Asymptotic slavery and transport anomalies in the cuprates

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Asymptotic slavery and transport anomalies in the
cuprates

• Thanks to
• Claudio Chamon, Boston Univ.
• Ting-Pong Choy, UIUC
• D. Galanakis, UIUC
• T. Stanescu, UIUC (Rutgers)

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2 electrons on 2 sites ?
2 electrons on 2 sites ( ) ?
E
n e r g y
DEU
QUIZWhat is the Ground state? (lowest energy
state)
3
Possibilities
,
a.)
gt
,
gt
gt
low energy

,
,
b.)
-
, gt

,
gt
c.)
(high energy)
0, gt
d.)
, 0gt

e.) bd
high low energy
f.) cd
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Answer

,
gt - , gt
Mottness
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Cuprate phase diagram
SG
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asymptotic
slavery
Scaling (single length scale)
Renormalization
Mottness
Effective Theory
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Anomalous Normal State Puzzles

• 1.)

Fermi liquid
2.) Pseudogap
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Batlogg, et. al., 1990
Straight line
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How Wide is theT-linear Region?
Not very
Raffy, et. al., 2001
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Ando, et. al. 2004
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(No Transcript)
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Why T-linear Resistivity?
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Leading explanation
Quantum criticality
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Quantum criticality

• Zero-temperature (quantum fluctuations)

Temporal Correlations Diverge
Spatial correlations diverge
dynamical exponent
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Quantum critical
T
order
disorder
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Quantum Critical modes
Carry the current
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Phase diagram of High-T_c materials
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Is this correct?
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General Result

• One critical length scale
• Charges are critical
• Charges are neither created nor annihilated
  (charge conservation)

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Vector potential
current
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scaling
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conductivity
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Charge conservation
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General result
T-linear resistivity
(d3 for cuprates)
Impossible?
Claudio Chamon
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Drude Conductivity
new energy scale
Not of scaling form Except for z-1
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Van der Marel, et. al. Nature 2004
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Scaling hypothesis
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One-parameter Scaling breaks down
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Big picture

• Quantum criticality is irrelevant?
• Fermions are not critical?
• But ARPES, optical conductivity
  

Singular boson scattering Is an irrelvant
perturbation for fermions
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Valla et. al., Science, v. 285, p. 2110
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New direction
(UV-IR mixing)
all energy scales are mixed
Asymptotic slavery
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Mott Problem (NiO)
Insulator ???????
Hotel Model (N rooms N guests)
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Mott insulator
U
N
N
PES
IPES
UV-IR Mixing
gt2x
N-1
N-1
2
PES
IPES
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Perturbation Theory
m0
0
m1
Heff
0
m2
Not Fock Space
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What fails when the high energy scale is removed?

Spectral function
Single occupancy
double

UV-IR mixing
LHB
UHB
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Sum rule
Pauli Priniciple
(in general)
Projected Models
(t-J model)
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When is this failure important?
Half-filling
Particle-hole symmetry
Projected Models work!
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What about away from half-filling?
No symmetry
Projected Models
Breakdown of Pauli Principle
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Why?
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Exclusion Statistics(Haldane)
?d?-?? g???N?
Particle number
Available states
metric
Free fermions
)
(
1 0 0 1
g
? d"0
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What about t-J model (projected models?
No double occupancy
)
(
1 1 1 1
g
? d"-1
exclusons
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Mind the Pseudogap
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pseudogap
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(No Transcript)
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Ting-Pong Choy and P2
Hubbard Model
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pseudogap
Low to High energy Spectral weight
transfer
1.)UV-IR mixing 2.) orthogonality catastrophe QP
weight0 3.) Insulating state at T0
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Ando, et. al.
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(No Transcript)
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Pseudogap (intrinsic effect)
Hole doping
magnetic polaron
Orthogonality catastrophe
No overlap with antiferromagnetic regions
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T-J model
Rosch, Wolfle, 2004
Metallic Not insulator
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summary

• Projected models Hubbard model

No Pauli principle
Pauli Principle
Z/ J/t
No QP. Z0
(Kane, Lee, Read, Prokofiev, 2001, Sorella)
Sorella, us, others
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U! 1
L! 1
Do not commute
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Predictions

• Insulator in clean limit
• The dynamical exponent is negative
• Local magnetism in pseudogap state (x)
• Cuprates are asymptotically slaved

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(No Transcript)
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2nd Puzzle
Breakdown of perturbation theory
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insulator
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Non-perturbative physics xgt0