Quantum criticality

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Quantum criticality and the phase diagram of the
cuprates
Talk online sachdev.physics.harvard.edu
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Victor Galitski, Maryland Ribhu Kaul, Harvard
Kentucky Max Metlitski, Harvard Eun Gook Moon,
Harvard Yang Qi, Harvard Cenke Xu, Harvard
Santa Barbara
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The cuprate superconductors
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Square lattice antiferromagnet
Ground state has long-range Néel order
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Central ingredients in cuprate phase diagram
antiferromagnetism, superconductivity, and change
in Fermi surface
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Crossovers in transport properties of hole-doped
cuprates
N. E. Hussey, J. Phys Condens. Matter 20,
123201 (2008)
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Crossovers in transport properties of hole-doped
cuprates
Strange metal
Pseudo- gap
N. E. Hussey, J. Phys Condens. Matter 20,
123201 (2008)
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Square lattice antiferromagnet
Ground state has long-range Néel order
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Square lattice antiferromagnet
J
J/
Weaken some bonds to induce spin entanglement in
a new quantum phase
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Square lattice antiferromagnet
J
J/
Ground state is a quantum paramagnet with spins
locked in valence bond singlets
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Pressure in TlCuCl3
Christian Ruegg, Bruce Normand, Masashige
Matsumoto, Albert Furrer, Desmond McMorrow, Karl
Kramer, HansUlrich Gudel, Severian Gvasaliya,
Hannu Mutka, and Martin Boehm, Phys. Rev. Lett.
100, 205701 (2008)
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Canonical quantum critical phase diagram of
coupled-dimer antiferromagnet
S. Sachdev and J. Ye, Phys. Rev. Lett. 69, 2411
(1992).
Christian Ruegg et al. , Phys. Rev. Lett. 100,
205701 (2008)
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Crossovers in transport properties of hole-doped
cuprates
Strange metal
Pseudo- gap
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Crossovers in transport properties of hole-doped
cuprates
Strange metal
S. Sachdev and J. Ye, Phys. Rev. Lett. 69, 2411
(1992). A. J. Millis, Phys. Rev. B 48,
7183 (1993). C. M. Varma, Phys. Rev. Lett.
83, 3538 (1999).
Pseudo- gap
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Only candidate quantum critical point observed at
low T
Strange metal
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Large Fermi surfaces in cuprates
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Spin density wave theory
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Spin density wave theory
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Hole-doped cuprates
Hole pockets
Electron pockets
S. Sachdev, A. V. Chubukov, and A. Sokol, Phys.
Rev. B 51, 14874 (1995). A. V. Chubukov and D.
K. Morr, Physics Reports 288, 355 (1997).
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Hole-doped cuprates
Hole pockets
Electron pockets
S. Sachdev, A. V. Chubukov, and A. Sokol, Phys.
Rev. B 51, 14874 (1995). A. V. Chubukov and D.
K. Morr, Physics Reports 288, 355 (1997).
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Spin density wave theory in hole-doped cuprates
Incommensurate order in YBa2Cu3O6x
A. J. Millis and M. R. Norman, Physical Review B
76, 220503 (2007). N. Harrison, Physical
Review Letters 102, 206405 (2009).
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Electron-doped cuprates
D. Senechal and A.-M. S. Tremblay, Physical
Review Letters 92, 126401 (2004) J. Lin, and A.
J. Millis, Physical Review B 72, 214506 (2005).
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Photoemission in NCCO
N. P. Armitage et al., Phys. Rev. Lett. 88,
257001 (2002).
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Quantum oscillations
T. Helm, M. V. Kartsovnik, M. Bartkowiak, N.
Bittner, M. Lambacher, A. Erb, J. Wosnitza, and
R. Gross, Phys. Rev. Lett. 103, 157002 (2009).
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Quantum oscillations
Nature 450, 533 (2007)
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Quantum oscillations
Nature 450, 533 (2007)
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Theory of quantum criticality in the cuprates
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Evidence for connection between linear
resistivity and stripe-ordering in a cuprate with
a low Tc
Linear temperature dependence of resistivity and
change in the Fermi surface at the pseudogap
critical point of a high-Tc superconductor R.
Daou, Nicolas Doiron-Leyraud, David LeBoeuf, S.
