Ribhu Kaul

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Destruction of Neel order in the cuprates by
electron doping
Ribhu Kaul Cenke Xu Subir Sachdev
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Phase diagram of electron-doped superconductors
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Spin correlations in the electron-doped
high-transition-temperature superconductor
Nd2-xCexCuO4 E. M. Motoyama, G. Yu, I. M. Vishik,
O. P. Vajk, P. K. Mang and M. Greven Nature 445,
186-189(11 January 2007)
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Photoemission
N. P. Armitage et al., Phys. Rev. Lett. 88,
257001 (2002).
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Photoemission
N. P. Armitage et al., Phys. Rev. Lett. 88,
257001 (2002).
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Photoemission
8 zero crossings not observed
N. P. Armitage et al., Phys. Rev. Lett. 88,
257001 (2002).
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Outline
1. Destruction of Neel order in the insulator
Deconfined criticality 2. Destruction of
Neel order in the metal Doublon metal -
an algebraic charge liquid 3. Destruction of
Neel order in the superconductor Deconfined
critical transition to a large Fermi surface
state
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Outline
1. Destruction of Neel order in the insulator
Deconfined criticality 2. Destruction of
Neel order in the metal Doublon metal -
an algebraic charge liquid 3. Destruction of
Neel order in the superconductor Deconfined
critical transition to a large Fermi surface
state
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Square lattice antiferromagnet
Ground state has long-range Néel order
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Square lattice antiferromagnet
Destroy Neel order by perturbations which
preserve full square lattice symmetry e.g.
second-neighbor or ring exchange.
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Square lattice antiferromagnet
Destroy Neel order by perturbations which
preserve full square lattice symmetry e.g.
second-neighbor or ring exchange.
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LGW theory for quantum criticality
S. Chakravarty, B.I. Halperin, and D.R. Nelson,
Phys. Rev. B 39, 2344 (1989)
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LGW theory for quantum criticality
A.V. Chubukov, S. Sachdev, and J.Ye, Phys. Rev. B
49, 11919 (1994)
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LGW theory for quantum criticality
A.V. Chubukov, S. Sachdev, and J.Ye, Phys. Rev. B
49, 11919 (1994)
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There is no state with a gapped, stable S1
quasiparticle and no broken symmetries
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There is no state with a gapped, stable S1
quasiparticle and no broken symmetries
Liquid of valence bonds has fractionalized
S1/2 excitations
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There is no state with a gapped, stable S1
quasiparticle and no broken symmetries
Liquid of valence bonds has fractionalized
S1/2 excitations
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There is no state with a gapped, stable S1
quasiparticle and no broken symmetries
Liquid of valence bonds has fractionalized
S1/2 excitations
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There is no state with a gapped, stable S1
quasiparticle and no broken symmetries
Liquid of valence bonds has fractionalized
S1/2 excitations
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There is no state with a gapped, stable S1
quasiparticle and no broken symmetries
Liquid of valence bonds has fractionalized
S1/2 excitations
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There is no state with a gapped, stable S1
quasiparticle and no broken symmetries
Liquid of valence bonds has fractionalized
S1/2 excitations
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Possible theory for fractionalization and
topological order
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Possible theory for fractionalization and
topological order
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Possible theory for fractionalization and
topological order
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Possible theory for fractionalization and
topological order
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Possible theory for fractionalization and
topological order
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Possible theory for fractionalization and
topological order
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Quantum theory for destruction of Neel order
Partition function on cubic lattice in spacetime
LGW theory weights in partition function are
those of a classical ferromagnet at a
temperature g
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Missing ingredient Spin Berry Phases
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Quantum theory for destruction of Neel order
Partition function on cubic lattice in spacetime
LGW theory weights in partition function are
those of a classical ferromagnet at a
temperature g
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Quantum theory for destruction of Neel order
Coherent state path integral on cubic lattice in
spacetime
Modulus of weights in partition function those
of a classical ferromagnet at a temperature g
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Quantum theory for destruction of Neel order
Partition function on cubic lattice
S. Sachdev and K. Park, Annals of Physics, 298,
58 (2002)
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Quantum theory for destruction of Neel order
Partition function on cubic lattice
Partition function expressed as a gauge theory of
spinor degrees of freedom
S. Sachdev and K. Park, Annals of Physics, 298,
58 (2002)
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or
?
g
0
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Monopole fugacity
Arovas-Auerbach state
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Phase diagram of S1/2 square lattice
antiferromagnet
or
g
T. Senthil, A. Vishwanath, L. Balents, S. Sachdev
and M.P.A. Fisher, Science 303, 1490 (2004).
