quantum phase transitions in condensed matter …qpt.physics.harvard.edu/talks/amherst11.pdfquantum...
TRANSCRIPT
Quantum phase transitions in condensed matter physics,
with connections to string theory
HARVARD
Amherst College, October 27, 2011
sachdev.physics.harvard.eduFriday, October 28, 2011
Max Metlitski, Harvard
HARVARD
Eun Gook Moon, Harvard
Friday, October 28, 2011
1. Quantum critical points and string theory Entanglement and emergent dimensions
2. High temperature superconductors and strange metals Holography of compressible quantum phases
Outline
Friday, October 28, 2011
1. Quantum critical points and string theory Entanglement and emergent dimensions
2. High temperature superconductors and strange metals Holography of compressible quantum phases
Outline
Friday, October 28, 2011
Square lattice antiferromagnet
H =�
�ij�
Jij�Si · �Sj
J
J/λ
Examine ground state as a function of λ
S=1/2spins
Friday, October 28, 2011
H =�
�ij�
Jij�Si · �Sj
J
J/λ
At large ground state is a “quantum paramagnet” with spins locked in valence bond singlets
=1√2
����↑↓�−
��� ↓↑��
Square lattice antiferromagnet
λ
Friday, October 28, 2011
H =�
�ij�
Jij�Si · �Sj
J
J/λ
=1√2
����↑↓�−
��� ↓↑��
Square lattice antiferromagnet
Nearest-neighor spins are “entangled” with each other.Can be separated into an Einstein-Podolsky-Rosen (EPR) pair.
Friday, October 28, 2011
Square lattice antiferromagnet
H =�
�ij�
Jij�Si · �Sj
J
J/λ
For λ ≈ 1, the ground state has antiferromagnetic (“Neel”) order,and the spins align in a checkerboard pattern
Friday, October 28, 2011
Square lattice antiferromagnet
H =�
�ij�
Jij�Si · �Sj
J
J/λ
For λ ≈ 1, the ground state has antiferromagnetic (“Neel”) order,and the spins align in a checkerboard pattern
No EPR pairs
Friday, October 28, 2011
λλc
=1√2
����↑↓�−
��� ↓↑��
Friday, October 28, 2011
Pressure in TlCuCl3
λλc
=1√2
����↑↓�−
��� ↓↑��
A. Oosawa, K. Kakurai, T. Osakabe, M. Nakamura, M. Takeda, and H. Tanaka, Journal of the Physical Society of Japan, 73, 1446 (2004).
Friday, October 28, 2011
TlCuCl3
An insulator whose spin susceptibility vanishes exponentially as the temperature T tends to zero.
Friday, October 28, 2011
TlCuCl3
Quantum paramagnet at ambient pressure
Friday, October 28, 2011
TlCuCl3
Neel order under pressureA. Oosawa, K. Kakurai, T. Osakabe, M. Nakamura, M. Takeda, and H. Tanaka, Journal of the Physical Society of Japan, 73, 1446 (2004).
Friday, October 28, 2011
λλc
=1√2
����↑↓�−
��� ↓↑��
Friday, October 28, 2011
λλcSpin S = 1“triplon”
Excitation spectrum in the paramagnetic phase
Friday, October 28, 2011
λλcSpin S = 1“triplon”
Excitation spectrum in the paramagnetic phase
Friday, October 28, 2011
λλcSpin S = 1“triplon”
Excitation spectrum in the paramagnetic phase
Friday, October 28, 2011
λλcSpin S = 1“triplon”
Excitation spectrum in the paramagnetic phase
Friday, October 28, 2011
λλc
Excitation spectrum in the paramagnetic phase
Spin S = 1“triplon”
Friday, October 28, 2011
λλc
Excitation spectrum in the Neel phase
Spin waves
Friday, October 28, 2011
λλc
Excitation spectrum in the Neel phase
Spin waves
Friday, October 28, 2011
λλc
Excitation spectrum in the Neel phase
Spin waves
Friday, October 28, 2011
Christian Ruegg, Bruce Normand, Masashige Matsumoto, Albert Furrer, Desmond McMorrow, Karl Kramer, Hans–Ulrich Gudel, Severian Gvasaliya,
Hannu Mutka, and Martin Boehm, Phys. Rev. Lett. 100, 205701 (2008)
Excitations of TlCuCl3 with varying pressure
0 0.5 1 1.5 2 2.5 30
0.2
0.4
0.6
0.8
1
1.2
Pressure [kbar]
Ener
gy [m
eV]
Friday, October 28, 2011
Christian Ruegg, Bruce Normand, Masashige Matsumoto, Albert Furrer, Desmond McMorrow, Karl Kramer, Hans–Ulrich Gudel, Severian Gvasaliya,
