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Condensed matter physicsand
string theory
HARVARDTalk online: sachdev.physics.harvard.edu
Wednesday, December 30, 2009
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One, two, three.... particles(quarks, gluons, gravitons....)
Comfort zone of string theory
Wednesday, December 30, 2009
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One, two, three.... particles(quarks, gluons, gravitons....)
Can have strong interactions during scattering events
Comfort zone of string theory
Wednesday, December 30, 2009
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One, two, three.... particles(quarks, gluons, gravitons....)
Can have strong interactions during scattering events
Works in curved spacetime(near black holes)
Comfort zone of string theory
Wednesday, December 30, 2009
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One, two, three.... particles(quarks, gluons, gravitons....)
Can have strong interactions during scattering events
Works in curved spacetime(near black holes)
Comfort zone of string theory
Lots of supersymmetry
Wednesday, December 30, 2009
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One, two, three.... particles(quarks, gluons, gravitons....)
Can have strong interactions during scattering events
Works in curved spacetime(near black holes)
Works at critical points where particle spectrum changes
(AdS/CFT correspondence)
Comfort zone of string theory
Lots of supersymmetry
Wednesday, December 30, 2009
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Infinite numbers of particles (non-zero density)with weak interactions:
electrons, trapped cold atoms
Comfort zone of condensed matter
Wednesday, December 30, 2009
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Comfort zone of condensed matter
Quantum phases with universal low energy properties, independent of
most interaction details:Fermi liquids, solids, superfluids
Infinite numbers of particles (non-zero density)with weak interactions:
electrons, trapped cold atoms
Wednesday, December 30, 2009
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x
y
In momentum space, Fermi surfaceseparates occupied and empty electron states
Fermi Liquid
Wednesday, December 30, 2009
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Ultracold 87Rbatoms - bosons
Wednesday, December 30, 2009
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Comfort zone of condensed matter
Quantum phases with universal low energy properties, independent of
most interaction details:Fermi liquids, solids, superfluids
Infinite numbers of particles (non-zero density)with weak interactions:
electrons, trapped cold atoms
Wednesday, December 30, 2009
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Fermi liquid theory (and its cousins) allow adiabatic continuation to strong interaction regime
Quantum phases with universal low energy properties, independent of
most interaction details:Fermi liquids, solids, superfluids
Infinite numbers of particles (non-zero density)with weak interactions:
electrons, trapped cold atoms
Comfort zone of condensed matter
Wednesday, December 30, 2009
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Move out of comfort zones,
and use tools developed in both fields
Wednesday, December 30, 2009
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1. Electrical resistance at non-zero temperature near quantum critical points
2. Zero temperature quantum phase transitions of Fermi liquids
Strong coupling problems in condensed matter
Wednesday, December 30, 2009
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1. Electrical resistance at non-zero temperature near quantum critical points
2. Zero temperature quantum phase transitions of Fermi liquids
Strong coupling problems in condensed matter
Wednesday, December 30, 2009
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M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
Ultracold 87Rbatoms - bosons
Superfluid-insulator transition
Wednesday, December 30, 2009
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g
T
gc
0
InsulatorSuperfluid
Quantumcritical
TKT
CFT at T>0
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Quantum critical transport
Quantum “perfect fluid”with shortest possiblerelaxation time, τR
τR � �kBT
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).Wednesday, December 30, 2009
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Quantum critical transport Transport co-oefficients not determined
by collision rate, but byuniversal constants of nature
Electrical conductivity
K. Damle and S. Sachdev, Phys. Rev. B 56, 8714 (1997).
σ =4e2
h× [Universal constant O(1) ]
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Requires long-time limit of correlations at non-zero
temperature.
Cannot be obtained numerically by computers even for the simplest
quantum problems. Is the sum of an exponentially large number of terms
which oscillate in sign.
Wednesday, December 30, 2009
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AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
Maldacena, Gubser, Klebanov, Polyakov, Witten
3+1 dimensional AdS space A 2+1
dimensional system at its
quantum critical point
Wednesday, December 30, 2009
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AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
Maldacena, Gubser, Klebanov, Polyakov, Witten
3+1 dimensional AdS space Quantum
criticality in 2+1
dimensionsBlack hole temperature
= temperature of quantum criticality
Wednesday, December 30, 2009
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AdS/CFT correspondenceThe quantum theory of a black hole in a 3+1-dimensional negatively curved AdS universe is
holographically represented by a CFT (the theory of a quantum critical point) in 2+1 dimensions
3+1 dimensional AdS space Quantum
criticality in 2+1
dimensionsFriction of quantum
criticality = waves
falling into black hole
Kovtun, Policastro, SonWednesday, December 30, 2009
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1. Electrical resistance at non-zero temperature near quantum critical points
2. Zero temperature quantum phase transitions of Fermi liquids
Strong coupling problems in condensed matter
Wednesday, December 30, 2009
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1. Electrical resistance at non-zero temperature near quantum critical points
2. Zero temperature quantum phase transitions of Fermi liquids
Strong coupling problems in condensed matter
Wednesday, December 30, 2009
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Fermi surface with full square lattice symmetry
Quantum criticality of Pomeranchuk instability
x
y
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Spontaneous elongation along x direction:Ising order parameter φ > 0.
Quantum criticality of Pomeranchuk instability
x
y
Wednesday, December 30, 2009
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Quantum criticality of Pomeranchuk instability
x
y
Spontaneous elongation along y direction:Ising order parameter φ < 0.
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λλc
Pomeranchuk instability as a function of coupling λ
�φ� = 0�φ� �= 0
Quantum criticality of Pomeranchuk instability
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A φ fluctuation at wavevector �q couples most efficiently tofermions near ±�k0.
Expand fermion kinetic energy at wavevectors about �k0Infinite set of 2+1 dimensional quantum-critical field theories,
one for each pair of points on the Fermi surface.Ward identities ensure consistency
of redundant description
M. A. Metlitksi and S. Sachdev, to appear
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Sung-Sik Lee, Physical Review B 80, 165102 (2009)
All planar graphs of ψ+ aloneare as important as the leading
term
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Conformal field theoryin 2+1 dimensions at T = 0
Einstein gravityon AdS4
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Conformal field theoryin 2+1 dimensions at T > 0,
with a non-zero chemical potential, µand applied magnetic field, B
Einstein gravity on AdS4
with a Reissner-Nordstromblack hole carrying electric
and magnetic chargesWednesday, December 30, 2009
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T. Faulkner, H. Liu, J. McGreevy, and D. Vegh, arXiv:0907.2694F. Denef, S. Hartnoll, and S. Sachdev, arXiv:0908.1788
Examine free energy and Green’s function of a probe particle
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Green’s function of a fermion
T. Faulkner, H. Liu, J. McGreevy, and D. Vegh,
arXiv:0907.2694
G(k,ω) ≈ 1ω − vF (k − kF )− iωθ(k)
See also M. Cubrovic, J. Zaanen, and K. Schalm, arXiv:0904.1993
F. Denef, S. Hartnoll, and S. Sachdev, arXiv:0908.1788
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Green’s function of a fermion
G(k,ω) ≈ 1ω − vF (k − kF )− iωθ(k)
Similar to non-Fermi liquid theories of Fermi surfaces coupled to gauge fields, and at quantum critical points
T. Faulkner, H. Liu, J. McGreevy, and D. Vegh,
arXiv:0907.2694
Wednesday, December 30, 2009