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Large scale Quantum Monte Carlo studies
A.W. Sandvik, S. Daul, R. R. P. Singh, and D. J.
Scalapino, Phys. Rev. Lett. 89, 247201
(2002) A.W. Sandvik and R.G. Melko, Phys. Rev. E
72, 026702 (2005).
A.W. Sandvik, Phys. Rev. Lett. 98, 227202
(2007). R.G. Melko and R.K. Kaul, Phys. Rev.
Lett. 100, 017203 (2008).
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Easy-plane model
Spin stiffness
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Easy-plane model
Valence bond solid (VBS) order in expectation
values of plaquette and exchange terms
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SU(2) invariant model
Strong evidence for a continuous deconfined
quantum critical point
T. Senthil, A. Vishwanath, L. Balents,
S. Sachdev and M.P.A. Fisher, Science 303, 1490
(2004).
A.W. Sandvik, Phys. Rev. Lett. 98, 2272020 (2007).
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SU(2) invariant model
R.G. Melko and R.K. Kaul, Phys. Rev. Lett. 100,
017203 (2008).
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SU(2) invariant model
Histogram of VBS order ? at quantum critical point
Emergent circular symmetry is evidence for U(1)
photon and topological order
A.W. Sandvik, Phys. Rev. Lett. 98, 2272020 (2007).
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Outline
1. Destruction of Neel order in the insulator
Deconfined criticality 2. Destruction of
Neel order in the metal Doublon metal -
an algebraic charge liquid 3. Destruction of
Neel order in the superconductor Deconfined
critical transition to a large Fermi surface
state
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Outline
1. Destruction of Neel order in the insulator
Deconfined criticality 2. Destruction of
Neel order in the metal Doublon metal -
an algebraic charge liquid 3. Destruction of
Neel order in the superconductor Deconfined
critical transition to a large Fermi surface
state
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Doublon metal non-Fermi liquid with a spin gap
AFM metal small Fermi surface
O(4) transition
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Outline
1. Destruction of Neel order in the insulator
Deconfined criticality 2. Destruction of
Neel order in the metal Doublon metal -
an algebraic charge liquid 3. Destruction of
Neel order in the superconductor Deconfined
critical transition to a large Fermi surface
state
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Outline
1. Destruction of Neel order in the insulator
Deconfined criticality 2. Destruction of
Neel order in the metal Doublon metal -
an algebraic charge liquid 3. Destruction of
Neel order in the superconductor Deconfined
critical transition to a large Fermi surface
state
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d-wave superconductor with a large Fermi
surface and 4 nodal points
Antiferromagnetic d-wave superconductor with a
small Fermi surface and no nodal points
deconfined criticality of CP1 model
Condensation of monopoles confines spinons with
doublons and holons, and leads to transformation
of the small Fermi surface to a large Fermi
surface
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t-J model of electrons
t-J model of bosons
AFM metal
AFM boson superfluid
O(4) criticality
O(4) criticality
Doublon metal
Paired boson superfluid
AFM superconductor
AFM paired boson superfluid
CP1 criticality
CP1 criticality
Large Fermi surface d-wave superconductor or
supersolid
Paired boson supersolid with periods determined
by total boson density
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doublon metal
large Fermi surface
small Fermi surface
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Photoemission
N. P. Armitage et al., Phys. Rev. Lett. 88,
257001 (2002).
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Conclusions
1. Theory of the loss of Neel order in square
lattice antiferromagnets via a deconfined
critical point, and its realization in numerical
studies 2. Loss of Neel order in the
electron-doped cuprates is accopanied by a Fermi
surface transformation from small to
large 3. Predicted a deconfined transition
from NSC to SC without an intermediate state
with 8 diagonal zero-energy fermion states 4.
Predictions for neutron scattering, NMR, and
photoemission experiments.