양자 홀로그래피와 강얽힘 연구센터

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1 디랙물질을통해서본강상관계의양자홀로그래피적조명 Sang-Jin Sin (Hanyang) 0

2 Unification of SpaceTime and Quantum Matter Sang-Jin Sin (Hanyang) 1

3 순서 1. Physics and Unification 2. 끈이론과강상호작용의역사 3. 양자홀로그래피의개념 4. 양자홀로그래피와실험물리학 5. 물리학의미래와결론 2

4 서론 : 물리학과통일 (Unification ) 물리학 = 최소의공리로최대의경험을설명하는것. 그방법론 = 단순화 ( 대칭성 )/ 정량화 ( 수학 )/ 통일 ( 동일시 ) 이론의심원성 = 동일시되는두가지개념의거리 Example : Maxwell ( 전기, 자기 ) + 약작용 + 강력 + 중력 그러나통일 = 다른것같게보기한분야의특징이아니라물리학의일반적방법론 3

5 양자역학 / 상대론에서의통일 1. 양자역학입자 = 파동 이해가아닌신비 (myth) 입자는위치를가지나파동은전공간에퍼져있슴. non-locality 문제 EPR dramatized 2. 상대론정지계 =( 관성 ) 운동계 시간 = 공간정지계 =( 가속 ) 운동계 중력 = 곡률 ( 힘이아니라 ) 3. 오늘의주제 : 양자물질 = 시공간 4

6 기본입자와듀얼리티 (Unification ) 입자란무엇인가? 정확한 P, S 의 eigen state ~ Plane wave. 한이론의기본입자는상호작용이크면입자가아니다. 이론을변형하여원래이론의복잡한덩어리상태가새이론의기본입자가되게할수있을때이를짝이론, 듀얼이론이라한다. 듀얼리티 : 원이론 ( 강상관계 )= 짝이론 ( 약상관계 ) 즉 unification 의방법론으로문제해결. 쉬뢰딩어방정식은한입자에촛점을맞추어다른모든입자와환경포텐셜로기술하는작업이다. 이를단일전자이론이라하고 제 1 원리계산 의기본골격이다. 그러나전자 - 전자간의상호작용이강하면이그림이깨진다. DMFT 등은이를보완하기위해 exchange correlation function 을넣는다. 홀로그래피는이를위한 canonical 한방법이있다. 5

7 끈이론과강상호작용의역사 1. 상호작용의크기는실험의 energy-scale 에따라다르다. ( next page) 양자색역학, 강상관계는 Low-energy strong[asymptotic freedom] 이란같은문제공유 2. 입자물리 : 실험목표가고에너지 OK, 응집, 핵물리 : 목표가저에너지 미해결. 3. 양자장론 60 년대 : Hadron 강작용 ( 계산불가 ) 입자장론포기 S-matrix 끈이론발견 40 년후 : 끈이론과쌍대성연구에의해강상호작용의장론문제로복귀. 6

8 RG and vacuum polarization(qed) QCD has opposite effect 7

9 강상호작용의효과 1. Loss of particle character : Non-Fermi Liquid 2. Rapid thermalization Hydro-dynamic description 8

10 입자성소멸후 : 강상관계의특징적현상들 기이한금속성 양자임계성 Violation of Wiedemann-Franz law Fermi Arc 9

11 준입자가사라진후무엇을볼것인가? 가장보편적 (universal) 양을보아야! 양자임계점 (QCP) 부근의수송계수, 상태밀도 QCP 분류 : dynamical exponent z Z, θ: ω=k z, [s]=d-θ QCP 10

12 방법론 : 양자홀로그래피 3 dim. Classical BH 2 dim. Quantum Matter 2 차원강상관계의 (QCP 부근에서의 ) 홀로그램 = 3 차원블랙홀 양자홀로그래피 11

13 홀로그래피적쌍대성 양자게이지이론 AdS 중력 중력 상호작용 중력의세기 ~ 1/( 물질간상호작용의세기 ) ~ 1/ 우주상수 원래의계가강상관, 양자적일수록쌍대계는약상관, 고전적! 12

14 양자홀로그래피연구의현황 (20 년간연구의결과 ) 블랙홀 금속성의강상관계 평형계, 유체역학적거동 수송계수가계산됨 ( 전통적유체역학에서수송계수는 input) 13

15 홀로그래피연구의방법론 초대칭 D-brane (Maldacena 1997 ) 초대칭등각대칭게이지이론, Theory of Quantum Matter 초대칭 AdS 중력이론 Classical Geometry 초대칭성이없을때의홀로그래피연구의두길 : i. 끈이론밖에서홀로그래피가성립하는이유를찾는다. ii. 홀로그래피를가정하고계산해서실험과비교해본다. 14

16 i) 홀로그래피의끈이론밖에서의증거 1. 등각장론에서의얽힘엔트로피 Ryu & Takayanagi (2006) 2. 텐서그물망 : (Multiscale Entanglement Renormalization Ansatz) [Swingle] 15

ii) 홀로그래피의실험적증거 Simplest QCP is z=1 : 그래핀 Q: 강상관계?. 10 년간추측 1.