Hannu Mutka, and Martin Boehm, Phys. Rev. Lett. 100, 205701 (2008)
0 0.5 1 1.5 2 2.5 30
0.2
0.4
0.6
0.8
1
1.2
Pressure [kbar]
Ener
gy [m
eV]
Excitations of TlCuCl3 with varying pressure
Broken valence bondexcitations of the
quantum paramagnet
Friday, October 28, 2011
Christian Ruegg, Bruce Normand, Masashige Matsumoto, Albert Furrer, Desmond McMorrow, Karl Kramer, Hans–Ulrich Gudel, Severian Gvasaliya,
Hannu Mutka, and Martin Boehm, Phys. Rev. Lett. 100, 205701 (2008)
0 0.5 1 1.5 2 2.5 30
0.2
0.4
0.6
0.8
1
1.2
Pressure [kbar]
Ener
gy [m
eV]
Excitations of TlCuCl3 with varying pressure
Spin wave
and longitudinal excitations
(similar to the Higgs particle)
of the Neel state.
Friday, October 28, 2011
Christian Ruegg, Bruce Normand, Masashige Matsumoto, Albert Furrer, Desmond McMorrow, Karl Kramer, Hans–Ulrich Gudel, Severian Gvasaliya,
Hannu Mutka, and Martin Boehm, Phys. Rev. Lett. 100, 205701 (2008)
0 0.5 1 1.5 2 2.5 30
0.2
0.4
0.6
0.8
1
1.2
Pressure [kbar]
Ener
gy [m
eV]
Excitations of TlCuCl3 with varying pressure
Spin wave
and longitudinal excitations
(similar to the Higgs particle)
of the Neel state.
“Higgs” particle appears at theoretically predicted energy
Friday, October 28, 2011
λλc
=1√2
����↑↓�−
��� ↓↑��
Friday, October 28, 2011
λλc
Quantum critical point with non-local entanglement in spin wavefunction
=1√2
����↑↓�−
��� ↓↑��
Friday, October 28, 2011
depth ofentanglement
D-dimensionalspace
Tensor network representation of entanglement at quantum critical point
Friday, October 28, 2011
• Long-range entanglement
• Long distance and low energy correlations near thequantum critical point are described by a quantumfield theory which is relativistically invariant (wherethe spin-wave velocity plays the role of the velocityof “light”).
• The quantum field theory is invariant under scale andconformal transformations at the quantum criticalpoint: a CFT3
Characteristics of quantum critical point
Friday, October 28, 2011
• Long-range entanglement
• Long distance and low energy correlations near thequantum critical point are described by a quantumfield theory which is relativistically invariant (wherethe spin-wave velocity plays the role of the velocityof “light”).
• The quantum field theory is invariant under scale andconformal transformations at the quantum criticalpoint: a CFT3
Characteristics of quantum critical point
Friday, October 28, 2011
• Long-range entanglement
• Long distance and low energy correlations near thequantum critical point are described by a quantumfield theory which is relativistically invariant (wherethe spin-wave velocity plays the role of the velocityof “light”).
• The quantum field theory is invariant under scale andconformal transformations at the quantum criticalpoint: a CFT3
Characteristics of quantum critical point
Friday, October 28, 2011
• Allows unification of the standard model of particlephysics with gravity.
• Low-lying string modes correspond to gauge fields,gravitons, quarks . . .
String theory
Friday, October 28, 2011
• A D-brane is a D-dimensional surface on which strings can end.
• The low-energy theory on a D-brane is an ordinary quantumfield theory with no gravity.
• In D = 2, we obtain strongly-interacting CFT3s. These are“dual” to string theory on anti-de Sitter space: AdS4.
Friday, October 28, 2011
• A D-brane is a D-dimensional surface on which strings can end.
• The low-energy theory on a D-brane is an ordinary quantumfield theory with no gravity.
• In D = 2, we obtain strongly-interacting CFT3s. These are“dual” to string theory on anti-de Sitter space: AdS4.
