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Qu-Transitions
P. Coleman(CMT, Rutgers)
IIT KanpurFeb 7, 2010.
Friday, February 12, 2010
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Qu-Transitions“Phase transitions in the quantum era”
P. Coleman(CMT, Rutgers)
IIT KanpurFeb 7, 2010.
Friday, February 12, 2010
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• Qu-era: revolutions always have a second part.• Classical vs quantum criticality.• Peierls’ question.• Heavy electron Quantum Criticality• New Ideas: breakup of the electron.• Qu-frustration.
http://physics.rutgers.edu/talks/kanpurcolloq09.pdf
Friday, February 12, 2010
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• Qu-era: revolutions always have a second part.• Classical vs quantum criticality.• Peierls’ question.• Heavy electron Quantum Criticality• New Ideas: breakup of the electron.• Qu-frustration.
• Qu-era: revolutions always have a second part.
Friday, February 12, 2010
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1758 in Paris: 72 years after “Principia”
Friday, February 12, 2010
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1758 in Paris: 72 years after “Principia”Classical revolution is still in full sway.
Friday, February 12, 2010
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1758 in Paris: 72 years after “Principia”
Return of Halley’s comet.
Publishers in Paris decide to bring out the 1st French Translation of Newton’s Principia, which they have held in proof form for ten years.
Classical revolution is still in full sway.
Friday, February 12, 2010
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1758 in Paris: 72 years after “Principia”
Return of Halley’s comet.
Publishers in Paris decide to bring out the 1st French Translation of Newton’s Principia, which they have held in proof form for ten years.
Classical revolution is still in full sway.
Friday, February 12, 2010
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1758 in Paris: 72 years after “Principia”
Marquise Emilie du Châtelet(1707-1749)
Mathematical Physicist:Translator and interpreter of Principia.
Classical revolution is still in full sway.
"ce beau probleme astronomico-geometrique"
Friday, February 12, 2010
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1758 in Paris: 72 years after “Principia”
Marquise Emilie du Châtelet(1707-1749)
Mathematical Physicist:Translator and interpreter of Principia.
du Chatelet reviews the conflicting world views of Leibniz and Newton.
Classical revolution is still in full sway.
"ce beau probleme astronomico-geometrique"
Friday, February 12, 2010
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1758 in Paris: 72 years after “Principia”
Marquise Emilie du Châtelet(1707-1749)
Mathematical Physicist:Translator and interpreter of Principia.
du Chatelet reviews the conflicting world views of Leibniz and Newton.
�
i
mi(vi)2�
i
mi�vi
Newtons Momentum Leibniz’ “vis vivre”
Classical revolution is still in full sway.
"ce beau probleme astronomico-geometrique"
Friday, February 12, 2010
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1758 in Paris: 72 years after “Principia”
Marquise Emilie du Châtelet(1707-1749)
Mathematical Physicist:Translator and interpreter of Principia.
du Chatelet reviews the conflicting world views of Leibniz and Newton.
�
i
mi(vi)2�
i
mi�vi
Newtons Momentum Leibniz’ “vis vivre”
Resolution of the controversy (and the missingfactor of a half) required a further 60-80 years.
Classical revolution is still in full sway.
"ce beau probleme astronomico-geometrique"
Friday, February 12, 2010
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108 years after Planck, many surprises later, the quantum era is in full sway.
Friday, February 12, 2010
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“With a heavy heart, I have been converted to the idea that Fermi -Dirac, not Einstein-Bose is the correct statistics. I wish to write a short note on its application to paramagnetism.”
W. Pauli, in letter to Schrödinger, Dec 1926.
!
T
108 years after Planck, many surprises later, the quantum era is in full sway.
Friday, February 12, 2010
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108 years after Planck, many surprises later, the quantum era is in full sway.
Friday, February 12, 2010
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108 years after Planck, many surprises later, the quantum era is in full sway.
Qubit
Friday, February 12, 2010
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108 years after Planck, many surprises later, the quantum era is in full sway.
Qubit
Qu-information
Friday, February 12, 2010
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David Pines in musicofthequantum.rutgers.edu
108 years after Planck, many surprises later, the quantum era is in full sway.
Friday, February 12, 2010
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Quantum zero point fluctuations:
Friday, February 12, 2010
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Quantum zero point fluctuations: major unsolved problem of the quantum era.
Friday, February 12, 2010
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Quantum zero point fluctuations:
•73% of the mass of the cosmos is “Dark Energy”: an unidentified form of zero point energy, causing the expansion to accelerate.
major unsolved problem of the quantum era.
Friday, February 12, 2010
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Quantum zero point fluctuations:
•Zero point fluctuationsprofoundly transformmatter, endowing it with markedtendency to develop new forms oforder.
major unsolved problem of the quantum era.
Friday, February 12, 2010
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• Qu-era: revolutions always have a second part.• Classical vs quantum criticality.• Peierls’ question.• Heavy electron Quantum Criticality• New Ideas: breakup of the electron.• Qu-frustration.
• Classical vs quantum criticality.
Friday, February 12, 2010
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Classical Criticality
Custers et al (2002)
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Classical Criticality
Custers et al (2002)
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Classical Criticality
Custers et al (2002)
Classical Critical Point
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Custers et al (2002)
Classical Critical Point
Oxygen. (Voronel et al 1963).
