From the Hubbard model to high temperature superconductivity HARVARD S. Sachdev Talk online: sachdev.physics.harvard.edu

Max Metlitski: Entanglement near strongly interacting quantum critical points in two and higher dimensions Yang Qi: Frustrated antiferromagnetism and spin liquids in organic insulators Posters HARVARD

The cuprate superconductors

Central ingredients in cuprate phase diagram: antiferromagnetism, superconductivity, and change in Fermi surface

Antiferro- magnetism Fermi surface d-wave supercon- ductivity

Central ingredients in cuprate phase diagram: antiferromagnetism, superconductivity, and change in Fermi surface

N. E. Hussey, J. Phys: Condens. Matter 20, (2008) Crossovers in transport properties of hole-doped cuprates

Strange metal Crossovers in transport properties of hole-doped cuprates Pseudo- gap

Strange metal Crossovers in transport properties of hole-doped cuprates Pseudo- gap

How is antiferromagnetism lost with increasing doping ? How does the Fermi surface evolve with loss of antiferromagnetism ? Do antiferromagnetic fluctuations induce d-wave superconductivity ? How does attraction between antiferromagnetism and superconductivity turn into competition ? Is there a broken symmetry in the pseudo-gap regime ? What is the role of nematic/valence-bond-solid/stripe order ? What is the physics of the strange metal ? Questions

Antiferro- magnetism Fermi surface d-wave supercon- ductivity

Antiferro- magnetism Fermi surface d-wave supercon- ductivity

Ground state has long-range Néel order Square lattice antiferromagnet

J J/ Weaken some bonds to induce spin entanglement in a new quantum phase

Square lattice antiferromagnet J J/ Ground state is a “quantum paramagnet” with spins locked in valence bond singlets

Pressure in TlCuCl 3

Quantum critical point with non-local entanglement in spin wavefunction

Spin waves

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, (2008) TlCuCl 3 with varying pressure

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, (2008) TlCuCl 3 with varying pressure

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, (2008) TlCuCl 3 with varying pressure

Prediction of quantum field theory

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, (2008)

Antiferro- magnetism Fermi surface d-wave supercon- ductivity

Antiferro- magnetism Fermi surface d-wave supercon- ductivity

“Large” Fermi surfaces in cuprates Hole states occupied Electron states occupied

Spin density wave theory

S. Sachdev, A. V. Chubukov, and A. Sokol, Phys. Rev. B 51, (1995). A. V. Chubukov and D. K. Morr, Physics Reports 288, 355 (1997). D. Senechal and A.-M. S. Tremblay, Phys. Rev. Lett. 92, (2004) Hole pockets Electron pockets Hole-doped cuprates

Electron pockets Hole pockets Electron-doped cuprates S. Sachdev, A. V. Chubukov, and A. Sokol, Phys. Rev. B 51, (1995). A. V. Chubukov and D. K. Morr, Physics Reports 288, 355 (1997). D. Senechal and A.-M. S. Tremblay, Phys. Rev. Lett. 92, (2004)

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

T. Helm, M. V. Kartsovnik, M. Bartkowiak, N. Bittner, M. Lambacher, A. Erb, J. Wosnitza, and R. Gross, Phys. Rev. Lett. 103, (2009).

Nature 450, 533 (2007) Quantum oscillations

Theory of quantum criticality in the cuprates

Antiferro- magnetism Fermi surface d-wave supercon- ductivity

Antiferro- magnetism Fermi surface d-wave supercon- ductivity

Theory of quantum criticality in the cuprates

Criticality of the coupled dimer antiferromagnet at x=x s

Theory of quantum criticality in the cuprates Criticality of the topological change in Fermi surface at x=x m

Theory of quantum criticality in the cuprates

++ _ _ D. J. Scalapino, E. Loh, and J. E. Hirsch, Phys. Rev. B 34, 8190 (1986) K. Miyake, S. Schmitt-Rink, and C. M. Varma, Phys. Rev. B 34, 6554 (1986)

Theory of quantum criticality in the cuprates

How is antiferromagnetism lost with increasing doping ? How does the Fermi surface evolve with loss of antiferromagnetism ? Do antiferromagnetic fluctuations induce d-wave superconductivity ? How does attraction between antiferromagnetism and superconductivity turn into competition ? Is there a broken symmetry in the pseudo-gap regime ? What is the role of nematic/valence-bond-solid/stripe order ? What is the physics of the strange metal ? Questions

Max Metlitski: Entanglement near strongly interacting quantum critical points in two and higher dimensions Yang Qi: Frustrated antiferromagnetism and spin liquids in organic insulators Posters HARVARD