CFTD+1
Friday, October 28, 2011
depth ofentanglement
D-dimensionalspace
Tensor network representation of entanglement at quantum critical point
M. Levin and C. P. Nave, Phys. Rev. Lett. 99, 120601 (2007)F. Verstraete, M. M. Wolf, D. Perez-Garcia, and J. I. Cirac, Phys. Rev. Lett. 96, 220601 (2006)
Friday, October 28, 2011
String theory near a D-brane
depth ofentanglement
D-dimensionalspace
Emergent directionof AdS4
Friday, October 28, 2011
depth ofentanglement
D-dimensionalspace
Tensor network representation of entanglement at quantum critical point
Emergent directionof AdS4 Brian Swingle, arXiv:0905.1317
Friday, October 28, 2011
ρA = TrBρ = density matrix of region A
Entanglement entropy SEE = −Tr (ρA ln ρA)
B
A
Entanglement entropy
Friday, October 28, 2011
depth ofentanglement
D-dimensionalspace
Entanglement entropy
A
Friday, October 28, 2011
depth ofentanglement
D-dimensionalspace
Entanglement entropy
A
Draw a surface which intersects the minimal number of links
Emergent directionof AdS4
Friday, October 28, 2011
The entanglement entropy of a region A on the boundary equals the minimal area of a surface in the higher-dimensional
space whose boundary co-incides with that of A.
This can be seen both the string and tensor-network pictures
Entanglement entropy
S. Ryu and T. Takayanagi, Phys. Rev. Lett. 96, 18160 (2006).Brian Swingle, arXiv:0905.1317
Friday, October 28, 2011
Field theories in D + 1 spacetime dimensions are
characterized by couplings g which obey the renor-
malization group equation
udg
du= β(g)
where u is the energy scale. The RG equation is
local in energy scale, i.e. the RHS does not depend
upon u.
Friday, October 28, 2011
u
Friday, October 28, 2011
uKey idea: ⇒ Implement u as an extra dimen-sion, and map to a local theory in D + 2 spacetimedimensions.
Friday, October 28, 2011
At the RG fixed point, β(g) = 0, the D + 1 di-mensional field theory is invariant under the scaletransformation
xµ → xµ/b , u → b u
Friday, October 28, 2011
At the RG fixed point, β(g) = 0, the D + 1 di-mensional field theory is invariant under the scaletransformation
xµ → xµ/b , u → b u
This is an invariance of the metric of the theory in
D + 2 dimensions. The unique solution is
ds2 =
� u
L
�2dxµdxµ + L2 du
2
u2.
Or, using the length scale z = L2/u
ds2 = L2 dxµdxµ + dz2
z2.
This is the space AdSD+2, and L is the AdS radius.
Friday, October 28, 2011
u
Friday, October 28, 2011
z
J. McGreevy, arXiv0909.0518
Friday, October 28, 2011
z
AdSD+2RD,1
Minkowski
CFTD+1
J. McGreevy, arXiv0909.0518
Friday, October 28, 2011
λλc
Quantum critical point with non-local entanglement in spin wavefunction
=1√2
����↑↓�−
��� ↓↑��
Friday, October 28, 2011
Classicalspin
waves
Dilutetriplon
gas
Quantumcritical
Neel orderPressure in TlCuCl3
S. Sachdev and J. Ye, Phys. Rev. Lett. 69, 2411 (1992).A. V. Chubukov, S. Sachdev, and J. Ye, Phys. Rev. B 49, 11919 (1994).
