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Exploring New Paradigm in Physics

Exploring New Paradigm in Physics. Yu Lu Institute of Physics Chinese Academy of Sciences. “ …The underlying physical laws necessary for the mathema- tical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is

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Exploring New Paradigm in Physics

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  1. Exploring New Paradigm in Physics Yu Lu Institute of Physics Chinese Academy of Sciences

  2. “…The underlying physical laws necessary for the mathema- tical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equat- ions much too complicated to be soluble.” P.A.M. Dirac, Proc. Roy. Soc. A123, 713 (1929)

  3. - Planck/unification scale (1028 eV) d u u d d u d d u u u d - - e e - - 4 He + 2e QCD  Nuclear physics scale (108-109 eV) - - - - - - - + + + + + + + + + + + + Condensed matter physics scale (100 eV) Na metal How do you do to get the Theory of Everything? The Theory of Everyday Everything!

  4. Great achievements of quantum theory and relativity: • Civilization of the information Age • Structure of matter: how chemistry ‘works’ • Electronic theory: transistors, IC, memories • Lasing principle: lasers, optical fibers… • Fission and fusion: nuclear energy… • Nuclear Techniques: MRI, PET, CT… Observations and exploitations of these remarkable quantum phenomena

  5. Is this truly The theory of Everything? Canone derive ALL exotic properties, from the Schrödinger equation??

  6. “We often think that when we have completed our study of one we know all about two, because ‘two’ is ‘one and one.’ We forget that we have still to make a study of ‘and.’ ” --Sir Arthur Eddington.

  7. Philip W. Anderson: More is different(1972) “The behavior of large and complex aggregations of elementary particles, … is not to be understood in terms of a simple extrapolation of the properties of a few particles. Instead,at each new level of complexity, entirely new properties appear, and the understanding of this behavior requires research as fundamental in its nature as any other…”

  8. Emergent features ofcondensed matter systems • Collective excitations—quasi-particles • Symmetry breaking • Renormalization • ……

  9. Lattice vibration and phonons • If ground state stable: low energy excitations • —harmonic oscillations. Quantization of these • oscillations — phonons • “Like” ordinary particles，dispersion  (p) • No restrictions on generation: bosons • They cease to exist, while away from crystals: • quasi-particles • Not sensitive to microscopic details，those details cannot be recovered from the phonons This was initiated byEinstein ！

  10. Landau Fermi Liquid Theory • Low energy excitations of interacting Fermi systems（like electrons in metals）can be mapped onto weakly interacting Fermi gas • These quasi-pariticles follow Fermi statistics， with dispersion  (p)，with the same Fermi volume as free fermions (Luttinger theorem). • They cease to exist if taken away from the matrix (metal) • Their properties not sensitive to microscopic interactions，which cannot be derived from these ‘coarse grained’ properties

  11. Basic assumption: Adiabaticity Question: How to justify it, if no gaps?

  12. Emergent features ofcondensed matter systems • Collective excitations—quasi-particles • Symmetry breaking • Renormalization • ……

  13. Superconductivity 1911 Kamerlingh Onnes discovered zero resistance Early 30s Meissner effect discovered, complete diamag- netism more fundamental London equations Wave function “rigidity” ansatz (London brothers)

  14. Superconductivity 1950 Ginzburg-Landau equation，introducing macroscopic wave function Bardeen realized: gap in spectrum leads to “rigidity” Cooper pairing：arbitrarily weak attraction gives rise to bound states at the Fermi surface —pairing energy is the gap

  15. Is SC a Bose-Einstein condensation of Cooper pairs?--a bit more complicated! BCS wave function： Problem solved！ Nobel prize was delayed by 15 years！! Particle number not conserved，change from one Hilbert space to another one — symmetry breaking—conceptual breakthrough

  16. Symmetry Breaking Discrete symmetry－－from up or down to definite up（down） Broken symmetry－reduction of symmetry elements Displacive phase transition “Usually”: “high temperature－high symmetry”, “low temperature－low symmetry”

  17. Broken continuous symmetry Ferromagnet--broken rotational symmetry Antiferromagnetic order – staggered magnetization (Landau & Néel)， －－not conserved quantity Macroscopic superconducting wave function －order parameter (Landau) breaking of U(1) gauge symmetry

  18. Anderson-Higgs mechanism Goldstone mode: collective excitations,recovering the symmetry – like spin waves When external (gauge) field coupled, becomes massive -- Meissner effect Unified weak-electromagnetic interactions－ 1979 Nobel prize in physics Weinberg- Salam- Glashow

  19. Josephson effect： visualization of the phase Using two Josephson junctions-- SQUID Most profound exhibition of emergence!

