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Universality and Dynamic Localization in Kibble- Zurek

Universality and Dynamic Localization in Kibble- Zurek

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Universality and Dynamic Localization in Kibble- Zurek

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

  2. Kibble-Zurek Scaling Disordered Ordered

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

  4. Kibble-Zurek scaling Ramp rate

  5. Kibble-Zurek scaling Ramp rate

  6. Kibble-Zurek scaling Ramp rate

  7. Kibble-Zurek scaling Ramp rate Fall out ofequilibrium

  8. Kibble-Zurek scaling Ramp rate Fall out ofequilibrium

  9. Kibble-Zurek scaling Ramp rate Slower

  10. Kibble-Zurek scaling Ramp rate Slower

  11. Kibble-Zurek scaling Ramp rate Slower

  12. Kibble-Zurek scaling Ramp rate Slower

  13. Kibble-Zurek scaling Ramp rate Slower

  14. Kibble-Zurek scaling • Recent work: Kibble-Zurek rampsshow non-equilibrium scaling • (in the limit of slow ramps) • [Chandran et. al., Deng et. al., etc.]

  15. Kibble-Zurek scaling • Recent work: Kibble-Zurek rampsshow non-equilibrium scaling • (in the limit of slow ramps) • More predictions than just defect production! • [Chandran et. al., Deng et. al., etc.]

  16. Kibble-Zurek scaling Excess heat

  17. Kibble-Zurek scaling

  18. Kibble-Zurek scaling

  19. Kibble-Zurek scaling

  20. Kibble-Zurek scaling Schrödinger Equation OR Observable

  21. Kibble-Zurek scaling Schrödinger Equation OR Observable Fixed

  22. Kibble-Zurek scaling Schrödinger Equation OR Observable Universaldynamics! = Fixed

  23. Transverse-field Ising chain

  24. Transverse-field Ising chain Paramagnet (PM) Ferromagnet (FM)

  25. Transverse-field Ising chain Paramagnet (PM) Ferromagnet (FM)

  26. Kibble-Zurek scaling Ramp rate Slower

  27. Kibble-Zurek scaling Ramp rate Slower

  28. Kibble-Zurek scaling Excess heat

  29. Kibble-Zurek scaling

  30. Kibble-Zurek scaling

  31. Kibble-Zurek scaling

  32. Kibble-Zurek scaling

  33. Kibble-Zurek scaling

  34. Kibble-Zurek scaling Dynamics does not depend on ramp rate!

  35. Outline • Part I: Universality of Kibble-Zurek scaling • Dynamics near QCP givesnon-equilibrium critical scaling theory • Part II: Kibble-Zurek with a dynamic field

  36. Outline • Part I: Universality of Kibble-Zurek scaling • Dynamics near QCP givesnon-equilibrium critical scaling theory • Are the results universal? • Part II: Kibble-Zurek with a dynamic field

  37. Universality Theory Sachdev et al. (2002) Experiment Greiner group (Harvard) Nagerl group (Innsbruck)

  38. Universality Theory Sachdev et al. (2002) Experiment Greiner group (Harvard) Nagerl group (Innsbruck)

  39. Universality or Theory Sachdev et al. (2002) Experiment Greiner group (Harvard) Nagerl group (Innsbruck)

  40. Universality Ramp the tilt linearly in time or Theory Sachdev et al. (2002) Experiment Greiner group (Harvard) Nagerl group (Innsbruck)

  41. Universality Ramp the tilt linearly in time: Solve numerically with DMRG or Theory Sachdev et al. (2002) Experiment Greiner group (Harvard) Nagerl group (Innsbruck)

  42. Universality

  43. Universality

  44. Universality

  45. Universality

  46. Universality

  47. Universality Dynamics are universal!

  48. Outline • Part I: Universality of Kibble-Zurek scaling • Dynamics near QCP givesnon-equilibrium critical scaling theory • Dynamics are universal to Ising-like QPTs • Part II: Kibble-Zurek with a dynamic field

  49. Outline • Part I: Universality of Kibble-Zurek scaling • Dynamics near QCP givesnon-equilibrium critical scaling theory • Dynamics are universal to Ising-like QPTs • Non-trivial scaling functions • Part II: Kibble-Zurek with a dynamic field

  50. Non-equilibrium properties Spin-spin correlation function