Friday, October 28, 2011
A 2+1 dimensional system at its
quantum critical point
AdS4-Schwarzschild black-brane
AdS/CFT correspondence at non-zero temperatures
Friday, October 28, 2011
A 2+1 dimensional system at its
quantum critical point
Black-brane at temperature of
2+1 dimensional quantum critical
system
AdS4-Schwarzschild black-brane
AdS/CFT correspondence at non-zero temperatures
Friday, October 28, 2011
A 2+1 dimensional system at its
quantum critical point
Black-brane at temperature of
2+1 dimensional quantum critical
system
AdS4-Schwarzschild black-brane
AdS/CFT correspondence at non-zero temperatures
Friction of quantum criticality = waves
falling into black brane Friday, October 28, 2011
A 2+1 dimensional system at its
quantum critical point
Black-brane at temperature of
2+1 dimensional quantum critical
system
AdS4-Schwarzschild black-brane
AdS/CFT correspondence at non-zero temperatures
Provides successful description of many properties of quantum
critical points at non-zero temperatures
Friday, October 28, 2011
1. Quantum critical points and string theory Entanglement and emergent dimensions
2. High temperature superconductors and strange metals Holography of compressible quantum phases
Outline
Friday, October 28, 2011
1. Quantum critical points and string theory Entanglement and emergent dimensions
2. High temperature superconductors and strange metals Holography of compressible quantum phases
Outline
Friday, October 28, 2011
The cuprate superconductors
DavisFriday, October 28, 2011
Ground state has long-range Néel order
Square lattice antiferromagnet
H =�
�ij�
Jij�Si · �Sj
Friday, October 28, 2011
Hole-doped
Electron-doped
Friday, October 28, 2011
Hole-doped
Electron-doped
Electron-doped cuprate superconductors
Friday, October 28, 2011
Hole-doped
Electron-doped
Resistivity∼ ρ0 +ATn
Electron-doped cuprate superconductors
Figure prepared by K. Jin and and R. L. Greenebased on N. P. Fournier, P. Armitage, and
R. L. Greene, Rev. Mod. Phys. 82, 2421 (2010).
AF
Friday, October 28, 2011
Hole-doped
Electron-doped
Resistivity∼ ρ0 +ATn
Electron-doped cuprate superconductors
Figure prepared by K. Jin and and R. L. Greenebased on N. P. Fournier, P. Armitage, and
R. L. Greene, Rev. Mod. Phys. 82, 2421 (2010).
AF
Friday, October 28, 2011
Hole-doped
Electron-doped
Resistivity∼ ρ0 +ATn
Electron-doped cuprate superconductors
Figure prepared by K. Jin and and R. L. Greenebased on N. P. Fournier, P. Armitage, and
R. L. Greene, Rev. Mod. Phys. 82, 2421 (2010).
StrangeMetal
AF
Friday, October 28, 2011
Ishida, Nakai, and HosonoarXiv:0906.2045v1
0 0.02 0.04 0.06 0.08 0.10 0.12
150
100
50
0
SC
Ort
AFM Ort/
Tet
S. Nandi, M. G. Kim, A. Kreyssig, R. M. Fernandes, D. K. Pratt, A. Thaler, N. Ni, S. L. Bud'ko, P. C. Canfield, J. Schmalian, R. J. McQueeney, A. I. Goldman,
Physical Review Letters 104, 057006 (2010).
Iron pnictides: a new class of high temperature superconductors
Friday, October 28, 2011
TSDW Tc
T0
2.0
0
!"
1.0 SDW
Superconductivity
BaFe2(As1-xPx)2
Temperature-doping phase diagram of the iron pnictides:
Resistivity∼ ρ0 +ATα
S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido, H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda,
Physical Review B 81, 184519 (2010)
AF
Friday, October 28, 2011
TSDW Tc
T0
2.0
0
!"
1.0 SDW
Superconductivity
BaFe2(As1-xPx)2
Temperature-doping phase diagram of the iron pnictides:
Resistivity∼ ρ0 +ATα
S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido, H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda,
Physical Review B 81, 184519 (2010)
AF
Friday, October 28, 2011
TSDW Tc
T0
2.0
0
!"
1.0 SDW
Superconductivity
BaFe2(As1-xPx)2
Temperature-doping phase diagram of the iron pnictides:
Resistivity∼ ρ0 +ATα
S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido, H. Ikeda, H. Takeya, K. Hirata, T. Terashima, and Y. Matsuda,
Physical Review B 81, 184519 (2010)
StrangeMetal
AF
Friday, October 28, 2011
Temperature-pressure phase diagram of an organic superconductor
N. Doiron-Leyraud, P. Auban-Senzier, S. Rene de Cotret, A. Sedeki, C. Bourbonnais, D. Jerome, K. Bechgaard, and Louis Taillefer, Physical Review B 80, 214531 (2009)
AF
Friday, October 28, 2011
2
Generally, the ground state of a Ce heavy-fermion sys-tem is determined by the competition of the indirect Ru-derman Kittel Kasuya Yosida (RKKY) interaction whichprovokes magnetic order of localized moments mediatedby the light conduction electrons and the Kondo interac-tion. This last local mechanism causes a paramagneticground state due the screening of the local moment ofthe Ce ion by the conduction electrons. Both interac-tions depend critically on the hybridization of the 4felectrons with the conduction electrons. High pressure isan ideal tool to tune the hybridization and the positionof the 4f level with respect to the Fermi level. Thereforehigh pressure experiments are ideal to study the criti-cal region where both interactions are of the same orderand compete. To understand the quantum phase transi-tion from the antiferromagnetic (AF) state to the para-magnetic (PM) state is actually one of the fundamen-tal questions in solid state physics. Di!erent theoreticalapproaches exist to model the magnetic quantum phasetransition such as spin-fluctuation theory of an itinerantmagnet [10–12], or a new so-called ’local’ quantum criti-cal scenario [13, 14]. Another e"cient source to preventlong range antiferromagnetic order is given by the va-lence fluctuations between the trivalent and the tetrava-lent configuration of the cerium ions [15].