Classical Criticality
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“New insights into physics often come from revisiting areas once thought to be closed.” Michael Fisher.
Custers et al (2002)
Classical Critical Point
Oxygen. (Voronel et al 1963).
Michael Fisher
Classical Criticality
Friday, February 12, 2010
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“New insights into physics often come from revisiting areas once thought to be closed.” Michael Fisher.
Custers et al (2002)
Classical Critical Point
Oxygen. (Voronel et al 1963).
Michael Fisher
Classical Criticality
Anatoly LarkinBen WidomLeo Kadanoff Ken Wilson
Friday, February 12, 2010
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“New insights into physics often come from revisiting areas once thought to be closed.” Michael Fisher.
Custers et al (2002)
Classical Critical Point
Oxygen. (Voronel et al 1963).
Michael Fisher
Classical Criticality
Anatoly LarkinBen WidomLeo Kadanoff Ken Wilson
“20th Century Revolution”
Friday, February 12, 2010
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“New insights into physics often come from revisiting areas once thought to be closed.” Michael Fisher.
Custers et al (2002)
Michael Fisher
Critical matter
Anatoly LarkinBen WidomLeo Kadanoff Ken Wilson
Classical Criticality
“20th Century Revolution”
Classical Critical Point
Friday, February 12, 2010
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“New insights into physics often come from revisiting areas once thought to be closed.” Michael Fisher.
Custers et al (2002)
Michael Fisher
Critical matter
Anatoly LarkinBen WidomLeo Kadanoff Ken Wilson
Classical Criticality
- universal
“20th Century Revolution”
Classical Critical Point
Friday, February 12, 2010
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Quantum Phase-Transition
Custers et al (2002)
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Quantum Phase-Transition
Custers et al (2002)
Phase transition driven by zero point motion.
Friday, February 12, 2010
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Quantum Phase-Transition
Custers et al (2002)
[H,ψ] �= 0
.
ψ =��
Seven − Sodd
�
.
Phase transition driven by zero point motion.
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Quantum Phase-Transition
Custers et al (2002)
[H,ψ] �= 0
Quantum Fluctuations
.
ψ =��
Seven − Sodd
�
.
Phase transition driven by zero point motion.
Friday, February 12, 2010
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Quantum Phase-Transition
Custers et al (2002)
[H,ψ] �= 0
Quantum Fluctuations
.
ψ =��
Seven − Sodd
�
.
Phase transition driven by zero point motion.
What happens when the timeand length scale of zero point quantum fluctuations diverges?
Friday, February 12, 2010
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Quantum Phase-Transition
Custers et al (2002)
[H,ψ] �= 0
Quantum Fluctuations
QCP
.
ψ =��
Seven − Sodd
�
.
Phase transition driven by zero point motion.
What happens when the timeand length scale of zero point quantum fluctuations diverges?
Friday, February 12, 2010
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Quantum Phase-Transition
Custers et al (2002)
[H,ψ] �= 0
Quantum Fluctuations
QCP
.
ψ =��
Seven − Sodd
�
.
Phase transition driven by zero point motion.
Quantum Critical matter
What happens when the timeand length scale of zero point quantum fluctuations diverges?
Friday, February 12, 2010
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• Qu-era: revolutions always have a second part.• Classical vs quantum criticality.• Peierls’ question.• Heavy electron Quantum Criticality• New Ideas: breakup of the electron.• Qu-frustration.
• Peierls’ question.
Friday, February 12, 2010
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Landau: interactions can be turned on adiabatically, preserving the excitation spectrum.
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Landau: interactions can be turned on adiabatically, preserving the excitation spectrum.
- Interactionsadiabatically
-
“Quasiparticle”
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Landau: interactions can be turned on adiabatically, preserving the excitation spectrum.
- Interactionsadiabatically
-
“Quasiparticle”
quasi-particle
quasi-hole
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Landau, JETP 3, 920 (1957)
Landau: interactions can be turned on adiabatically, preserving the excitation spectrum.
- Interactionsadiabatically
-
“Quasiparticle”
quasi-particle
quasi-hole
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Landau, JETP 3, 920 (1957)
He-3 (1950/60s)(Fairbanks, many others) Landau: interactions can be turned on
adiabatically, preserving the excitation spectrum.
- Interactionsadiabatically
-
“Quasiparticle”
quasi-particle
quasi-hole
Friday, February 12, 2010
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Landau’s Question.
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Landau’s Question.
Landau
DysonLarkin
Abrikosov
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Landau’s Question.
Landau
DysonLarkin
Abrikosov
Peierls
Friday, February 12, 2010
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Landau’s Question.
Landau
DysonLarkin
Abrikosov
PeierlsBut what happens when the interaction becomes too large?
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0Fermi Liquid
X~U/t
But what happens when the interaction becomes too large?
Friday, February 12, 2010
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0Fermi Liquid
“Electrons order”
Landau 1936
X~U/t
Xc
Long range order
But what happens when the interaction becomes too large?
