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Universality and Dynamic Localization in Kibble- Zurek Scaling of the Quantum Ising Chain

Universality and Dynamic Localization in Kibble- Zurek Scaling of the Quantum Ising Chain. Michael Kolodrubetz Boston University In collaboration with: B.K. Clark, D. Huse (Princeton) A. Polkovnikov , A. Katz (BU). Outline.

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Universality and Dynamic Localization in Kibble- Zurek Scaling of the Quantum Ising Chain

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  1. Universality and Dynamic Localization in Kibble-ZurekScaling of the Quantum IsingChain Michael Kolodrubetz Boston University In collaboration with: B.K. Clark, D. Huse (Princeton)A. Polkovnikov, A. Katz (BU)

  2. Outline • Part I: Kibble-Zurek scaling of the transverse-field Ising chain • Part II: Transverse-field Isingchain with a dynamic field

  3. Transverse-field Ising chain One-dimensional transverse-field Ising chain

  4. Transverse-field Ising chain One-dimensional transverse-field Ising chain

  5. Transverse-field Ising chain One-dimensional transverse-field Ising chain Paramagnet (PM)

  6. Transverse-field Ising chain One-dimensional transverse-field Ising chain Paramagnet (PM) Ferromagnet (FM)

  7. Transverse-field Ising chain One-dimensional transverse-field Ising chain Paramagnet (PM) Ferromagnet (FM) Quantum phase transition

  8. Quantum phase transition [Smirnov, php.math.unifi.it/users/paf/LaPietra/files/Chelkak01.ppt]

  9. Quantum phase transition [Smirnov, php.math.unifi.it/users/paf/LaPietra/files/Chelkak01.ppt]

  10. Quantum phase transition [Smirnov, php.math.unifi.it/users/paf/LaPietra/files/Chelkak01.ppt]

  11. Quantum phase transition [Smirnov, php.math.unifi.it/users/paf/LaPietra/files/Chelkak01.ppt]

  12. Quantum phase transition , [Smirnov, php.math.unifi.it/users/paf/LaPietra/files/Chelkak01.ppt]

  13. Quantum phase transition , [Smirnov, php.math.unifi.it/users/paf/LaPietra/files/Chelkak01.ppt]

  14. Quantum phase transition , Dynamiccritical exponent Correlation lengthcritical exponent [Smirnov, php.math.unifi.it/users/paf/LaPietra/files/Chelkak01.ppt]

  15. Quantum phase transition Ising: , Dynamiccritical exponent Correlation lengthcritical exponent

  16. Quantum phase transition Ising: Can these results be extended to non-equilbrium dynamics? , Dynamiccritical exponent Correlation lengthcritical exponent

  17. Kibble-Zurek ramps Ramp rate Kibble-ZurekRamp through the critical point at a constant, finite rate

  18. Kibble-Zurek ramps Ramp rate

  19. Kibble-Zurek ramps Ramp rate

  20. Kibble-Zurek ramps Ramp rate Fall out ofequilibrium

  21. Kibble-Zurek ramps Ramp rate Fall out ofequilibrium

  22. Kibble-Zurek ramps Ramp rate Fall out ofequilibrium

  23. Kibble-Zurek ramps Ramp rate Fall out ofequilibrium

  24. Kibble-Zurek ramps Ramp rate Slower

  25. Kibble-Zurek ramps Ramp rate Slower

  26. Kibble-Zurek ramps Ramp rate Slower

  27. Kibble-Zurek ramps Ramp rate Slower

  28. Kibble-Zurek ramps Ramp rate Slower

  29. Kibble-Zurek ramps • Kibble-Zurek ramps shownon-equilibrium scaling • [Chandran et. al., Deng et. al., etc.]

  30. Kibble-Zurek ramps • Kibble-Zurek ramps shownon-equilibrium scaling • (in the limit of slow ramps) • [Chandran et. al., Deng et. al., etc.]

  31. Kibble-Zurek ramps • Kibble-Zurek ramps shownon-equilibrium scaling • (in the limit of slow ramps) • More than a theory of defect production! • [Chandran et. al., Deng et. al., etc.]

  32. Kibble-Zurek ramps • Kibble-Zurek ramps shownon-equilibrium scaling • (in the limit of slow ramps) • More than a theory of defect production! • [Chandran et. al., Deng et. al., etc.]

  33. Kibble-Zurek scaling Excess heat

  34. Kibble-Zurek observables

  35. Kibble-Zurek observables

  36. Kibble-Zurek observables

  37. Kibble-Zurek observables

  38. Kibble-Zurek observables

  39. Kibble-Zurek scaling

  40. Kibble-Zurek scaling

  41. Kibble-Zurek scaling

  42. Transverse-field Ising chain Sachdev: “Quantum Phase Transitions”

  43. Transverse-field Ising chain Wigner fermionize Sachdev: “Quantum Phase Transitions”  phase

  44. Transverse-field Ising chain Wigner fermionize Sachdev: “Quantum Phase Transitions”  phase

  45. Transverse-field Ising chain Wigner fermionize • Quadratic  Integrable Sachdev: “Quantum Phase Transitions”  phase

  46. Transverse-field Ising chain Wigner fermionize • Quadratic  Integrable • Work in subspace where each mode(k,-k) is either occupied or unoccupied Sachdev: “Quantum Phase Transitions”  phase

  47. Transverse-field Ising chain Wigner fermionize • Quadratic  Integrable • Work in subspace where each mode(k,-k) is either occupied or unoccupied Sachdev: “Quantum Phase Transitions”  phase

  48. Equilibrium scaling “Spin up”  (k,-k) unoccupied “Spin down”  (k,-k) occupied

  49. Equilibrium scaling “Spin up”  (k,-k) unoccupied “Spin down”  (k,-k) occupied

  50. Equilibrium scaling “Spin up”  (k,-k) unoccupied “Spin down”  (k,-k) occupied Low energy, long wavelength theory?

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