Quantum entanglement and the phases of matter

1. HARVARD Quantum entanglement and the phases of matter Colloquium Ehrenfestii Leiden University May 9, 2012 sachdev.physics.harvard.edu

2. Max Metlitski Liza Huijse Brian Swingle

3. Sommerfeld-Bloch theory of metals, insulators, and superconductors: many-electron quantum states are adiabatically connected to independent electron states

4. Sommerfeld-Bloch theory of metals, insulators, and superconductors: many-electron quantum states are adiabatically connected to independent electron states Band insulators An even number of electrons per unit cell

5. Sommerfeld-Bloch theory of metals, insulators, and superconductors: many-electron quantum states are adiabatically connected to independent electron states Metals An odd number of electrons per unit cell

6. Sommerfeld-Bloch theory of metals, insulators, and superconductors: many-electron quantum states are adiabatically connected to independent electron states Superconductors

7. Modern phases of quantum matter Not adiabatically connected to independent electron states:

8. Modern phases of quantum matter Not adiabatically connected to independent electron states: many-particle, long-range quantum entanglement

9. Quantum superposition and entanglement

10. Quantum Entanglement: quantum superposition with more than one particle

11. Quantum Entanglement: quantum superposition with more than one particle Hydrogen atom:

12. Quantum Entanglement: quantum superposition with more than one particle Hydrogen atom: Hydrogen molecule: _ = Superposition of two electron states leads to non-local correlations between spins

13. Quantum Entanglement: quantum superposition with more than one particle _

14. Quantum Entanglement: quantum superposition with more than one particle _

15. Quantum Entanglement: quantum superposition with more than one particle _

16. Quantum Entanglement: quantum superposition with more than one particle _ Einstein-Podolsky-Rosen “paradox”: Non-local correlations between observations arbitrarily far apart

17. Mott insulator: Triangular lattice antiferromagnet Nearest-neighbor model has non-collinear Neel order

18. Mott insulator: Triangular lattice antiferromagnet

19. Mott insulator: Triangular lattice antiferromagnet N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991) X.-G. Wen, Phys. Rev. B44, 2664 (1991)

20. = Mott insulator: Triangular lattice antiferromagnet Spin liquid obtained in a generalized spin model with S=1/2 per unit cell P. Fazekas and P. W. Anderson, Philos. Mag.30, 23 (1974).

21. = Mott insulator: Triangular lattice antiferromagnet Spin liquid obtained in a generalized spin model with S=1/2 per unit cell P. Fazekas and P. W. Anderson, Philos. Mag.30, 23 (1974).

22. = Mott insulator: Triangular lattice antiferromagnet Spin liquid obtained in a generalized spin model with S=1/2 per unit cell P. Fazekas and P. W. Anderson, Philos. Mag.30, 23 (1974).

23. = Mott insulator: Triangular lattice antiferromagnet Spin liquid obtained in a generalized spin model with S=1/2 per unit cell P. Fazekas and P. W. Anderson, Philos. Mag.30, 23 (1974).

24. = Mott insulator: Triangular lattice antiferromagnet Spin liquid obtained in a generalized spin model with S=1/2 per unit cell P. Fazekas and P. W. Anderson, Philos. Mag.30, 23 (1974).

25. = Mott insulator: Triangular lattice antiferromagnet Spin liquid obtained in a generalized spin model with S=1/2 per unit cell P. Fazekas and P. W. Anderson, Philos. Mag.30, 23 (1974).

26. Topological order in the Z2 spin liquid ground state B A

27. Topological order in the Z2 spin liquid ground state B A

28. Topological order in the Z2 spin liquid ground state B A M. Levin and X.-G. Wen, Phys. Rev. Lett.96, 110405 (2006); A. Kitaev and J. Preskill, Phys. Rev. Lett.96, 110404 (2006); Y. Zhang, T. Grover, and A. Vishwanath, Phys. Rev. B84, 075128 (2011).

29. Promising candidate: the kagome • antiferromagnet Numerical evidence for a gapped spin liquid: Simeng Yan, D. A. Huse, and S. R. White, Science332, 1173 (2011). Young Lee, APS meeting, March 2012

30. Quantum superposition and entanglement

31. Quantum superposition and entanglement Black holes String theory Quantum critical points of electrons in crystals

32. Quantum superposition and entanglement Black holes String theory Quantum critical points of electrons in crystals

33. Spinning electrons localized on a square lattice S=1/2 spins J J/ Examine ground state as a function of

34. Spinning electrons localized on a square lattice J J/ At large ground state is a “quantum paramagnet” with spins locked in valence bond singlets

35. Spinning electrons localized on a square lattice J J/

36. Spinning electrons localized on a square lattice J J/

37. Spinning electrons localized on a square lattice J J/ No EPR pairs

39. Pressure in TlCuCl3 A. Oosawa, K. Kakurai, T. Osakabe, M. Nakamura, M. Takeda, and H. Tanaka, Journal of the Physical Society of Japan, 73, 1446 (2004).

40. TlCuCl3 An insulator whose spin susceptibility vanishes exponentially as the temperature T tends to zero.

41. TlCuCl3 Quantum paramagnet at ambient pressure

42. TlCuCl3 Neel order under pressure A. Oosawa, K. Kakurai, T. Osakabe, M. Nakamura, M. Takeda, and H. Tanaka, Journal of the Physical Society of Japan, 73, 1446 (2004).

46. Spin waves

47. Spin waves

48. Spin waves

49. Excitations of TlCuCl3 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, 205701 (2008)

50. Excitations of TlCuCl3 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, 205701 (2008)