Friday, February 12, 2010
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0Fermi Liquid
“Electrons order”
Landau 1936
X~U/t
Xc
Long range order
But what happens when the interaction becomes too large?
“Electrons localize”
Peierls/Mott 1939
Friday, February 12, 2010
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0Fermi Liquid
“Electrons order”
Landau 1936
“Moments form”
Anderson 1961
X~U/t
Xc
Long range order
But what happens when the interaction becomes too large?
“Electrons localize”
Peierls/Mott 1939
Friday, February 12, 2010
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0Fermi Liquid
“Electrons order”
Landau 1936
“Moments form”
Anderson 1961
X~U/t
Xc
Strange MetalT
“QCP”
Hertz, 1976
Long range order
But what happens when the interaction becomes too large?
“Electrons localize”
Peierls/Mott 1939
Friday, February 12, 2010
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Cuprates Tc=11-92K
T(K)0 200 400 600 800 1000
0.0
0.2
0.4
0.6
0.8
1.0
Takagi et al, PRL ‘92
“Avoided Criticality”
Friday, February 12, 2010
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Cuprates Tc=11-92K
T(K)0 200 400 600 800 1000
0.0
0.2
0.4
0.6
0.8
1.0
Takagi et al, PRL ‘92
x
Marginal Fermi liquid
Quantum critical point
Pseudogapmetal
Fermi liquid
T T*
AFM
“Avoided Criticality”
Friday, February 12, 2010
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Cuprates Tc=11-92K
T(K)0 200 400 600 800 1000
0.0
0.2
0.4
0.6
0.8
1.0
Takagi et al, PRL ‘92
x
Marginal Fermi liquid
Quantum critical point
Pseudogapmetal
Fermi liquid
T T*
AFM
“Avoided Criticality”
Data: Tuson ParkFigure rendition: Mathias Graf
Tuson Park, (2007).
Friday, February 12, 2010
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• Qu-era: revolutions always have a second part.• Classical vs quantum criticality.• Peierls’ question.• Heavy electron Quantum Criticality• New Ideas: breakup of the electron.• Qu-frustration.
• Heavy electron Quantum Criticality
Friday, February 12, 2010
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Kondo effect
Friday, February 12, 2010
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Kondo effect (a digression)
Friday, February 12, 2010
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Kondo effect (a digression)
“Kondo”
Kondo KHR-2 HV, the robot that plays soccer, fights with other bots and dances salsa
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Kondo effect
T
(a digression)
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Kondo effect
T
“A 75 year odyssey”
(a digression)
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Kondo effect
Kondo (1962)
T
“A 75 year odyssey”
“Kondo Temperature”
(a digression)
Fe
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Kondo effect
Kondo (1962)
Spins asymptotically free
T
“A 75 year odyssey”
“Kondo Temperature”
(a digression)
Fe
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Kondo effect (a digression)
Kondo (1962)+ .....
Spins asymptotically free
+
“Kondo Temperature”
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-
Kondo effect (a digression)
Kondo (1962)+ .....
Spins asymptotically free
+
“Kondo Temperature”
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-
Kondo effect (a digression)
Kondo (1962)+ .....
Spins asymptotically free
“Nozieres Local Fermi liquid” (Nozieres 76)
+
“Kondo Temperature”Spins absorbed into singlet ground-state
Friday, February 12, 2010
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-
Kondo effect (a digression)
Kondo (1962)+ .....
Spins asymptotically free
“Nozieres Local Fermi liquid” (Nozieres 76)
+
“Kondo Temperature”
χ ∼ 1/T
χ TK
T
1TK
TK
Spins absorbed into singlet ground-state
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Kondo Lattice Model(Kasuya, 1951)
DONIACH’SHypothesis.Doniach (1977)
Friday, February 12, 2010
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Kondo Lattice Model(Kasuya, 1951)
DONIACH’SHypothesis.Doniach (1977)
Friday, February 12, 2010
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Kondo Lattice Model(Kasuya, 1951)
DONIACH’SHypothesis.Doniach (1977)
Friday, February 12, 2010
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Kondo Lattice Model(Kasuya, 1951)
DONIACH’SHypothesis.Doniach (1977)
Friday, February 12, 2010
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Kondo Lattice Model(Kasuya, 1951)
DONIACH’SHypothesis.Doniach (1977)
>
TK = D exp[−1/2Jρ]
QC
The main result ... is that there should be a second-order transition at zero temperature, as the exchange coupling is varied, between an antiferromagnetic ground state for weak J and a Kondo-like state in which the local moments are quenched.Friday, February 12, 2010
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Kondo Lattice Model(Kasuya, 1951)
DONIACH’SHypothesis.Doniach (1977)
>
TK = D exp[−1/2Jρ]
QC
The main result ... is that there should be a second-order transition at zero temperature, as the exchange coupling is varied, between an antiferromagnetic ground state for weak J and a Kondo-like state in which the local moments are quenched.Friday, February 12, 2010
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Kondo Lattice Model(Kasuya, 1951)
DONIACH’SHypothesis.Doniach (1977)
>
TK = D exp[−1/2Jρ]
QC
Large Fermi surface of composite Fermions
+
+
++
+
++
+
++
+
+++ +
Friday, February 12, 2010
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Kondo Lattice Model(Kasuya, 1951)
DONIACH’SHypothesis.Doniach (1977)
>
TK = D exp[−1/2Jρ]
QC
Large Fermi surface of composite Fermions
+
+
++
+
++
+
++
+
+++ +
?