Y. Li, Francis Laliberté, Olivier Cyr-Choinière,
Y. J. Jo, L. Balicas, J.-Q. Yan, J.-S. Zhou, J.
B. Goodenough Louis Taillefer, Nature Physics
5, 31 - 34 (2009)
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Theory of quantum criticality in the cuprates
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Theory of quantum criticality in the cuprates
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Theory of quantum criticality in the cuprates
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Theory of quantum criticality in the cuprates
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Theory of quantum criticality in the cuprates
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Theory of quantum criticality in the cuprates
Criticality of the coupled dimer antiferromagnet
at xxs
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Theory of quantum criticality in the cuprates
Criticality of the topological change in Fermi
surface at xxm
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Hc2
Quantum oscillations
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Hsdw
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Hsdw
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B. Lake, H. M. Rønnow, N. B. Christensen, G.
Aeppli, K. Lefmann, D. F. McMorrow, P.
Vorderwisch, P. Smeibidl, N. Mangkorntong, T.
Sasagawa, M. Nohara, H. Takagi, and T. E. Mason,
Nature 415, 299 (2002)
B. Lake, G. Aeppli, K. N. Clausen, D. F.
McMorrow, K. Lefmann, N. E. Hussey, N.
Mangkorntong, M. Nohara, H. Takagi, T. E.
Mason, and A. Schröder Science 291, 1759 (2001).
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J. Chang, Ch. Niedermayer, R. Gilardi,
N.B. Christensen, H.M. Ronnow,
D.F. McMorrow, M. Ay, J. Stahn, O. Sobolev,
A. Hiess, S. Pailhes, C. Baines, N. Momono, M.
Oda, M. Ido, and J. Mesot, Physical Review B 78,
104525 (2008).
J. Chang, N. B. Christensen, Ch.
Niedermayer, K. Lefmann, H. M. Roennow, D.
F. McMorrow, A. Schneidewind, P. Link, A.
Hiess, M. Boehm, R. Mottl, S. Pailhes, N.
Momono, M. Oda, M. Ido, and J. Mesot, Phys. Rev.
Lett. 102, 177006 (2009).
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D. Haug, V. Hinkov, A. Suchaneck, D. S. Inosov,
N. B. Christensen, Ch. Niedermayer, P. Bourges,
Y. Sidis, J. T. Park, A. Ivanov, C. T. Lin, J.
Mesot, and B. Keimer, Phys. Rev. Lett. 103,
017001 (2009)
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E. M. Motoyama, G. Yu, I. M. Vishik, O. P. Vajk,
P. K. Mang, and M. Greven,Nature 445, 186 (2007).
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V. Galitski and S. Sachdev, Physical Review B
79, 134512 (2009).
Eun Gook Moon and S. Sachdev, Physical Review B
80, 035117 (2009).
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V. Galitski and S. Sachdev, Physical Review B
79, 134512 (2009).
Eun Gook Moon and S. Sachdev, Physical Review B
80, 035117 (2009).
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Similar phase diagram for CeRhIn5
G. Knebel, D. Aoki, and J. Flouquet,
arXiv0911.5223
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Hertz-Moriya-Millis (HMM) theory
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Hertz-Moriya-Millis (HMM) theory
Ar. Abanov and A.V. Chubukov, Phys. Rev. Lett.
93, 255702 (2004).
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Max Metlitski
M. Metlitski and S. Sachdev, to appear Ar.
Abanov, A.V. Chubukov, and J. Schmalian,
Advances in Physics 52, 119 (2003)
Sung-Sik Lee, arXiv0905.4532.
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Hole-doped cuprates
Hole pockets
Electron pockets
S. Sachdev, A. V. Chubukov, and A. Sokol, Phys.
Rev. B 51, 14874 (1995). A. V. Chubukov and D.
K. Morr, Physics Reports 288, 355 (1997).
75
Hole-doped cuprates
Hole pockets
Electron pockets
S. Sachdev, A. V. Chubukov, and A. Sokol, Phys.
Rev. B 51, 14874 (1995). A. V. Chubukov and D.
K. Morr, Physics Reports 288, 355 (1997).
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Y. Huh and S. Sachdev, Phys. Rev. B 78, 064512
(2008).
