1、Exploring New Paradigm in Physics,Yu LuInstitute of PhysicsChinese Academy of Sciences,P.A.M. Dirac, Proc. Roy. Soc. A123, 713 (1929),“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 difficul
2、ty is only that the exact application of these laws leads to equat-ions much too complicated to be soluble.”,How do you do to get the Theory of Everything?,Planck/unification scale (1028 eV),The Theory of Everyday Everything!,Great achievements of quantum theory and relativity: Civilization of the i
3、nformation 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 theseremarkable quantum phenomena,Is this truly The theo
4、ry ofEverything?,Can one derive ALL exotic properties,from the Schrdinger equation?,“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.,Philip W. Anderson: More i
5、s 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 behavio
6、r requires research as fundamental in its nature as any other”,Emergent features ofcondensed matter systems,Collective excitationsquasi-particles Symmetry breaking Renormalization ,Lattice vibration and phonons,If ground state stable: low energy excitations harmonic oscillations. Quantization of the
7、se 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 by Einstein ！,Landau Fermi
8、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
9、 away from the matrix (metal),Their properties not sensitive to microscopic interactions，which cannot be derived from these coarse grained properties,Basic assumption: AdiabaticityQuestion: How to justify it, if no gaps?,Emergent features ofcondensed matter systems,Collective excitationsquasi-partic
10、les Symmetry breaking Renormalization,Superconductivity,1911 Kamerlingh Onnes discovered zero resistance,Early 30s Meissner effect discovered, complete diamag-netism more fundamental,Wave function “rigidity” ansatz (London brothers),London equations,1950 Ginzburg-Landau equation，introducing macrosco
11、pic wave function,Bardeen realized: gap in spectrum leads to “rigidity”,Superconductivity,Cooper pairing：arbitrarily weak attraction gives rise to bound states at the Fermi surface pairing energy is the gap,Is SC a Bose-Einstein condensation of Cooper pairs?-a bit more complicated!,BCS wave function
12、：,Problem solved！Nobel prize was delayed by 15 years！!,Particle number not conserved，change from one Hilbert space to another one symmetry breakingconceptual breakthrough,Symmetry Breaking,Discrete symmetryfrom up or down to definite up（down）,Broken symmetryreduction of symmetry elements,“Usually”:
13、“high temperaturehigh symmetry”, “low temperaturelow symmetry”,Displacive phase transition,Ferromagnet-broken rotational symmetry,Broken continuous symmetry,Antiferromagnetic order staggered magnetization (Landau & Nel)， not conserved quantity,Macroscopic superconducting wave function order paramete
14、r (Landau) breaking of U(1) gauge symmetry,Goldstone mode: collective excitations, recovering the symmetry like spin waves,Anderson-Higgs mechanism,Unified weak-electromagnetic interactions 1979 Nobel prize in physics Weinberg- Salam- Glashow,When external (gauge) field coupled, becomes massive - Me
15、issner effect,Josephson effect： visualization of the phase,Most profound exhibition of emergence!,Using two Josephson junctions- SQUID,Josephson Effect,S2,S1,Bardeen - Josephson dispute,Andersons lecture Josephsons calculation Bardeens added note Dispute at LT 8,BCS mentor againstthe most convincing
16、 proof of his theory!,Emergent features ofcondensed matter systems,Collective excitationsquasi-particles Symmetry breaking Renormalization,Failure of Mean Field Theory！,MFT,Experiment,Theory valid in space dimensions beyond 4 ！,Kenneth K. Wilson,Renormalization Group (RG) Theory of Critical Phenomen
17、a - 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.,Experimental verif
18、ication of RG theory,Newest results of RGa=-0.0110.004,Space experiment (7 decades)a=-0.01270.0003,Full agreement withinaccuracy,Power of Theoretical Physics !,Justification of Landau Fermi -liquid theory Weakly interacting fermionsystems renormalize to its fixedPointFree fermions,Paradigm in studyi
19、ng Emergent phenomena,Low energy excitations: quasi particles Landau Fermi liquid theory Symmetry breaking Renormalization .,Very successful, common features ofphenomena at very different scales,but is it a universal recipe?,Integer Quantum Hall Effect 1985 Nobel in Physics,No symmetry breakingFailu
20、re of Landau paradigm !,X.G. Wen,Topological properties of QHE,e2/h=1/(25 812.807 572 ) accuracy 109,N=n Chern number,QHE and Quantum Spin Hall Effect,Qi & Zhang,Bulk-insulator, surface-metallic, no time-reversal symmetry breaking, no back-scattering, guaranteed by topological Chern parity!,Topologi
21、cal insulators,Plausible exotic excitations,Charge+monopole-Dyon,Majorana fermionAxion?,X.L. Qi et al.,YBCO - YBa2Cu3O6+y,No answer yet to the challenge Posed by Mller-Bednorz!,LSCO La2-xSrxCuO4+d,Not so much the Tc so high, super-glue?,Even more profound problem: the Fermi liquid theory fails!,“Ano
22、malous” normal state properties mysterious linear resistivity,H. Takagi et al.PRL, 1992,Pseudogap of High-Tc(dark entropy),Missing of entropy at low energies,Concept of quasi-Particle not applicable,Attempts to explore new paradigm,Topology + quantum geometry (D. Haldane) Topology + long range entan
23、glements (X.G. Wen),Fractional charge, fractional statistics,Is this a complete description?,Laughlins wave function for FQHE,New question raised by Haldane,Are these two circles the same?,Using geometrical approach they are notthe same!The latter is described by the “guiding centers” which obey non
24、-commutative geometry!,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 state
25、s, protected by symmetry, chiral spin state, ,What is the most fundamental?,X.G. Wen,Quantum Entanglement,Classical orders (crystals, ferromagnets)-untangled,Even the quantum order-superfluidity-untangled,EPR paradox,Classification of entanglements,Short range entanglement,Landau symmetry breaking s
26、tates No symmetry breaking- Symmetry protectedtopological order like topological insulators,Haldane spin 1 chain,Long range entanglement,Symmetry breaking like P+iP superconductivityNo symmetry breaking: FQHE, spin liquids,Non-trivial topological order= long range entanglement in MB states,Some key words,Topology Geometry (non-commutative) Long-range entanglements Entanglement spectrum, instead of just a number (von Neumann entropy),Thank you all!,