Friday, February 12, 2010
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0Fermi Liquid
X~U/t
Xc
T
“QCP”Long range order
Friday, February 12, 2010
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0Fermi Liquid
X~U/t
Xc
T
“QCP”Long range order
“Moments form”
Friday, February 12, 2010
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0Fermi Liquid
X~U/t
Xc
T
“QCP”Long range order
J ~ 1/U
“Moments form”
Friday, February 12, 2010
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0Fermi Liquid
X~U/t
Xc
T
“QCP”Long range order
J ~ 1/U
“Moments form”
J ~ 1/U
Friday, February 12, 2010
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TK = D exp[−1/2Jρ]
0Fermi Liquid
X~U/t
Xc
T
“QCP”Long range order
J ~ 1/U
QCP
“Moments form”
J ~ 1/U
Friday, February 12, 2010
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TK=Dexp[−1/2Jρ]
0Fermi Liquid
X~U/t
Xc
T
“QCP”Long range order
J ~ 1/U
QCP
“Moments form”
J ~ 1/U
Friday, February 12, 2010
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Heavy Fermion Metals Review: cond-mat/0612006
UBe13
Friday, February 12, 2010
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Heavy Fermion Metals Review: cond-mat/0612006
UBe13
Friday, February 12, 2010
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Heavy Fermion Metals Review: cond-mat/0612006
UBe13
Coherent Heavy Fermi Liquid
Friday, February 12, 2010
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• Qu-era: revolutions always have a second part.• Classical vs quantum criticality.• Peierls’ question.• Heavy electron Quantum Criticality• New Ideas: breakup of the electron.• Qu-frustration.
• Heavy electron Quantum Criticality:
Experiments
Friday, February 12, 2010
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Pc P
AFMmetal
Heavy FermionMaterials
H. Von Lohneyson (1996)
Quantum Criticality: divergent specific heat capacity
Quantum CriticalPoint
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Pc P
AFMmetal
Heavy FermionMaterials
H. Von Lohneyson (1996)
Quantum Criticality: divergent specific heat capacity
Quantum CriticalPoint
Friday, February 12, 2010
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Pc P
AFMmetal
Heavy FermionMaterials
H. Von Lohneyson (1996)
Quantum Criticality: divergent specific heat capacity
Quantum CriticalPoint
Friday, February 12, 2010
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Gegenwart et al (2002)T-Linear T-Linear
T2 T2
T2
Divergence ofInteraction and Effective Mass
Friday, February 12, 2010
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Gegenwart et al (2002)T-Linear T-Linear
T2 T2
T2
Divergence ofInteraction and Effective Mass
Friday, February 12, 2010
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“How do fermions get heavy and die?” PC, Pepin, Si and Ramazashvili, J. Cond Matt. ,13}, R723 (2001).
anticipated an abrupt change in FS when a composite heavy electron undergoes a Kondo “breakdown”.
Friday, February 12, 2010
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S. Paschen et al, Nature 432, 881 (2004)
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S. Paschen et al, Nature 432, 881 (2004)
Jump in the Hall constant at a field tuned QCP.
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Data: Tuson ParkFigure rendition: Mathias Graf
Reconstruction of the Fermi Surfaceand mass divergence
Tuson Park, (2007).CeRhIn5
Friday, February 12, 2010
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Data: Tuson ParkFigure rendition: Mathias Graf
Reconstruction of the Fermi Surfaceand mass divergence
Tuson Park, (2007).CeRhIn5
Friday, February 12, 2010
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Data: Tuson ParkFigure rendition: Mathias Graf
Shishido et al (2006)
Reconstruction of the Fermi Surfaceand mass divergence
Tuson Park, (2007).CeRhIn5
Friday, February 12, 2010
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Data: Tuson ParkFigure rendition: Mathias Graf
Shishido et al (2006)
Reconstruction of the Fermi Surfaceand mass divergence
Tuson Park, (2007).CeRhIn5
Friday, February 12, 2010
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Data: Tuson ParkFigure rendition: Mathias Graf
Shishido et al (2006)
Reconstruction of the Fermi Surfaceand mass divergence
Tuson Park, (2007).CeRhIn5
Friday, February 12, 2010
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Data: Tuson ParkFigure rendition: Mathias Graf
Shishido et al (2006)
Reconstruction of the Fermi Surfaceand mass divergence
Tuson Park, (2007).CeRhIn5
Friday, February 12, 2010
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Data: Tuson ParkFigure rendition: Mathias Graf
Shishido et al (2006)
Reconstruction of the Fermi Surfaceand mass divergence
Tuson Park, (2007).CeRhIn5
Friday, February 12, 2010
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• Qu-era: revolutions always have a second part.• Classical vs quantum criticality.• Peierls’ question.• Heavy electron Quantum Criticality• New Ideas: breakup of the electron.• Qu-frustration.
• Heavy electron Quantum Criticality:
“Black hole in the phase diagram”
Friday, February 12, 2010
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“Black Hole in the Phase Diagram”.