The interesting point is that in these strongly corre-lated electron systems the same electrons (or renormal-ized quasiparticles) are responsible for both, magnetismand superconductivity. The above mentioned Ce-115family is an ideal model system, as it allows to studyboth, the quantum critical behavior and the interplay ofthe magnetic order with a superconducting state. Espe-cially, as we will be shown below, unexpected observa-tions will be found, if a magnetic field is applied in thecritical pressure region.
PRESSURE-TEMPERATURE PHASE DIAGRAM
In this article we concentrate on the compoundCeRhIn5. At ambient pressure the RKKY interactionis dominant in CeRhIn5 and magnetic order appears atTN = 3.8 K. However, the ordered magnetic moment ofµ = 0.59µB at 1.9 K is reduced of about 30% in com-parison to that of Ce ion in a crystal field doublet with-out Kondo e!ect [17]. Compared to other heavy fermioncompounds at p = 0 the enhancement of the Sommerfeldcoe"cient of the specific heat (! = 52 mJ mol!1K!2) [18]and the cylotron masses of electrons on the extremal or-bits of the Fermi surface is rather moderate [19, 20]. Thetopologies of the Fermi surfaces of CeRhIn5 are cylin-drical and almost identical to that of LaRhIn5 which isthe non 4f isostructural reference compound. From thisit can be concluded that the 4f electrons in CeRhIn5
are localized and do not contribute to the Fermi volume[19, 20].
By application of pressure, the system can be tunedthrough a quantum phase transition. The Neel temper-
FIG. 2. Pressure–temperature phase diagram of CeRhIn5 atzero magnetic field determined from specific heat measure-ments with antiferromagnetic (AF, blue) and superconduct-ing phases (SC, yellow). When Tc < TN a coexistence phaseAF+SC exist. When Tc > TN the antiferromagnetic order isabruptly suppressed. The blue square indicate the transitionfrom SC to AF+SC after Ref. 16.
ature shows a smooth maximum around 0.8 GPa andis monotonously suppressed for higher pressures. How-ever, CeRhIn5 is also a superconductor in a large pres-sure region from about 1.3 to 5 GPa. It has been shownthat when the superconducting transition temperatureTc > TN the antiferromagnetic order is rapidly sup-pressed (see figure 2) and vanishes at a lower pressurethan that expected from a linear extrapolation to T = 0.Thus the pressure where Tc = TN defines a first criticalpressure p!
c and clearly just above p!c anitferromagnetism
collapses. The intuitive picture is that the opening of asuperconducting gap on large parts of the Fermi surfaceabove p!
c impedes the formation of long range magneticorder. A coexisting phase AF+SC in zero magnetic fieldseems only be formed if on cooling first the magnetic or-der is established. We will discuss below the microscopicevidence of an homogeneous AF+SC phase.
At ambient pressure CeRhIn5 orders in an incommen-surate magnetic structure [21] with an ordering vectorof qic=(0.5, 0.5, ") and " = 0.297 that is a magneticstructure with a di!erent periodicity than the one of thelattice. Generally, an incommensurate magnetic struc-ture is not favorable for superconductivity with d wavesymmetry, which is realized in CeRhIn5 above p!
c [22].Neutron scattering experiments under high pressure donot give conclusive evidence of the structure under pres-sures up to 1.7 GPa which is the highest pressure studiedup to now [23–25]. The result is that at 1.7 GPa the in-commensurability has changed to " ! 0.4. The main dif-ficulty in these experiments with large sample volume isto ensure the pressure homogeneity. Near p!
c the controlof a perfect hydrostaticity is a key issue as the materialreacts quite opposite on uniaxial strain applied along thec and a axis.
