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Many Body
Physics:
An Unfinished Revolution.
Piers Coleman- Rutgers U.
Thanks to: P. W. Anderson, E. Abrahams, P. Chandra
and my Rutgers Colleagues.
Piers Coleman: Rutgers University
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Extraordinary
Sequence of Discoveries
40
60
50
70
80
90
2000
30
20
• Fractional Q. H. E.
• Cuprate S. C.
• Heavy Fermion Materials
• Quantum Critical Points
• 1D +2D Conductors
Viewed from a historical perspective:
What are : the key new questions?
the prospects for further new discovery?
Mathematics
Concepts
Experiment
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OVERVIEW:
• 1926- 1940. Early Quantum Physics.
Exclusion Principle
Sommerfeld Metal
1
nk
kF
1947-1975. Many Body Physics
in the Cold War.
•Life without Feynman diagrams. (50s)
Landau Fermi Liquid.
•Broken Symmetry and Superflow.
•Renormalization Group.
k
Fermi Liquid
1
Z=m/m*
nk
kF
k
• 1976- . Strong correlation Physics.
• New phases of matter:
Non Fermi Liquid.
Quantum Hall Effect.
Heavy Fermion metals.
High Tc superconductors.
2D Metal-Insulator transition.
Piers Coleman: Rutgers University
Luttinger Liquid
1
nk
kF
k
3
Quote
by
Pauli.
“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, on electrons in letter to Schrödinger,
Dec 1926.

T
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Superconductivity
Meissner Effect ‘33
London ‘37
Anti ferromagnetism
Experimental
Challenges of the 50s
Schoenberg ‘40
Sarachik ‘63
Local moments -resistance minimum
first observed in the 30s.
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•Quantum Plasma Bohm and Pines ‘51-53, Tomonaga ‘53
Many Body Physics in
w
the
Cold
War
S HS=H
Plasmon
P
-1
Plasmon
Electron
•Quantum Field Theory-
Rise of the Feynman diagram
Brueckner ’55,Goldstone ‘57,Edwards ‘57, Hubbard ‘57
•Imaginary time
e-
itH
Heisenberg
~ e -b H
t  i 
w  iw n
Matsubara ‘55
Abrikosov, Gorkov,
Dzyaloshinski ‘59
Boltzmann
•Quasiparticle Concept
Landau ‘56
electron
m
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quasiparticle
m*
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Broken Symmetry

Phase transition: symmetry reduction.
Landau ‘37
• Off diagonal Long-Range Order
Boguilubov ‘47,
Bardeen, Cooper, Schrieffer ‘57, Gorkov ‘58
x’
x
F ( x  x' )  N  2   ( x )  ( x' ) N
PAIR CONDENSATE
w
photon mass
wP  c / L
q
Anderson Higgs mechanism
Anderson ‘59, Higgs ‘64
• Generalized Rigidity
Anderson ‘62
jsupercurrent  
Symmetry
Superflow
State
Gauge
Spin Rotn
Translation
Matter/charge
Spin
Momentum
(shear)
Superfluid
Magnet
Solid
Time
translation
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? Energy
?
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Renormalization Group
Fisher, Kadanoff, Kogut, Khmelnitskii, Larkin, Ma,
Wegner,Widom, Yulu,
High energy, short distances
Wilson (75)
• New Language
•Universality
•Fixed Point (FP)
•Critical Dimension
FP
FP
Low energy, long distances
•Scaling
•Cross-over
•Kondo Model
“QCD of Condensed Matter Physics”
Kondo ‘65, Anderson, Yuval & Hamann ‘70,
Wilson ‘75, Nozieres ‘75
, Andrei ‘82, Weigmann ‘82