Zachary Fisk
Friday, February 12, 2010
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Pc P
AFMmetal
“Black Hole in the Phase Diagram”.
Zachary Fisk
Friday, February 12, 2010
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Pc P
AFMmetal
“Black Hole in the Phase Diagram”.
Zachary Fisk
Friday, February 12, 2010
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Pc P
AFMmetal
P.C and A. Schofield, Nature (2005)
“Black Hole in the Phase Diagram”.
Zachary Fisk
Friday, February 12, 2010
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Pc P
AFMmetal
P.C and A. Schofield, Nature (2005)
“Black Hole in the Phase Diagram”.
\ “PHASE
HORIZON”
Zachary Fisk
Friday, February 12, 2010
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Pc P
AFMmetal
P.C and A. Schofield, Nature (2005)
N
“Black Hole in the Phase Diagram”.
\ “PHASE
HORIZON”
Zachary Fisk
Friday, February 12, 2010
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Pc P
AFMmetal
P.C and A. Schofield, Nature (2005)
“Black Hole in the Phase Diagram”.
D
\ “PHASE
HORIZON”
Zachary Fisk
Friday, February 12, 2010
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Pc P
AFMmetal
P.C and A. Schofield, Nature (2005)
A
“Black Hole in the Phase Diagram”.
\ “PHASE
HORIZON”
Zachary Fisk
Friday, February 12, 2010
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Pc P
AFMmetal
John Hertz: Critical droplet is Quantum if
P.C and A. Schofield, Nature (2005)
A
“Black Hole in the Phase Diagram”.
\ “PHASE
HORIZON”
Zachary Fisk
Friday, February 12, 2010
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Feynman Hertz
Friday, February 12, 2010
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Feynman Hertz
Quantum Criticality: Casimir effect in time
QCP
Temperature NOT a tuning Parameter,
but a finite size effect in time.
(Hertz, PRB, 14, 1165 (1973).
Finite size
ωn = 2πkBT × n, ξτ =�
kBT
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Feynman Hertz
Quantum Criticality: Casimir effect in time
QCP
Temperature NOT a tuning Parameter,
but a finite size effect in time.
(Hertz, PRB, 14, 1165 (1973).
Finite size
ωn = 2πkBT × n, ξτ =�
kBT
Temperature: Boundary condition in time.Sachdev (1999), Continentino (2001), Palova (2009).
Friday, February 12, 2010
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Pc P
AFMmetal
Feynman Hertz
Quantum Criticality: Casimir effect in time
QCP
Temperature NOT a tuning Parameter,
but a finite size effect in time.
(Hertz, PRB, 14, 1165 (1973).
Finite size
ωn = 2πkBT × n, ξτ =�
kBT
Temperature: Boundary condition in time.Sachdev (1999), Continentino (2001), Palova (2009).
Friday, February 12, 2010
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Pc P
AFMmetal
Feynman Hertz
Quantum CriticalBubble
Temperature: Boundary condition in time.Sachdev (1999), Continentino (2001), Palova (2009).
Friday, February 12, 2010
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Quantum CriticalBubble
Pc P
AFMmetal
Feynman Hertz
Quantum CriticalBubble
Temperature: Boundary condition in time.Sachdev (1999), Continentino (2001), Palova (2009).
Friday, February 12, 2010
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Quantum CriticalBubble
Pc P
AFMmetal
(Q) Quantum critical region:interior of correlation bubble.
Feynman Hertz
(Q)
Quantum CriticalBubble
Temperature: Boundary condition in time.Sachdev (1999), Continentino (2001), Palova (2009).
Friday, February 12, 2010
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Quantum CriticalBubble
Pc P
AFMmetal
(P) Paramagnet: probesexterior of correlation bubble
(Q) Quantum critical region:interior of correlation bubble.
Feynman Hertz
(Q)
Quantum CriticalBubble
(P)
Temperature: Boundary condition in time.Sachdev (1999), Continentino (2001), Palova (2009).
Friday, February 12, 2010
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Quantum CriticalBubble
Pc P
AFMmetal
(P) Paramagnet: probesexterior of correlation bubble
(Q) Quantum critical region:interior of correlation bubble.
Feynman Hertz
(Q)
Quantum CriticalBubble
(P)
Temperature: Boundary condition in time.Sachdev (1999), Continentino (2001), Palova (2009).
Friday, February 12, 2010
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Quantum CriticalBubble
Pc P
AFMmetal
(P) Paramagnet: probesexterior of correlation bubble
(Q) Quantum critical region:interior of correlation bubble.
Feynman Hertz
(Q)
Quantum CriticalBubble
(P)
Temperature: Boundary condition in time.Sachdev (1999), Continentino (2001), Palova (2009).
Friday, February 12, 2010
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E/T Scaling:
Meigan Aronson
M. C. Aronson et al, PRL 75, 725 (1995).
Friday, February 12, 2010
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E/T Scaling:
Meigan Aronson
M. C. Aronson et al, PRL 75, 725 (1995).
Friday, February 12, 2010
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E/T Scaling:
Meigan Aronson
M. C. Aronson et al, PRL 75, 725 (1995).
CeCu6-xAux (x=0.1)Schroeder et al, Nature407,351 (2000).
