFT
e.g.
• A chemical potential μ
A magnetic field BCFT
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For experimental applications, we must move away from the ideal CFT
e.g.
CFT
• A chemical potential μ
A magnetic field B
• An impurity scattering rate 1/τimp (its T dependence follows from scaling arguments)
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For experimental applications, we must move away from the ideal CFT
e.g.
• A chemical potential μ
A magnetic field B
• An impurity scattering rate 1/τimp (its T dependence follows from scaling arguments)
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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S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007)
Solve initial value problem and relateresults to response functions (Kadanoff+Martin)
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From 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)
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From 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)
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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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From 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)
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From 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)
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From 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)
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Nernst experiment
H
ey
Hm
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From 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)
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To the solvable supersymmetric, Yang-Mills theory CFT, we add
• A chemical potential μA magnetic field B
After the AdS/CFT mapping, we obtain the Einstein-Maxwell theory of a black hole with
• An electric charge
A magnetic charge
The exact results are found to be in precise accord with all hydrodynamic results presented earlier
S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, Phys. Rev. B 76 144502 (2007)
Exact Results
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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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• Doubled U(1) Chern-Simons theory is useful for building a global phase diagram of two-dimensional quantum antiferromagnets. The same theory with a U(N) gauge group and extended supersymmetry describes M theory on AdS4
• 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.
• Doubled U(1) Chern-Simons theory is useful for building a global phase diagram of two-dimensional quantum antiferromagnets. The same theory with a U(N) gauge group and extended supersymmetry describes M theory on AdS4
• 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.
ConclusionsConclusions
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• Doubled U(1) Chern-Simons theory is useful for building a global phase diagram of two-dimensional quantum antiferromagnets. The same theory with a U(N) gauge group and extended supersymmetry describes M theory on AdS4
• 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.
• Doubled U(1) Chern-Simons theory is useful for building a global phase diagram of two-dimensional quantum antiferromagnets. The same theory with a U(N) gauge group and extended supersymmetry describes M theory on AdS4
• 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.
ConclusionsConclusions
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• Doubled U(1) Chern-Simons theory is useful for building a global phase diagram of two-dimensional quantum antiferromagnets. The same theory with a U(N) gauge group and extended supersymmetry describes M theory on AdS4
• 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.
• Doubled U(1) Chern-Simons theory is useful for building a global phase diagram of two-dimensional quantum antiferromagnets. The same theory with a U(N) gauge group and extended supersymmetry describes M theory on AdS4
• 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.
ConclusionsConclusions