H I  J (0). S

J 0
J 
Fermi Liquid (Nozieres ‘75)
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More
is
Different:
“...at each new level of complexity,
entirely newEmergent
properties appear, and the
understanding of these behaviors
requiresPhenomenon.
research which I think is as
fundamental in its nature as any other.”
P. W. Anderson, “More is different”, 1972.
•New phases of matter:
-Non Fermi Liquid.
3D
-Heavy Fermion metals.
-High Tc superconductors.
-Quantum Hall Effect.
-2D Metal-Insulator transition.
-Conducting Polymers
-Quantum Dots
0D
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High Tc
Heavy Fermions
New groundstates of
matter.
FQHE.
OTT et al ‘83
Gossard, Stormer, Tsui ‘81
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2D Metal Insulator
Transition
Kravechenko et al ‘97
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Fractional Quantum Hall Effect:
Most strongly interacting system.
Laughlin ‘82
2
2
  | z j | / 2l0
2
l

1
  ( z  z )
e
L i j i
j
Tsui, Stormer,Gossard.
•Fractional Charge
•Fractional Statistics
•Edge States
•Chern-Simons Theory
•Composite Fermions
PROFUSION OF
NEW PHASES :
AWAKENS US TO
VAST POSSIBILITIES
FOR NEW GROUND
STATES.
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1/2 FILLED
FERMI SURFACE
OF COMPOSITE
QUASIPARTICLES
2kF
•HALPERIN, LEE, READ
•JAIN
PARTICLE-HOLE
SYMMETRY?
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High Tc

Extraordinary stimulus to new ideas:
1D and 2D physicsfrustrated magnetism
new ideas for normal state
NON FERMI LIQUID ?
T
2D ``Luttinger’’ Liquid?
(Anderson ‘92)
Marginal Fermi Liquid?
(Varma,Abrahams,Ruckenstein and Schmitt-Rink ‘88)
D-wave pairing
SC
x
Ding et al, ‘?, Z. X. Shen et al, ‘?
Quantum critical fluctuations ?
•Stripes?
•SO(5)?
Magnetism
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(Kivelson and Emery, many others…..)
(S.C.Zhang ‘97)
Superconductivity.
•Pair fluctuations?
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Two
relaxation
times?
 T
H  T
tr
2
•Hot and Cold Spots.
Hot region.
Cold spot ?
tr  cons
H  T 2
Cooper et al., ‘94
Hlublina and Rice ‘95
Stokjovic and Pines ‘96
Ioffe and Millis, ‘98
C.f. Kaons
•Two Lifetimes
Anderson and Ong, ‘92
(spin-charge decoupling)
Coleman , Schofield, Tsvelik ‘96
e

 eLONG  e
 H ~ T 2,
SHORT
tr ~ T
eLONG  ( e  h ) / 2
eSHORT  ( e  h ) / 2
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Quantum Critical Points



Controlled axis to new fixed
point
Genesis of local moment vs
Fermi surface+ hot lines.
Scaling.
Or ?
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Genesis of Local Moments?
CeCu6 x Au x
Schroeder et al ‘99
(Schroeder et al ‘99)
χ 1 (q, E )  c [ f (q)  ( iE T ) ]
  0.75
Spatially local E/T scaling
Genesis of Local moments?
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Further Horizons.
 Areas
of Extraordinary
Challenge
–
–
–
–
2D Metal Insulator Transition
FQHE.
1D Conductors.
0D Quantum Dots -Non equilibrium physics
 Unsolved
Problems :
– 1/D expansion.
Local Physics
Band Theoretic Detail
– Further Links with Particle Physics : e.g
Supersymmetry Magnetism.
– Links between 1D and 2D


Non Fermi Liquids that live in 1 and 2 D?
Dirt + Interactions in 2D metals.
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Quantum Dots


First Simple
Laboratory for looking
at non-equilibrium
quantum mechanics.
Possible analogy with
convective cells and
Josephson effect.
Avishai et al ‘99
Coherent Radiation ?
V
w
?
eV/ TK
Meir, Wingreen, Lee
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“…We used to think that if we knew one,
we knew two, because one and one are
two. We are finding that we must learn a
great deal more about ‘and’. ”
Sir Arthur Eddington.
Timescale
Outlook.
• New experiments & materials
• New concepts
• New formalism
Piers Coleman: Rutgers University
More Young
People !
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