Almut Schroeder
Friday, February 12, 2010
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E/T Scaling:
Physics Below the upperCritical Dimension.
Meigan Aronson
M. C. Aronson et al, PRL 75, 725 (1995).
CeCu6-xAux (x=0.1)Schroeder et al, Nature407,351 (2000).
Almut Schroeder
Friday, February 12, 2010
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• Qu-era: revolutions always have a second part.• Classical vs quantum criticality.• Peierls’ question.• Heavy electron Quantum Criticality• New Ideas: breakup of the electron.• Qu-frustration.
• Heavy electron Quantum Criticality:
Failure of the Standard model
Friday, February 12, 2010
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Standard Model: Quantum SDW?
•Moriya, Doniach, Schrieffer (60s)•Hertz (76)•Millis (93)
F.S. instability
Fermi
Surface
HertzDoniach Schrieffer Millis Moriya
Friday, February 12, 2010
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Standard Model: Quantum SDW?
•Moriya, Doniach, Schrieffer (60s)•Hertz (76)•Millis (93)
F.S. instability
Fermi
Surfacevertex non- singular
HertzDoniach Schrieffer Millis Moriya
Friday, February 12, 2010
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Standard Model: Quantum SDW?
•Moriya, Doniach, Schrieffer (60s)•Hertz (76)•Millis (93)
F.S. instability
Fermi
Surfacevertex non- singular
HertzDoniach Schrieffer Millis Moriya
Friday, February 12, 2010
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Standard Model: Quantum SDW?
•Moriya, Doniach, Schrieffer (60s)•Hertz (76)•Millis (93)
Time counts as z =2 scaling dimensions
F.S. instability
Fermi
Surfacevertex non- singular
HertzDoniach Schrieffer Millis Moriya
Friday, February 12, 2010
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Standard Model: Quantum SDW?
•Moriya, Doniach, Schrieffer (60s)•Hertz (76)•Millis (93)
If d + z = d + 2 > 4 :"4 terms “irrelevent”Critical modes are Gaussian.T is not the only energy scale.
Time counts as z =2 scaling dimensions
F.S. instability
Fermi
Surfacevertex non- singular
HertzDoniach Schrieffer Millis Moriya
Friday, February 12, 2010
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Singular potential is rapidly modulated:only affects electrons along hot-lines.
Predicts:
Landau’s Fermi Liquid ShouldSurvive at a Quantum Critical Point.
Friday, February 12, 2010
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Singular potential is rapidly modulated:only affects electrons along hot-lines.
Q
Predicts:
Landau’s Fermi Liquid ShouldSurvive at a Quantum Critical Point.
Friday, February 12, 2010
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Singular potential is rapidly modulated:only affects electrons along hot-lines.
Q
k-qk
q
Predicts:
Landau’s Fermi Liquid ShouldSurvive at a Quantum Critical Point.
Friday, February 12, 2010
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Singular potential is rapidly modulated:only affects electrons along hot-lines.
Q
k-qk
q
divergent
Predicts:
Landau’s Fermi Liquid ShouldSurvive at a Quantum Critical Point.
Friday, February 12, 2010
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Singular potential is rapidly modulated:only affects electrons along hot-lines.
Q
finite
k-qk
q
divergent
Predicts:
Landau’s Fermi Liquid ShouldSurvive at a Quantum Critical Point.
Friday, February 12, 2010
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Singular potential is rapidly modulated:only affects electrons along hot-lines.
Q
finite
k-qk
q
divergent
Predicts:
Landau’s Fermi Liquid ShouldSurvive at a Quantum Critical Point.
Friday, February 12, 2010
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• Qu-era: revolutions always have a second part.• Classical vs quantum criticality.• Peierls’ question.• Heavy electron Quantum Criticality• New Ideas: breakup of the electron.• Qu-frustration.• New Ideas: breakup of the electron.
Friday, February 12, 2010
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New Ideas
Friday, February 12, 2010
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• Local quantum criticality (Si, Ingersent, Smith, Rabello, Nature 2001): Spin is the critical mode,Fluctuations critical in time.
Requires a two dimensional spin fluid
New Ideast
HSi, Ingersent
Friday, February 12, 2010
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• Local quantum criticality (Si, Ingersent, Smith, Rabello, Nature 2001): Spin is the critical mode,Fluctuations critical in time.
Requires a two dimensional spin fluid
New Ideas
Schroeder et al, Nature 407,351(2000).
Locality of critical fluctuations
T.0.75(K0.75)
t
HSi, Ingersent
Friday, February 12, 2010
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t
HNew Ideas Si, Ingersent
• Local quantum criticality (Si, Ingersent, Smith, Rabello, Nature 2001): Spin is the critical mode,Fluctuations critical in time.
Requires a two dimensional spin fluid
Friday, February 12, 2010
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• Deconfined Criticality: Two diverging length-scales. (Hermele et al 2004; Senthil et al, Science 2004).
t
H
Critical Matter
Free spinons
Magnetic order
New Ideas
Senthil Sachdev Vishwanath
Si, Ingersent
• Local quantum criticality (Si, Ingersent, Smith, Rabello, Nature 2001): Spin is the critical mode,Fluctuations critical in time.
