Many Body Physics:

1. Many Body Physics: An Unfinished Revolution. Piers Coleman- Rutgers U. Thanks to: P. W. Anderson, E. Abrahams, P. Chandra and my Rutgers Colleagues.

2. Mathematics Concepts Experiment ExtraordinarySequence of Discoveries 20 30 • Fractional Q. H. E. • Cuprate S. C. • Heavy Fermion Materials • Quantum Critical Points • 1D +2D Conductors 40 50 60 70 80 90 2000 Viewed from a historical perspective: What are : the key new questions? the prospects for further new discovery?

3. OVERVIEW: • 1926- 1940. Early Quantum Physics. • 1947-1975. Many Body Physics • in the Cold War. • Life without Feynman diagrams. (50s) • Landau Fermi Liquid. • Broken Symmetry and Superflow. • Renormalization Group. • 1976- . Strong correlation Physics. • New phases of matter: • Non Fermi Liquid. • Quantum Hall Effect. • Heavy Fermion metals. • High Tc superconductors. 2D Metal-Insulator transition. Sommerfeld Metal 1 Exclusion Principle nk kF k Fermi Liquid 1 Z=m/m* nk kF k Luttinger Liquid 1 nk k kF

4. 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

5. Superconductivity Meissner Effect ‘33 London ‘37 Experimental Challenges of the 50s Anti ferromagnetism Schoenberg ‘40 Sarachik ‘63 Localmoments -resistance minimum first observed in the 30s.

6. Plasmon wP S-1HS=H Plasmon Electron • Quantum Plasma Bohm and Pines ‘51-53, Tomonaga ‘53 Many Body Physics in the Cold War • Quantum Field Theory- Rise of the Feynman diagram • Brueckner ’55,Goldstone ‘57,Edwards ‘57, Hubbard ‘57 • Imaginary time Matsubara ‘55 Abrikosov, Gorkov, Dzyaloshinski ‘59 e- i tH ~ e-bH Heisenberg Boltzmann • Quasiparticle Concept Landau ‘56 electron quasiparticle m m*

7. Phase transition: symmetry reduction. Landau ‘37 • Generalized Rigidity Anderson ‘62 Symmetry Superflow State Gauge Matter/charge Superfluid Spin Rotn Spin Magnet Translation Momentum Solid (shear) Time translation ? ? Energy Broken Symmetry • Off diagonal Long-Range Order Boguilubov ‘47, Bardeen, Cooper, Schrieffer ‘57, Gorkov ‘58 x’ x PAIR CONDENSATE w photon mass Anderson Higgs mechanism Anderson ‘59, Higgs ‘64 q

8. High energy, short distances FP FP Low energy, long distances Fisher, Kadanoff, Kogut, Khmelnitskii, Larkin, Ma, Wegner,Widom, Yulu, Wilson (75) Renormalization Group • New Language • Universality • Fixed Point (FP) • Critical Dimension • Scaling • Cross-over • Kondo Model “QCD of Condensed Matter Physics” Kondo ‘65, Anderson, Yuval & Hamann ‘70, Wilson ‘75, Nozieres ‘75 , Andrei ‘82, Weigmann ‘82 Fermi Liquid (Nozieres ‘75)

9. 3D 0D More is Different: Emergent Phenomenon. “...at each new level of complexity, entirely new properties appear, and the understanding of these behaviors requires 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. • -Heavy Fermion metals. • -High Tc superconductors. • -Quantum Hall Effect. -2D Metal-Insulator transition. • -Conducting Polymers • -Quantum Dots

10. High Tc New ground-states of matter. Heavy Fermions OTT et al ‘83 FQHE. Gossard, Stormer, Tsui ‘81 2D Metal Insulator Transition Kravechenko et al ‘97

11. Fractional Quantum Hall Effect: Most strongly interacting system. Laughlin ‘82 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. 1/2 FILLED FERMI SURFACE OF COMPOSITE QUASIPARTICLES 2kF • HALPERIN, LEE, READ • JAIN PARTICLE-HOLE SYMMETRY?

12. SPIN GAP SC AFM High Tc NON FERMI LIQUID ? • Extraordinary stimulus to new ideas: 1D and 2D physics- frustrated magnetism new ideas for normal state T 2D ``Luttinger’’ Liquid? (Anderson ‘92) Marginal Fermi Liquid? (Varma,Abrahams,Ruckenstein and Schmitt-Rink ‘88) D-wavepairing x Ding et al, ‘?, Z. X. Shen et al, ‘? • Quantum critical fluctuations ? • Stripes? (Kivelson and Emery, many others…..) • SO(5)? (S.C.Zhang ‘97) • Magnetism Superconductivity. • Pair fluctuations?

13. Two relaxation times? rab (mW cm) • Hot and Cold Spots. Cooper et al., ‘94 Hlublina and Rice ‘95 Stokjovic and Pines ‘96 Ioffe and Millis, ‘98 Hot region. Cold spot ? C.f. Kaons • Two Lifetimes Anderson and Ong, ‘92 (spin-charge decoupling) Coleman , Schofield, Tsvelik ‘96

14. Quantum Critical Points • Controlled axis to new fixed point • Genesis of local moment vs Fermi surface+ hot lines. • Scaling. Or ?

15. Genesis of Local Moments? Schroeder et al ‘99 (Schroeder et al ‘99) Spatially local E/T scaling Genesis of Local moments?

16. 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.

17. 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 ? w V eV/ TK Meir, Wingreen, Lee

18. “…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. Outlook. Timescale • New experiments & materials • New concepts • New formalism More Young People !