  20. Josephson Effect S2 S1

  21. Bardeen -Josephson dispute • Anderson’s lecture • Josephson’s calculation • Bardeen’s added note • Dispute at LT 8 BCS mentor against the most convincing proof of his theory!!

  22. Quark-Gluon Plasma Neutron Stars, Color Superconductivity High Tc Superconductivity Low Tc Superconductivity Heavy Electron Superconductivity 3He Superfluidity Atom traps, BEC, Superfluidity 10-9 10-6 10-3 1 103 106 109 1012 Nano-K micro-K milli-K K kilo-K mega-K giga-K tera-K

  23. Emergent features ofcondensed matter systems • Collective excitations—quasi-particles • Symmetry breaking • Renormalization • ……

  24. a 0 (jump）  0 b 1/2  1/3! g 1  4/3! d 3 5! n 1/2  2/3 !  0  0 Failure of Mean Field Theory！！ Experiment MFT Theory valid in space dimensions beyond 4 ！

  25. Renormalization Group (RG) Theory of Critical Phenomena -- 1982 Physics Nobel Basic Ideas: First integrate out short range fluctuations to find out how coupling constant changes with scale. Using expansion around “ fixed ” point to calculate the critical exponents, in full agreement with experiments, without any adjustable parameters. Kenneth K. Wilson

  26. Experimental verification of RG theory Newest results of RG a=-0.0110.004 Space experiment (7 decades) a=-0.01270.0003 Full agreement within accuracy Power of Theoretical Physics !!

  27. Justification of Landau Fermi -liquid theory —Weakly interacting fermion systems renormalize to its ‘fixed Point’—Free fermions

  28. Paradigm in studying Emergent phenomena • Low energy excitations: quasi particles • Landau Fermi liquid theory • Symmetry breaking • Renormalization • ……. Very successful, common features of phenomena at very different scales, but is it a universal recipe??

  29. Integer Quantum Hall Effect － 1985 Nobel in Physics No symmetry breaking Failure of Landau paradigm !!

  30. X.G. Wen

  31. Topological properties of QHE e2/h=1/(25 812.807 572 Ω) accuracy 10－9 N=n Chern number

  32. QHE and Quantum Spin Hall Effect Qi & Zhang

  33. Topological insulators Bulk-insulator, surface-metallic, no time- reversal symmetry breaking, no back-scattering, guaranteed by topological Chern parity!!

  34. Plausible exotic excitations Majorana fermion Axion? Charge+monopole-‘Dyon’ X.L. Qi et al.

  35. No answer yet to the challenge Posed by Müller-Bednorz!! LSCO –La2-xSrxCuO4+d YBCO -- YBa2Cu3O6+y

  36. Not so much the Tc so high, • super-glue? • Even more profound problem: the Fermi liquid theory fails!

  37. “Anomalous” normal state properties mysterious linear resistivity H. Takagi et al. PRL, 1992

  38. Pseudogap of High-Tc(dark entropy) Missing of entropy at low energies Concept of quasi- Particle not applicable

  39. Attempts to explore new paradigm • Topology + quantum geometry (D. Haldane) • Topology + long range entanglements (X.G. Wen)

  40. Laughlin’s wave function for FQHE Fractional charge, fractional statistics, …… Is this a complete description??

  41. New question raised by Haldane Are these two ‘circles’ the same? Using geometrical approach they are not the same!! The latter is described by the “guiding centers” which obey ‘non-commutative geometry’!!

  42. How to characterize topological order? • No symmetry breaking, nor local order parameter, different quantum Hall states have the same symmetry • Non-local topological order parameter • Ground state degeneracy-Berry phase • Abelian-Non-Abelian edge states (CFT) • Gapped spin-liquid states, protected by symmetry, chiral spin state, …… What is the most fundamental?? X.G. Wen

  43. QuantumEntanglement EPR paradox Classical orders (crystals, ferromagnets)-untangled Even the ‘quantum order’-superfluidity-untangled

  44. Classification of entanglements • Short range entanglement • Landau symmetry breaking states • No symmetry breaking- Symmetry protected • topological orderlike topological insulators, • Haldane spin 1 chain…… • Long range entanglement • Symmetry breaking like P+iP superconductivity • No symmetry breaking: FQHE, spin liquids Non-trivial topological order = long range entanglement in MB states

  45. Some key words • Topology • Geometry (non-commutative) • Long-range entanglements • Entanglement spectrum, instead of just a number (von Neumann entropy) • ……

  46. Thank you all!

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