Requires a two dimensional spin fluid
Friday, February 12, 2010
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• Deconfined Criticality: Two diverging length-scales. (Hermele et al 2004; Senthil et al, Science 2004).
t
HNew Ideas
Senthil Sachdev Vishwanath
Si, Ingersent
• Local quantum criticality (Si, Ingersent, Smith, Rabello, Nature 2001): Spin is the critical mode,Fluctuations critical in time.
Requires a two dimensional spin fluid
Friday, February 12, 2010
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Friday, February 12, 2010
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P. Gegenwart, T. Westerkamp et al., Science 315, 5814 (2007)
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New Ideas
•Large N Approaches. •(PC et al JCM, 2001, Rech et al 2005, •Lebanon et al 2006, Pepin 2006, 2008, •Paul Pepin, Norman 2008).
Pepin
Friday, February 12, 2010
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ψ(x, τ)
S[ψ]
τ, x
Wild quantum fluctuations!
New Ideas
•Large N Approaches. •(PC et al JCM, 2001, Rech et al 2005, •Lebanon et al 2006, Pepin 2006, 2008, •Paul Pepin, Norman 2008).
Pepin
Friday, February 12, 2010
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Large N limit
ψ(x, τ)
S[ψ]
τ, x
Wild quantum fluctuations!
New Ideas
•Large N Approaches. •(PC et al JCM, 2001, Rech et al 2005, •Lebanon et al 2006, Pepin 2006, 2008, •Paul Pepin, Norman 2008).
Pepin
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Large N limit
ψ(x, τ)
S[ψ]
τ, x
Wild quantum fluctuations!
New Ideas
•Large N Approaches. •(PC et al JCM, 2001, Rech et al 2005, •Lebanon et al 2006, Pepin 2006, 2008, •Paul Pepin, Norman 2008).
Pepin
Friday, February 12, 2010
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Large N limit
ψ(x, τ)
S[ψ]
τ, x
1N∼ �eff
New Ideas
•Large N Approaches. •(PC et al JCM, 2001, Rech et al 2005, •Lebanon et al 2006, Pepin 2006, 2008, •Paul Pepin, Norman 2008).
Pepin
Friday, February 12, 2010
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ψ(x, τ)
S[ψ]
τ, x
1N∼ �eff
Large N limit
New Ideas
•Large N Approaches. •(PC et al JCM, 2001, Rech et al 2005, •Lebanon et al 2006, Pepin 2006, 2008, •Paul Pepin, Norman 2008).
Pepin
Friday, February 12, 2010
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ψ(x, τ)
S[ψ]
τ, x
1N∼ �eff
classi
cal p
ath
Large N limit
New Ideas
•Large N Approaches. •(PC et al JCM, 2001, Rech et al 2005, •Lebanon et al 2006, Pepin 2006, 2008, •Paul Pepin, Norman 2008).
Pepin
Electron
Spinon
Holon
Electron
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ψ(x, τ)
S[ψ]
τ, x
1N∼ �eff
classi
cal p
ath
Large N limit
New Ideas
•Large N Approaches. •(PC et al JCM, 2001, Rech et al 2005, •Lebanon et al 2006, Pepin 2006, 2008, •Paul Pepin, Norman 2008).
Pepin
Electron
Spinon
Holon
Electron
ZaanenM Cubrovic, J Zaanen, K Schalm - Science, 2009
Liu McGreevy
Friday, February 12, 2010
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• Qu-era: revolutions always have a second part.• Classical vs quantum criticality.• Peierls’ question.• Heavy electron Quantum Criticality• New Ideas: breakup of the electron.• Qu-frustration.• Qu-frustration.
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Qu- frustration• Frustration and Kondo have different effects.
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Qu- frustration• Frustration and Kondo have different effects.
AFM
K ~ TK/JH
Large FS Heavy Fermi Liquid
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Qu- frustration• Frustration and Kondo have different effects.
AFM
Q
Spin Liquid
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Qu- frustration• Frustration and Kondo have different effects.
AFM
Q
Spin Liquid
Large FS Heavy Fermi Liquid
K ~ TK/JH
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Qu- frustration• Frustration and Kondo have different effects.
AFM
Q
Spin Liquid
Large FS Heavy Fermi Liquid
K ~ TK/JH
metal
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f~1/S
“Doniach” TK/JH
AFM
SLM
Large FS Heavy Fermi Liquid
S. Nakatsuji et al, Nature Physics (2008).
!-YbAlB4
Experimental Support
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f~1/S
“Doniach” TK/JH
AFM
SLM
Large FS Heavy Fermi Liquid
S. Nakatsuji et al, Nature Physics (2008).
!-YbAlB4
Experimental Support
Friday, February 12, 2010
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f~1/S
“Doniach” TK/JH
AFM
SLM
Large FS Heavy Fermi Liquid
S. Nakatsuji et al, Nature Physics (2008).
!-YbAlB4
Experimental Support
Non-Fermi liquid at B=0.Small field restores Fermi liquid behavior.
