Quantum Matter with Classical Spacetime

Transcription

1 Can we understand d-electrons with warped spacetime? Quantum Matter with Classical Spacetime Sang-Jin Sin (Hanyang) Postech

2 溫故知新 Brief history of physics revolution

3 Revolution 1.0: first law Only after separating out friction, we can realize that we do not need force to keep the velocity of motion. Galilean relativity: v is nothing! Velocity should not enter into the law of motion. Newton : dv/dt is the first non-trivial thing and should match the force Second law. [Aristotle: F ~ v] 3

4 Revolution 1.1 : Relativity In 1905: Einstein said: *constant velocity is nothing (relativity). **speed of light is a law not a velocity (since it was there in Maxwell s eq.) Time ~ Space In 1910, Einstein claimed Can it be true that any non-inertial frame change can be immaterial? Gravity satisfy such request due to the equivalence principle. gravity ~ geometry (not a force). Although truly remarkable, not a revolution but an evolution. (everything understandable.) 4

5 Revolution 2.0: Quantum Mech. Particle ~ Wave Schroedinger eq. = Wave eq. of a particle. Familiar but impossible to understand: Probability, Collapse of state by measurement, etc. This is why it was a true revolution unfinished! 5

6 Revolution 3, Unification Ver. 3.1: Electricity ~ Magnetism just one object (EM) viewed in different frame ~ Tensor Ver 3.2 : In 1967: Weinberg succeeded in: EM~weak GUT: EM~ weak~strong (nonabelian gauge theory). String theory: EM~weak~strong~gravity. 6

7 Lessons: 1. Divide objects into simpler things. (atom) find out all forces and eliminate all. 2. Unify : View different things as the same Relativity, unifications. Simplification. 3. Emergence : Look at 10^23 particles. *If Gap is there, a vast simplification happens below that energy scale. only collective behavior discarding individual.(sc) **Classicality out of quantum coherence! If S=Ns, not s1+s2+s3+, then change in s cause drastic change in S. path integral view gives dominance of one configuration. 7

8 If there occurs drastic simplification, we call it a revolution. Today s message: Revolution 4 is undergoing by Matter ~ spacetime This scenario was suggested by the string theory 8

9 Issues of 21C? Not much new phenomena. Then, solve unsolved eq., model, conjecture 1. Fluid mechanics for high Reynold Number, (nonlinearity) 2. QCD low energy, (strong coupling) 3. Strongly correlated electron system. What is more important? More applicable one. One implies the other, I believe. 9

10 Strong interaction in e-e int.? For Nuclear physics, QCD: yes g^2 ~ 1 for low energy. But condensed matter which is controlled by QED, Isn t it g^2 ~ 1/137, the fine structure constant? How ee interaction can be strong? 10

11 What is interaction? Yukawa / Feynman. Lippman-Schiwinger GoV=V/K: Slow electrons interact strongly. 11

12 Dual Nature - itinerant and localized state of 3d, 5f, 4f electrons. Or spin and charge separation,. Bandwidth (ev) d 4d 3d 5f 4f 0 Atomic Number Electrons in the unfilled shell become progressively more localized in the sequence 5d 4d 3d 5f 4f From YK.Bang s talk

13 Also such definition based on free particle and their local interaction is ok only if interaction is weak, but useless for strong coupling. This is the huddle that forbid Nucl.P and scm for more than half centuries. Strong interaction invalidate Band theory, which is based on one elctron in a fixed potential picture, which is not valid if e-e interaction is valid. Strong interaction can destroy the Fermi Sea. 13

14 Example: QCD in low E: strongly int. Weak in high Enegy // Strong in low energy Not clear how to separate particle from interaction. Need new frame

15 Any idea? Reformulate theory in terms of new degree of freedom whose interactions are weak. Duality

16 t x Open closed duality Open String : gauge theory Theory of Matter Closed string: gravity Theory of space-time t Open st. 1-loop x closed st. tree Two are dual to each other through D-brane: 16

17 D-brane and AdS/CFT Membrane like solution of CS (gravity) Whose vibration ~ open string (gauge theory). Stack of D-brane space time warp near D: AdS geometry. AdS/CFT CFT: since gauge theory has a conformal symmetry which is the same group as the isometry group. Holography: need one more dimension. 17

18 Summary of AdS/CFT 1. String in AdS5 is dual to SYM in 4d. 2. 5d v.s 4d Holographic corresp. 3. For large coupling, closed string can be replaced by gravity gravity/gauge dualtiy 4. string scale cancel due to conformal inv. 18

19 Consequence of duality 1. Gluon dynamics is replaced by ads gravity. (Matter~Geometry) 2. For large N_c, gravity is weakly coupled. 3. Correlation function in 4d can be calculated by the classical dynamics at the 5d AdS. holographic.

20 Meaning of extra dimension Einstein eq. encodes flow. Figure from by Faulkner et.al

21 Thermalized system ~ BH in ads [E.Witten 1998] Figure: Hartnoll

22 System with dense matter: charge BH [KY.Kim+I.Zahed+sjs,2006]

23 What can we do? Mostly, transport and two point functions AC conductivities in a holographic modelphic model of momentum relaxation 1409.XXXX K-Y Kim, Kyung Kiu Kim, Yunseok Seo, and Sang-Jin Sin 23

24 Electric, Thermoelectric, Thermal conductivity Fluctuations EOMs Boundary action Linear response Two issues for generalisation 1. more than one equation 2. identify the sources and currents Hartnoll

25 Thermal and thermoelectric conductivity DC results: Donos and Gauntlett

26 Holographic superconductor Gubser,Hartnoll+Herzog+Horowitz

27 Electron star(no horizon) dual to T=0, fermi surface Takayanagi 27

28 Quantum criticality 28

29 Fig. from Zaanen s talk 29

30 Perhaps we need more general scaling solution. 30

31 Holy Grail: Linear registivity 31

32 From J. Zaanen s talk 32

33 Secret of linear Registivity 33

34 Why strongly interacting system thermalize so fast? Extreme example: in RHIC, Heavy ion collision fireball equilibrate just in passing time: 34

35 In terms of the gravity dual, Thermal State is dual to AdS BH Formation of AdS BH Thermalization. Question: Does a generic (non-spherical) collapse in AdS give a black hole in one dynamical time.

36 In flat space, it is impossible to make a BH in one dynamical time.

37 In AdS space Claim: Generic collapse will give a black hole.

38 Then Why in ads? Falling time is the same independent of the initial condition of particle. Let E be the first integral, then Some integrability is at work!

39 Eq. of Motion: An integrable non-linear oscillator period is amplitude independent!

40 Prediction 1. Thermalization time < One Dynamical time, 2. Thermalization: Soft first and Hard later. (for pure gluon int. in the large N.) [ lower energy particles arrive at the wouldbe-horizon earlier. ]

41 Future direction Can we realize the fermions with pseudo gap in holographic way? Is it possible to have PG and linear registivity in the same modtion el? HOMES s law? Embedding Real Lattice into theory. 1-electron theory in warped space time. 41

42 Caution Caution: Not straightforward generalization of AdS/CFT. Broken Conformal Symmetry. SUSY. Large N? Analogy: Schroedinger equation with potential. Only after solving the equation and comparing with experimental data justify it. If true, real revolution. 42

43 Conclusion We can use gravity to understand strongly interacting system s strange behavior. We can calculate transport and spectral fct and optical conductivity. Early thermalization: We identified the mechanism as the time focusing effect. There is certain jump. Not completely logical. We need to compare with experimental data directly rather than old theory. Successful? Then Next revolution

44 Thank you