17 ii) 홀로그래피의실험적증거 Simplest QCP is z=1 : 그래핀 Q: 강상관계?. 10 년간추측 near Dirac Point : Tiny FS No (insufficient) screening 16

(see the Perspective by fluid in thin wires of PdCoO 2 had a maj Bandurin et al.

18 This copy is for y 실험적증거 4 March 2016 Editor's Summary Neg gra D. A Tom Nov M. P Scie orig Electrons that flow like a fluid Electrons inside a conductor are of flow rarely resembles anything like the f counterexamples (see the Perspective by fluid in thin wires of PdCoO 2 had a maj Bandurin et al. found evidence in graph fluid flowing through a small opening. F transport in graphene, a signature of so-c Science, this issue p. 1061, 1055, 1 Article Tools Permissions Visit the onli article tools: Obtain inform Simple Pure Hard! 17

$유체역학적계산결과 (Harvard) With \Without$

19 유체역학적계산결과 (Harvard) With \Without effect of puddle (inhomogeneity) \

20 홀로그래피계산과실험비교 Idea : neutral current Enhance the heat conductivity 4 basic parameters. 19

21 Origin of two currents: Kinematics on Dirac cone h + h + + h + + e. are suppressed kinematically due to E,p, conservation, In graphene, however, Foster+Almeiner these processes ( ) ar suppressed by the conservation of energy tum p,because the spectrum ε(p) of the q not decaying d 2 ε(p) d 2 p 0. FIG. 1: K inematical constraints for imbalance relaxation. The left figure shows the Feynman diagram for the typical two-particle decay process given by Eq. (1.1a); ε i and p i respectively denote the energy and momentum of the i th electron or hole. T he right figure depicts momentum conservation for this process. T he length of the dashed path L f p 2 + p 3 + p 4 traced out by the sum of decay product momenta is always greater than or equal to the length L i p 1 of the parent particle momentum: L f L i.ifthe β laxation of popu st rate that the r both κ and the t ing and tempera cally large syste balance relaxatio the ends of a gra disparate temper ted to flow, stea ertheless occur; imbalance relaxa device. T hermo tion of the grap incorporate into non-ideal 20 contac (Negative curvature of the spectrum K arises due to the logarithmic reno

22 Additivities of Transports 21

23 The story was published as Phys.Rev.Lett. 118 (2017) no.3, Editors' Suggestion 22

24 Other z=1 material? Dirac material is a class ( ): 우리예측 : so is the anomalous transport. 선택 : Surface of TI Similar, but differ by strong spin-orbit interaction 23

25 How to encode Spin-Orbit interaction? 1. ee int is already included by gravity but e-lattice should be encoded explicitly. 2. i. Integrate out massive fermion in 2+1 Chern-Simon ii. Lift it to the bulk F^F iii. Axionize for dynamical effect time reversal invariant case time reversal Sym broken case 3. We Focus on T-broken case. Test by Magnetization/Anomalous Hall effect 24

26 Model with strong Spin-Orbit interaction TRS breaking case 25

27 Surface states of TI [ , 서, 송, 신 ] 26

28 Surface states of TI [ , 서, 송, 신 ] Weak cor. Strong cor. Weak cor. 27

29 Transition regime is strongly correlated Our theory fits well the data near the Transition WAL WL (But only for T>2K). Transition regime is strongly correlated. Exp. data Our result Data v.s Theory 28

30 Disappearance of horn of WAL for lightly doped. TI with strong correlation will not show sharp peak of WAL for lightly doped case. WAL is based on the cancelation of two amplitudes for a path and its TRS pair. No quasiparticle fuzzy paths. 29

31 물리학의미래 세상은넓고데이터는많다. 수십년간쌓인.( 주기율표 ) 물리학의역사 = end of physics 의역사 Laplace, Wigner and Von Laue, 우리앞엔강상관계이론을정립할목표가있다. 30

32 puzzle 21 세기엔 21 세기의문제와그해결을통해얻어질새로운문명이있다. 31

33 Conclusion 강상관계를위한새로운물리학이양자홀로그래피와디랙물질에관한실험들에의거해만들어지고있다. 전이금속일반에관한이론 (Lifshitz class, Cuprate class) 으로확장하는것도가까운미래. 물리학은반도체에비할만한신물질, 신문명을만들것. 21 세기의물리학은이론적흥미와실질적응용이동행. 32

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