Friday, February 12, 2010
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f~1/S
“Doniach” TK/JH
AFM
SLM
Large FS Heavy Fermi Liquid
S. Nakatsuji et al, Nature Physics (2008).
!-YbAlB4
Experimental Support
Non-Fermi liquid at B=0.Small field restores Fermi liquid behavior.
Critical Phase?
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f~1/S
“Doniach” TK/JH
AFM
SLM
Large FS Heavy Fermi Liquid
?
S. Nakatsuji et al, Nature Physics (2008).
!-YbAlB4
Experimental Support
Non-Fermi liquid at B=0.Small field restores Fermi liquid behavior.
Critical Phase?
See:A. Nevidomskyy & PC PRL (2009).T. Senthil, S.Sachdev, M.Vojta,PRL 90,216403; PRB 69, 035111 (2004);P. W.Anderson, arXiv:0810.0279 (2008)
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Q
K ~ TK/JH
AFM
SLM
Large FS Heavy Fermi Liquid
Experimental Support II
Canfield et al (unpublished)
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Q
K ~ TK/JH
AFM
SLM
Large FS Heavy Fermi Liquid
Experimental Support II
Canfield et al (unpublished)
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Q
K ~ TK/JH
AFM
SLM
Large FS Heavy Fermi Liquid
Experimental Support II
Canfield et al (unpublished)
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Conclusions.
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• Heavy electron quantum criticality appears to involve a partial Mott localization involving a soft composite charge degree of freedom.
Conclusions.
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• Heavy electron quantum criticality appears to involve a partial Mott localization involving a soft composite charge degree of freedom.
• Fermi surface expansion and the loss of AFM need not coincide.
• Heavy electron quantum criticality appears to involve a partial Mott localization involving a soft composite charge degree of freedom.
Conclusions.
Friday, February 12, 2010
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• Heavy electron quantum criticality appears to involve a partial Mott localization involving a soft composite charge degree of freedom.
• Fermi surface expansion and the loss of AFM need not coincide.
• Introduction of the “frustration” axis permits a unified treatment of spin liquid and Kondo effects.
• Heavy electron quantum criticality appears to involve a partial Mott localization involving a soft composite charge degree of freedom.
• Fermi surface expansion and the loss of AFM need not coincide.
Conclusions.
Friday, February 12, 2010
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• Heavy electron quantum criticality appears to involve a partial Mott localization involving a soft composite charge degree of freedom.
• Fermi surface expansion and the loss of AFM need not coincide.
• Introduction of the “frustration” axis permits a unified treatment of spin liquid and Kondo effects.
• Heavy electron quantum criticality appears to involve a partial Mott localization involving a soft composite charge degree of freedom.
• Fermi surface expansion and the loss of AFM need not coincide.
Spin Liquid
AFM
“Frustration”1/S
Large FS Heavy Fermi Liquid
“Doniach” TK/JH
metalConclusions.
Friday, February 12, 2010
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• Heavy electron quantum criticality appears to involve a partial Mott localization involving a soft composite charge degree of freedom.
• Fermi surface expansion and the loss of AFM need not coincide.
• Introduction of the “frustration” axis permits a unified treatment of spin liquid and Kondo effects.
• Spin liquid Kondo states may have been observed in three Yb heavy electron systems. More experiments needed.
• Heavy electron quantum criticality appears to involve a partial Mott localization involving a soft composite charge degree of freedom.
• Fermi surface expansion and the loss of AFM need not coincide.
• Introduction of the “frustration” axis permits a unified treatment of spin liquid and Kondo effects.
Spin Liquid
AFM
“Frustration”1/S
Large FS Heavy Fermi Liquid
“Doniach” TK/JH
metalConclusions.
Friday, February 12, 2010
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• Heavy electron quantum criticality appears to involve a partial Mott localization involving a soft composite charge degree of freedom.
• Fermi surface expansion and the loss of AFM need not coincide.
• Introduction of the “frustration” axis permits a unified treatment of spin liquid and Kondo effects.
• Spin liquid Kondo states may have been observed in three Yb heavy electron systems. More experiments needed.
• Heavy electron quantum criticality appears to involve a partial Mott localization involving a soft composite charge degree of freedom.
• Fermi surface expansion and the loss of AFM need not coincide.
• Introduction of the “frustration” axis permits a unified treatment of spin liquid and Kondo effects.
• Spin liquid Kondo states may have been observed in three Yb heavy electron systems. More experiments needed.
Spin Liquid
AFM
“Frustration”1/S
Large FS Heavy Fermi Liquid
“Doniach” TK/JH
metalConclusions.
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51
Collaborators
Rebecca Flint RutgersAndriy Nevidomskyy RutgersMaxim Dzero U. MarylandJerome Rech, CNRS, MarseilleEran Lebanon, Israel.Indranil Paul, CNRS, GrenobleLucia Palova RutgersPremi Chandra RutgersGergely Zarand BudapestOlivier Parcollet SpHT Paris.Andy Schofield BirminghamQimiao Si Rice, HoustonCatherine Pepin SpHT Paris.Almut Schroeder Kent StateGabriel Aeppli LCNHilbert v. Lohneysen Karlsruhe
37
Flint Nev. Dzero Rech Lebanon
Friday, February 12, 2010