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Subir Sachdev arXiv:0804.1794 Subir Sachdev arXiv:0804.1794 Loss of Neel order in insulators and superconductors Ribhu Kaul Max Metlitski Cenke Xu

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Phase diagram of electron-doped superconductors Neel order (AFM)

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Spin correlations in the electron-doped high-transition-temperature superconductor Nd 2- xCe x CuO 4 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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Charge carriers in the lightly-doped cuprates with Neel order Electron pockets Hole pockets

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N. P. Armitage et al., Phys. Rev. Lett. 88, 257001 (2002). Photoemission in NCCO

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Spin density wave theory

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++ - - ++ - - ++ - - ++ - - ++ - - ++ - - ++ - - ++ - -

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Nature 450, 533 (2007)

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Outline 1. Loss of Neel order in insulating square lattice antiferromagnets Distinct universality classes for half-integer, odd integer, and even integer spin S 2. Low energy theory for doped S=1/2 antiferromagnets d-wave superconductivity 3. Loss of Neel order in the d-wave superconductor Same universality classes as in general S insulators, leading to transitions to a valence bond supersolid, a nematic superconductor, or a vanilla superconductor

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Outline 1. Loss of Neel order in insulating square lattice antiferromagnets Distinct universality classes for half-integer, odd integer, and even integer spin S 2. Low energy theory for doped S=1/2 antiferromagnets d-wave superconductivity 3. Loss of Neel order in the d-wave superconductor Same universality classes as in general S insulators, leading to transitions to a valence bond supersolid, a nematic superconductor, or a vanilla superconductor

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Bond modulation weakens Neel order J J/

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Ground state is a product of pairs of entangled spins. J J/

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M. Matsumoto, C. Yasuda, S. Todo, and H. Takayama, Phys. Rev.B 65, 014407 (2002). Coupled dimer antiferromagnet

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Ground state has long-range Néel order Square lattice antiferromagnet

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Destroy Neel order by perturbations which preserve full square lattice symmetry e.g. second-neighbor or ring exchange. Square lattice antiferromagnet

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Destroy Neel order by perturbations which preserve full square lattice symmetry e.g. second-neighbor or ring exchange. Square lattice antiferromagnet

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Theory for loss of Neel order

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Perturbation theory

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Distinct universality from O(3) model

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Non-perturbative effects F. D. M. Haldane, Phys. Rev. Lett. 61, 1029 (1988).

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N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989). Half-odd-integer S Loss of Neel order leads to a Valence Bond Solid (VBS)

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Odd integer S Loss of Neel order leads to a (charge) nematic N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).

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Even integer S Loss of Neel order leads to a state with no broken symmetry N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989).

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Outline 1. Loss of Neel order in insulating square lattice antiferromagnets Distinct universality classes for half-integer, odd integer, and even integer spin S 2. Low energy theory for doped S=1/2 antiferromagnets d-wave superconductivity 3. Loss of Neel order in the d-wave superconductor Same universality classes as in general S insulators, leading to transitions to a valence bond supersolid, a nematic superconductor, or a vanilla superconductor

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1. Loss of Neel order in insulating square lattice antiferromagnets Distinct universality classes for half-integer, odd integer, and even integer spin S 2. Low energy theory for doped S=1/2 antiferromagnets d-wave superconductivity 3. Loss of Neel order in the d-wave superconductor Same universality classes as in general S insulators, leading to transitions to a valence bond supersolid, a nematic superconductor, or a vanilla superconductor Outline

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Hole dynamics in an antiferromagnet across a deconfined quantum critical pointHole dynamics in an antiferromagnet across a deconfined quantum critical point, R. K. Kaul, A. Kolezhuk, M. Levin, S. Sachdev, and T. Senthil, Physical Review B 75, 235122 (2007). Algebraic charge liquids and the underdoped cupratesAlgebraic charge liquids and the underdoped cuprates, R. K. Kaul, Y. B. Kim, S. Sachdev, and T. Senthil, Nature Physics 4, 28 (2008).

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Conventional phases AF Metal

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Conventional phases AF d-wave superconductor 4 Dirac points (+ 4 shadows) ++ - -

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Conventional phases AF d-wave superconductor Fermions fully gapped ++ - -

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Outline 1. Loss of Neel order in insulating square lattice antiferromagnets Distinct universality classes for half-integer, odd integer, and even integer spin S 2. Low energy theory for doped S=1/2 antiferromagnets d-wave superconductivity 3. Loss of Neel order in the d-wave superconductor Same universality classes as in general S insulators, leading to transitions to a valence bond supersolid, a nematic superconductor, or a vanilla superconductor

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1. Loss of Neel order in insulating square lattice antiferromagnets Distinct universality classes for half-integer, odd integer, and even integer spin S 2. Low energy theory for doped S=1/2 antiferromagnets d-wave superconductivity 3. Loss of Neel order in the d-wave superconductor Same universality classes as in general S insulators, leading to transitions to a valence bond supersolid, a nematic superconductor, or a vanilla superconductor Outline

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Loss of Neel order in AFM d-wave superconductor Fermions fully gapped ++ - -

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Perturbation theory

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Recall non-perturbative effects in insulator F. D. M. Haldane, Phys. Rev. Lett. 61, 1029 (1988).

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Non-perturbative effects in superconductor

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Transitions match those found in insulators for different S

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4 Dirac points (+ 4 shadows) ++ - - Loss of Neel order in AFM d-wave superconductor with gapless fermions ++ - -

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Perturbation theory R. K. Kaul, Y. B. Kim, S. Sachdev, and T. Senthil, Nature Physics 4, 28 (2008)

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Non-perturbative effects in superconductor

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Theory for the loss of Neel order in d-wave superconductors For superconductors with gapped Bogoliubov quasiparticles, we found 3 distinct transitions, to a valence bond supersolid, a nematic superconductor, and a vanilla superconductor These transitions in the compressible superconductor of S=1/2 electrons match the classification of transitions in the incompressible Mott insulator of general S spins. Theory for the loss of Neel order in d-wave superconductors For superconductors with gapped Bogoliubov quasiparticles, we found 3 distinct transitions, to a valence bond supersolid, a nematic superconductor, and a vanilla superconductor These transitions in the compressible superconductor of S=1/2 electrons match the classification of transitions in the incompressible Mott insulator of general S spins. Conclusions

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