1. Quantum-critical transport

1
(No Transcript)
2
(No Transcript)
3
1. Quantum-critical transport
Collisionless-t0-hydrodynamic crossover of
CFT3s 2. Quantum criticality of Dirac fermions
Vector 1/N expansion 3. Quantum
criticality of Fermi surfaces The genus
expansion
4
1. Quantum-critical transport
Collisionless-t0-hydrodynamic crossover of
CFT3s 2. Quantum criticality of Dirac fermions
Vector 1/N expansion 3. Quantum
criticality of Fermi surfaces The genus
expansion
5
Superfluid-insulator transition
M. Greiner, O. Mandel, T. Esslinger, T. W.
Hänsch, and I. Bloch, Nature 415, 39 (2002).
6
Insulator (the vacuum) at large U
7
Excitations
8
Excitations
9
Excitations of the insulator
10
CFT3
11
(No Transcript)
12
CFT at Tgt0
13
Quantum critical transport
S. Sachdev, Quantum Phase Transitions, Cambridge
(1999).
14
Quantum critical transport
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714
(1997).
15
Quantum critical transport
P. Kovtun, D. T. Son, and A. Starinets, Phys.
Rev. Lett. 94, 11601 (2005) , 8714 (1997).
16
Quantum critical transport
17
Quantum critical transport
18
Density correlations in CFTs at T gt0
19
Quantum critical transport
20
Quantum critical transport
21
Density correlations in CFTs at T gt0
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714
(1997).
22
Collisionless to hydrodynamic crossover of SYM3
P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son,
Phys. Rev. D 75, 085020 (2007)
23
Collisionless to hydrodynamic crossover of SYM3
P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son,
Phys. Rev. D 75, 085020 (2007)
24
1. Quantum-critical transport
Collisionless-t0-hydrodynamic crossover of
CFT3s 2. Quantum criticality of Dirac fermions
Vector 1/N expansion 3. Quantum
criticality of Fermi surfaces The genus
expansion
25
Nematic order in YBCO
V. Hinkov, D. Haug, B. Fauqué, P. Bourges, Y.
Sidis, A. Ivanov, C. Bernhard, C. T. Lin, and B.
Keimer , Science 319, 597 (2008)
26
Broken rotational symmetry in the pseudogap phase
of a high-Tc superconductor
R. Daou, J. Chang, David LeBoeuf, Olivier
Cyr-Choiniere, Francis Laliberte, Nicolas
Doiron-Leyraud, B. J. Ramshaw, Ruixing Liang, D.
A. Bonn, W. N. Hardy, and Louis Taillefer arXiv
0909.4430
S. A. Kivelson, E. Fradkin, and V. J. Emery,
Nature 393, 550 (1998).
27
1. Quantum-critical transport
Collisionless-t0-hydrodynamic crossover of
CFT3s 2. Quantum criticality of Dirac fermions
Vector 1/N expansion 3. Quantum
criticality of Fermi surfaces The genus
expansion
28
1. Quantum-critical transport
Collisionless-t0-hydrodynamic crossover of
CFT3s 2. Quantum criticality of Dirac fermions
Vector 1/N expansion 3. Quantum
criticality of Fermi surfaces The genus
expansion
29
d-wave superconductivity in cuprates
Electron states occupied
30
d-wave superconductivity in cuprates
-


-
31
d-wave superconductivity in cuprates
-


-
32
d-wave superconductivity in cuprates
4 two-component Dirac fermions
33
d-wave superconductivity in cuprates
34
Time-reversal symmetry breaking
35
Lattice rotation symmetry breaking
36
M. Vojta, Y. Zhang, and S. Sachdev, Phys. Rev.
Lett. 85, 4940 (2000) E.-A. Kim, M. J. Lawler, P.
Oreto, S. Sachdev, E. Fradkin, S.A. Kivelson,
Phys. Rev. B 77, 184514 (2008).
37
Ising order and Dirac fermions couple via a
Yukawa term.
Nematic ordering
Time reversal symmetry breaking
M. Vojta, Y. Zhang, and S. Sachdev, Physical
Review Letters 85, 4940 (2000)
38
Ising order and Dirac fermions couple via a
Yukawa term.
Nematic ordering
Time reversal symmetry breaking
M. Vojta, Y. Zhang, and S. Sachdev, Physical
Review Letters 85, 4940 (2000)
39
Expansion in number of fermion spin components Nf
Integrating out the fermions yields an effective
action for the scalar order parameter
Y. Huh and S. Sachdev, Physical Review B 78,
064512 (2008).
40
(No Transcript)
41
1. Quantum-critical transport
Collisionless-t0-hydrodynamic crossover of
CFT3s 2. Quantum criticality of Dirac fermions
Vector 1/N expansion 3. Quantum
criticality of Fermi surfaces The genus
expansion
42
1. Quantum-critical transport
Collisionless-t0-hydrodynamic crossover of
CFT3s 2. Quantum criticality of Dirac fermions
Vector 1/N expansion 3. Quantum
criticality of Fermi surfaces The genus
expansion
43
Quantum criticality of Pomeranchuk instability
44
Electron Greens function in Fermi liquid (T0)
45
Electron Greens function in Fermi liquid (T0)
46
Quantum criticality of Pomeranchuk instability
47
Quantum criticality of Pomeranchuk instability
48
Quantum criticality of Pomeranchuk instability
49
Quantum criticality of Pomeranchuk instability
50
Quantum criticality of Pomeranchuk instability
Quantum critical
51
Quantum criticality of Pomeranchuk instability
Quantum critical
Classical d2 Ising criticality
52
Quantum criticality of Pomeranchuk instability
Quantum critical
D21 Ising criticality ?
53
Quantum criticality of Pomeranchuk instability
54
Quantum criticality of Pomeranchuk instability
55
Quantum criticality of Pomeranchuk instability
56
Quantum criticality of Pomeranchuk instability
57
Quantum criticality of Pomeranchuk instability
58
Quantum criticality of Pomeranchuk instability
Hertz theory
59
(No Transcript)
60
Quantum criticality of Pomeranchuk instability
Sung-Sik Lee, Physical Review B 80, 165102 (2009)
61
Quantum criticality of Pomeranchuk instability
A string theory for the Fermi surface ?
62
(No Transcript)
63
(No Transcript)
64
(No Transcript)
65
(No Transcript)
66
(No Transcript)
67
(No Transcript)
68
(No Transcript)
69
(No Transcript)
70
(No Transcript)
71
(No Transcript)
72
(No Transcript)
73
(No Transcript)
74
(No Transcript)
75
Greens function of a fermion
T. Faulkner, H. Liu, J. McGreevy, and D. Vegh,
arXiv0907.2694
See also M. Cubrovic, J Zaanen, and K. Schalm,
arXiv0904.1993
76
Greens function of a fermion
T. Faulkner, H. Liu, J. McGreevy, and D. Vegh,
arXiv0907.2694
Similar to non-Fermi liquid theories of Fermi
surfaces coupled to gauge fields, and at quantum
critical points
77
Free energy from gravity theory
F. Denef, S. Hartnoll, and S. Sachdev,
arXiv0908.1788
78
Conclusions
The AdS/CFT offers promise in providing a new
understanding of strongly interacting quantum
matter at non-zero density