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Non-equilibrium dynamic critical scaling of the quantum Ising chain

Non-equilibrium dynamic critical scaling of the quantum Ising chain. Michael Kolodrubetz Princeton University In collaboration with: Bryan Clark, David Huse David Pekker Krishnendu Sengupta. Quantum state of transverse-field Ising model during slow ramp is…. Universal

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Non-equilibrium dynamic critical scaling of the quantum Ising chain

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  1. Non-equilibrium dynamic critical scaling of the quantum Ising chain Michael Kolodrubetz Princeton University In collaboration with: Bryan Clark, David Huse David Pekker KrishnenduSengupta

  2. Quantum state of transverse-field Ising model during slow ramp is… • Universal • Non-equilibrium • Experimentally viable • Non-thermal • Dephasing resistant

  3. Classical Phase Transitions “Magnetization” Landau-Ginzburg functional

  4. Classical Phase Transitions “Magnetization”

  5. Classical Phase Transitions “Magnetization”  Thermal fluctuations

  6. Quantum Phase Transitions One-dimensional transverse-field Ising chain

  7. Quantum Phase Transitions One-dimensional transverse-field Ising chain Paramagnet (PM) Ferromagnet (FM)

  8. Quantum Phase Transitions One-dimensional transverse-field Ising chain Paramagnet (PM) Ferromagnet (FM)  Quantum fluctuations

  9. Critical Scaling [Smirnov, php.math.unifi.it/users/paf/LaPietra/files/Chelkak01.ppt]

  10. Critical Scaling [Smirnov, php.math.unifi.it/users/paf/LaPietra/files/Chelkak01.ppt]

  11. Critical Scaling , Dynamiccritical exponent Correlation lengthcritical exponent [Smirnov, php.math.unifi.it/users/paf/LaPietra/files/Chelkak01.ppt]

  12. Critical Scaling Ising: , Dynamiccritical exponent Correlation lengthcritical exponent

  13. Critical Scaling Ising: Order parametercritical exponent , Dynamiccritical exponent Correlation lengthcritical exponent

  14. Critical Scaling Ising: Order parametercritical exponent , Dynamiccritical exponent Correlation lengthcritical exponent

  15. Kibble-Zurek ramps Ramp rate

  16. Kibble-Zurek ramps Ramp rate

  17. Kibble-Zurek ramps Ramp rate Adiabatic

  18. Kibble-Zurek ramps Ramp rate Impulse Adiabatic

  19. Kibble-Zurek ramps Ramp rate Impulse Adiabatic

  20. Kibble-Zurek ramps Ramp rate Impulse Adiabatic

  21. Kibble-Zurek ramps Ramp rate Impulse Adiabatic

  22. Kibble-Zurek ramps Ramp rate Impulse Adiabatic

  23. Kibble-Zurek ramps

  24. Kibble-Zurek ramps

  25. Kibble-Zurek ramps Ramp rate Impulse Adiabatic

  26. Kibble-Zurek ramps Ramp rate Impulse Adiabatic

  27. Kibble-Zurek ramps Ramp rate Impulse Adiabatic

  28. Kibble-Zurek ramps Ramp rate Impulse Adiabatic

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

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

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

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

  33. Transverse-field Ising chain Wigner fermionize • Quadratic  Integrable • Hamiltonian conserves parity for each mode k Sachdev: “Quantum Phase Transitions”  phase

  34. Transverse-field Ising chain Wigner fermionize • Quadratic  Integrable • Hamiltonian conserves parity for each mode k • Work in subspace where parity is even Sachdev: “Quantum Phase Transitions”  phase

  35. Transverse-field Ising chain Wigner fermionize • Quadratic  Integrable • Hamiltonian conserves parity for each mode k • Work in subspace where parity is even Sachdev: “Quantum Phase Transitions”  phase

  36. Transverse-field Ising chain

  37. Transverse-field Ising chain

  38. Transverse-field Ising chain

  39. Transverse-field Ising chain

  40. Transverse-field Ising chain

  41. Transverse-field Ising chain

  42. Transverse-field Ising chain Low energy, long wavelength theory

  43. Kibble-Zurek ramps Low energy, long wavelength theory? Ramp rate Impulse Adiabatic

  44. Kibble-Zurek ramps Low energy, long wavelength theory Ramp rate Impulse Adiabatic

  45. Kibble-Zurek ramps Low energy, long wavelength theory Ramp rate Impulse Adiabatic

  46. Kibble-Zurek scaling limit Schrödinger Equation OR Observable Fixed

  47. Kibble-Zurek scaling limit

  48. Kibble-Zurek scaling limit

  49. Kibble-Zurek scaling limit

  50. Kibble-Zurek scaling limit

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