Antoine%20Georges

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Mean field theories of quantum spin glasses
Antoine Georges Olivier Parcollet Nick Read Subir
Sachdev Jinwu Ye
Talk online Sachdev
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Classical Sherrington-Kirkpatrick model
Jij a Gaussian random variable with zero mean
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Two routes to quantization
A. Quantum rotor model
n1 Ising model is a transverse field g
g
Spectrum at Jij0
n3 randomly coupled spin dimers
g
Spectrum at Jij0
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Two routes to quantization
B. Heisenberg spins
Spectrum at Jij0
(2S1)-fold degeneracy
Generalize model to SU(N) spins and explore phase
diagram in N, S plane
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Outline

1. Insulating quantum rotors.
2. Insulating Heisenberg spins
3. DMFT of a random t-J model
4. Metallic spin glasses DMFT of a random Kondo
   lattice

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A. Insulating quantum rotors
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A. Quantum rotor model
Jij a Gaussian random variable with zero mean
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Local dynamic spin susceptibility
T0 phases
Spin glass
Paramagnet
Specific heat C T (?)
g
D.A. Huse and J. Miller, Phys. Rev. Lett. 70,
3147 (1993). J. Ye, S. Sachdev, and N. Read,
Phys. Rev. Lett. 70, 4011 (1993). N. Read, S.
Sachdev, and J. Ye, Phys. Rev. B 52, 384
(1995). A. Georges, O. Parcollet, and S. Sachdev,
Phys. Rev. B 63, 134406 (2001).
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T gt 0 phase diagram
gc
g
J. Ye, S. Sachdev, and N. Read, Phys. Rev. Lett.
70, 4011 (1993). N. Read, S. Sachdev, and J. Ye,
Phys. Rev. B 52, 384 (1995).
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B. Insulating Heisenberg spins
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B. Heisenberg spin glass
Jij a Gaussian random variable with zero mean
S. Sachdev and J. Ye, Phys. Rev. Lett. 70, 3339
(1993).
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T0 phase diagram
S
Spin glass order
Specific heat C T (C T2 ?)
N
S. Sachdev and J. Ye, Phys. Rev. Lett. 70, 3339
(1993). A. Georges, O. Parcollet, and S. Sachdev,
Phys. Rev. Lett. 85, 840 (2000). A. Camjayi and
M. J. Rozenberg, Phys. Rev. Lett. 90, 217202
(2003).
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Quantum critical phase is described by
fractionalized S1/2 neutral spinon excitations
Spinon spectral density
w
S. Sachdev and J. Ye, Phys. Rev. Lett. 70, 3339
(1993).
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T gt 0 phase diagram
S. Sachdev and J. Ye, Phys. Rev. Lett. 70, 3339
(1993). A. Georges, O. Parcollet, and S. Sachdev,
Phys. Rev. Lett. 85, 840 (2000). A. Camjayi and
M. J. Rozenberg, Phys. Rev. Lett. 90, 217202
(2003).
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C. Doping the quantum critical spin liquid
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C. DMFT of a random t-J model
Jij a Gaussian random variable with zero mean
O. Parcollet and A. Georges, Phys. Rev. B 59,
5341 (1999).
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carrier density
O. Parcollet and A. Georges, Phys. Rev. B 59,
5341 (1999).
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Physical consequences of quantum criticality
1. Electron spectral function (photoemission)
Momentum resolved spectral density
O. Parcollet and A. Georges, Phys. Rev. B 59,
5341 (1999).
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Physical consequences of quantum criticality
2. d.c Resistivity
O. Parcollet and A. Georges, Phys. Rev. B 59,
5341 (1999).
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Physical consequences of quantum criticality
3. NMR 1/T1 relaxation rate
O. Parcollet and A. Georges, Phys. Rev. B 59,
5341 (1999).
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Physical consequences of quantum criticality
4. Optical conductivity
O. Parcollet and A. Georges, Phys. Rev. B 59,
5341 (1999).
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Phenomenological phase diagram for cuprates
O. Parcollet and A. Georges, Phys. Rev. B 59,
5341 (1999).
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D. Metallic spin glasses
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C. DMFT of a random Kondo lattice model
Jij a Gaussian random variable with zero mean
S. Sachdev, N. Read, and R. Oppermann, Phys. Rev.
B 52, 10286 (1995). A. M. Sengupta and A.
Georges, Phys. Rev. B 52, 10295 (1995).  
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JK
S. Sachdev, N. Read, and R. Oppermann, Phys. Rev.
B 52, 10286 (1995). A. M. Sengupta and A.
Georges, Phys. Rev. B 52, 10295 (1995).  
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Outlook

• Spin glass order is an attractive candidate for
  a quantum critical point in the cuprates, on both
  theoretical and experimental grounds. (Impurities
  break the translational symmetry associated with
  charge-ordered states, and the Imry-Ma argument
  then prohibits a quantum critical point
  associated with charge order in the presence of
  randomness in two dimensions)
• A simple mean-field theory of a doped Heisenberg
  spin glass naturally reproduces all the
  marginal phenomenology.
• Needed better theory of fluctuations in low
  dimensions