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RG-improved Migdal-Eliashberg theory
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RG-improved Migdal-Eliashberg theory
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RG-improved Migdal-Eliashberg theory
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RG-improved Migdal-Eliashberg theory
Dynamical Nesting
Bare Fermi surface
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RG-improved Migdal-Eliashberg theory
Dynamical Nesting
Dressed Fermi surface
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RG-improved Migdal-Eliashberg theory
Dynamical Nesting
Bare Fermi surface
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RG-improved Migdal-Eliashberg theory
Dynamical Nesting
Dressed Fermi surface
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RG-improved Migdal-Eliashberg theory
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Dangerous
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R. Shankar, Rev. Mod. Phys. 66, 129 (1994). S. W.
Tsai, A. H. Castro Neto, R. Shankar, and D. K.
Campbell, Phys. Rev. B 72, 054531 (2005).
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Graph is planar after turning fermion propagators
also into double lines by drawing additional
dotted single line loops for each fermion loop
Sung-Sik Lee, arXiv0905.4532
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A consistent analysis requires resummation of all
planar graphs
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Theory for the onset of spin density wave order
in metals is strongly coupled in two dimensions
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Theory of underdoped cuprates
S. Sachdev, A. V. Chubukov, and A. Sokol, Phys.
Rev. B 51, 14874 (1995). A. V. Chubukov and D.
K. Morr, Physics Reports 288, 355 (1997).
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Theory of underdoped cuprates
H. J. Schulz, Physical Review Letters 65, 2462
(1990) B. I. Shraiman and E. D. Siggia, Physical
Review Letters 61, 467 (1988). J. R. Schrieffer,
Journal of Superconductivity 17, 539 (2004)
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Theory of underdoped cuprates
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Theory of underdoped cuprates
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Quantum phase transitions in metal
S. Sachdev, M. A. Metlitski, Y. Qi, and C. Xu,
Physical Review B 80, 155129 (2009)
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Quantum phase transitions in metal
Fermi liquid phases
S. Sachdev, M. A. Metlitski, Y. Qi, and C. Xu,
Physical Review B 80, 155129 (2009)
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Quantum phase transitions in metal
S. Sachdev, M. A. Metlitski, Y. Qi, and C. Xu,
Physical Review B 80, 155129 (2009)
108
Quantum phase transitions in metal
S. Sachdev, M. A. Metlitski, Y. Qi, and C. Xu,
Physical Review B 80, 155129 (2009)
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Theory of underdoped cuprates
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Theory of underdoped cuprates
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R. K. Kaul, Y. B. Kim, S. Sachdev, and T.
Senthil, Nature Physics 4, 28 (2008)
Y. Qi and S. Sachdev, arXiv0912.xxxx
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Theory of underdoped cuprates
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Theory of underdoped cuprates
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R. K. Kaul, M. Metlitksi, S. Sachdev, and Cenke
Xu, Phys. Rev. B 78, 045110 (2008).
V. Galitski and S. Sachdev, Physical Review B
79, 134512 (2009).
Eun Gook Moon and S. Sachdev, Physical Review B
80, 035117 (2009).
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-2e bosons at antinodes, e fermion arcs at
nodes, and proximity Josephson coupling
Similar features in our theory
V. Galitski and S. Sachdev, Physical Review B 79,
134512 (2009).
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Naturally formulated in route B theory of
fluctuating Fermi pockets
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VBS and/or nematic
Onset of superconductivity induces confinement
R. K. Kaul, M. Metlitksi, S. Sachdev, and Cenke
Xu, Physical Review B 78, 045110 (2008).
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Nature Physics 4, 696 (2008)
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S. A. Kivelson, E. Fradkin, and V. J. Emery,
Nature 393, 550 (1998).
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)
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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, Nature, in press
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VBS and/or nematic
Onset of superconductivity induces confinement
R. K. Kaul, M. Metlitksi, S. Sachdev, and Cenke
Xu, Physical Review B 78, 045110 (2008).
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Conclusions
Identified quantum criticality in cuprate
superconductors with a critical point at optimal
doping associated with onset of spin density wave
order in a metal
Elusive optimal doping quantum critical point has
been hiding in plain sight. It is shifted to
lower doping by the onset of superconductivity
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Conclusions
Theory for the onset of spin density wave order
in metals is strongly coupled in two dimensions