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

2. 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

3. The cuprate superconductors

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

5. Antiferro- magnetism Fermi surface d-wave supercon- ductivity

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

7. N. E. Hussey, J. Phys: Condens. Matter 20, 123201 (2008) Crossovers in transport properties of hole-doped cuprates

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

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

10. 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

11. Antiferro- magnetism Fermi surface d-wave supercon- ductivity

12. Antiferro- magnetism Fermi surface d-wave supercon- ductivity

13. Ground state has long-range Néel order Square lattice antiferromagnet

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

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

16. Pressure in TlCuCl 3

17. Quantum critical point with non-local entanglement in spin wavefunction

24. Spin waves

38. 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, 205701 (2008) TlCuCl 3 with varying pressure

39. 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, 205701 (2008) TlCuCl 3 with varying pressure

40. 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, 205701 (2008) TlCuCl 3 with varying pressure

41. Prediction of quantum field theory

42. 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, 205701 (2008)

43. Antiferro- magnetism Fermi surface d-wave supercon- ductivity

44. Antiferro- magnetism Fermi surface d-wave supercon- ductivity

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

46. Spin density wave theory

48. 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). D. Senechal and A.-M. S. Tremblay, Phys. Rev. Lett. 92, 126401 (2004) Hole pockets Electron pockets Hole-doped cuprates

49. Electron pockets Hole pockets Electron-doped 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). D. Senechal and A.-M. S. Tremblay, Phys. Rev. Lett. 92, 126401 (2004)

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

51. T. Helm, M. V. Kartsovnik, M. Bartkowiak, N. Bittner, M. Lambacher, A. Erb, J. Wosnitza, and R. Gross, Phys. Rev. Lett. 103, 157002 (2009).

52. Nature 450, 533 (2007) Quantum oscillations

53. Theory of quantum criticality in the cuprates

54. Antiferro- magnetism Fermi surface d-wave supercon- ductivity

55. Antiferro- magnetism Fermi surface d-wave supercon- ductivity

56. Theory of quantum criticality in the cuprates

60. Criticality of the coupled dimer antiferromagnet at x=x s

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

62. Theory of quantum criticality in the cuprates

63. ++ _ _ 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)

64. Theory of quantum criticality in the cuprates

66. 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

67. 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