From recent nuclear quadrupol resonance (NQR) data
G. Knebel, D. Aoki, and J. Flouquet, arXiv:0911.5223.Tuson Park, F. Ronning, H. Q. Yuan, M. B. Salamon, R. Movshovich, J. L. Sarrao, and J. D. Thompson, Nature 440, 65 (2006)
Temperature-pressure phase diagram of an heavy-fermion superconductor
Friday, October 28, 2011
Fermi surface+antiferromagnetism
The electron spin polarization obeys�
�S(r, τ)�
= �ϕ(r, τ)eiK·r
where K is the ordering wavevector.
+
Metal with “large” Fermi surface
Friday, October 28, 2011
Metal with “large” Fermi surface
Fermi surface+antiferromagnetism
��ϕ� = 0
Metal with electron and hole pockets
Increasing SDW order
��ϕ� �= 0
Increasing interactionFermi surface reconstruction and
onset of antiferromagnetism
AF
Friday, October 28, 2011
Nd2−xCexCuO4
T. Helm, M. V. Kartsovnik, M. Bartkowiak, N. Bittner,
M. Lambacher, A. Erb, J. Wosnitza, and R. Gross,
Phys. Rev. Lett. 103, 157002 (2009).
Quantum oscillations
Increasing SDW order
s
Friday, October 28, 2011
Metal with “large” Fermi surface
Fermi surface+antiferromagnetism
��ϕ� = 0
Metal with electron and hole pockets
Increasing SDW order
��ϕ� �= 0
s
AF
Friday, October 28, 2011
Metal with “large” Fermi surface
Fermi surface+antiferromagnetism
��ϕ� = 0
Metal with electron and hole pockets
Increasing SDW order
��ϕ� �= 0
s
Quantum critical point realizes a strong-coupled non-Fermi liquid
compressible phaseAF
Friday, October 28, 2011
T
s
Fermi liquid with “large”
Fermi surface
AF metal with “small”
Fermi pocketsIncreasing SDW order
Friday, October 28, 2011
T
s
Fermi liquid with “large”
Fermi surface
AF metal with “small”
Fermi pocketsIncreasing SDW order
Strange metal ?
D.J. Scalapino, E. Loh, and J.E. Hirsch, Phys. Rev. B 34, 8190 (1986)Ar. Abanov, A. V. Chubukov, and A. M. Finkel'stein, Europhys. Lett. 54, 488 (2001)
S. Raghu, S.A. Kivelson, and D.J. Scalapino, Phys. Rev. B 81, 224505 (2010)M. A. Metlitski and S. Sachdev, Phys. Rev. B 85, 075127 (2010)
Superconductor ✓
DavisFriday, October 28, 2011
Challenge to string theory:
Describe quantum critical points and the phases of a compressible metallic systems
Friday, October 28, 2011
Challenge to string theory:
Describe quantum critical points and the phases of a compressible metallic systems
Can we obtain holographic theories of superfluids and Fermi liquids?
Friday, October 28, 2011
Challenge to string theory:
Describe quantum critical points and the phases of a compressible metallic systems
Can we obtain holographic theories of superfluids and Fermi liquids?
Yes
Friday, October 28, 2011
Challenge to string theory:
Describe quantum critical points and the phases of a compressible metallic systems
Can we obtain holographic theories of superfluids and Fermi liquids?
Yes
Are there any other compressible phases like strange metals?
Friday, October 28, 2011
Challenge to string theory:
Describe quantum critical points and the phases of a compressible metallic systems
Can we obtain holographic theories of superfluids and Fermi liquids?
Yes
Are there any other compressible phases like strange metals? Yes....
Friday, October 28, 2011
Holographic representation: AdS4
A 2+1 dimensional
CFTat T=0
Friday, October 28, 2011
++
+
+
+ +Electric flux
There is “charge” density on the boundary, which sources an electric field in the bulk
Holographic theory of a metalS. SachdevarXiv:1107.5321
Friday, October 28, 2011
1. Quantum critical points and string theory Entanglement and emergent dimensions
2. High temperature superconductors and strange metals Holography of compressible quantum phases
Conclusions
Friday, October 28, 2011