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What we talk about when we talk about Learning in many-body physics Stories Zi Yang Meng Raymond Carver Anton Chekhov of American literature I was going to tell you about something. I mean, I was going to prove a point. You

  1. What we talk about when we talk about Learning in many-body physics Stories Zi Yang Meng 孟 子 杨

  3. Raymond Carver Anton Chekhov of American literature “I was going to tell you about something. I mean, I was going to prove a point. You see, this happened a few months ago, but it’s still going on right now, and it ought to make us feel ashamed when we talk like we know what we’re talking about when we talk about love.”

  4. ➢ Rich analytic literature, sum particular series of diagrams ➢ The ultimate desire is to obtain the exact forms of fermionic and bosonic ➢ PNAS 116 (34), 16760-16767 (2019) propagators in NFL in D>1 ➢ Alternative numerical approaches QMC ➢ Lattice models, large sizes and low T ➢ Numerics and Analytics would converge

  5. Monte Carlo

  6. Monte Carlo Calculation of Pi ➢ Optimization ➢ Numerical integration ➢ Generate probability distributions

  7. Monte Carlo – Ising Model ● Metropolis – Hastings

  8. Metropolis – Hastings: cluster

  9. Metropolis – Hastings: autocorrelation Modified Ising with four spin interaction Quantum rotor (2+1)D XY

  10. Monte Carlo

  11. Quantum many-body system - Bosons/Spins ➢ Nature 518, 179 (2015) CPL 34, 077502 (2017) ➢ ➢ PRL 119, 227208 (2017) Science, under review ➢

  12. Quantum many-body system - Fermions Twisted double bilayer Graphene Ferromagnetic fluctuations ArXiv:1903.06952 Nature under review ● FM / AFM / Nematic fluctuations of itinerant electron systems ● Non-Fermi liquid, fluctuation induced superconductivity ● Fermionic QCP Ce-based heavy fermion metal, arXiv:1907.10470 Huiqiu Yuan’s group at Zhejiang University

  13. Quantum Monte Carlo

  14. Quantum Monte Carlo

  15. Computing facilities

  16. Determinant quantum Monte Carlo

  17. Determinant quantum Monte Carlo

  18. Determinant quantum Monte Carlo

  19. Determinantal quantum Monte Carlo ● Hubbard-Stratonovich Transformation ● Measurements ➢ PRX 7, 031052 (2017) SAC SAC ➢ PRL 123, 157601 (2019)

  20. What we talk about ● Fermions couple to critical bosonic modes ● Itinerant quantum critical point ● Non-Fermi-liquid ● Self-learning Monte Carlo methods ● Matter fields couple to guage fields ● Alegbraic spin liquid, orthogonal metal …... ● Designer spin/boson models QMC ● DQCP & Gauge and matter fields ● Emergent continuous symmetry ● Dynamical signatures of topological order and spin liquids ● Duality between SPT transitions and DQCP …...

  21. People Revealing Fermionic Quantum Criticality from New Monte Carlo Techniques Topical Review, J. Phys.: Condens. Matter 31, 463001 (2019)

  22. Model

  23. Model ➢ PRX 7, 031101 (2017)

  24. SLMC

  25. Metropolis – Hastings: Self-learning Xiao Yan Xu IOP, HKUST, UCSD Junwei Liu IOP, MIT, HKUST Qi Yang MIT, Fudan Liang Fu MIT Yuki Nagai MIT, Japan Atomic Energy Agency, RIKEN ➢ PRB 95, 041101(R) (2017) …... ➢ PRB 95, 041101(R) (2017) ➢ PRB 96, 041119(R) (2017) ➢ PRL 122, 077601 (2019) …...

  26. SLMC ➢ PRB 95, 041101 (2017) ➢ PRB 96, 041119 (2017) ➢ PRL 122, 077601 (2019)

  27. SLMC

  28. SLMC

  29. Non-Fermi-liquid

  30. FM-QCP

  31. AFM-QCP ➢ PNAS 116 (34), 16760-16767 (2019)

  32. EMUS (elective momentum ultra-size) QMC ➢ PRB 99, 085114 (2019)

  33. EMUS ➢ PRB 99, 085114 (2019) ● Computational complexity ● Naturally integrated in SLMC ● Generic in finite Q models

  34. AFM-QCP ➢ PNAS 116 (34), 16760-16767 (2019) Bare boson (2+1)D Ising

  35. AFM-QCP ➢ PNAS 116 (34), 16760-16767 (2019)

  36. AFM-QCP ➢ PNAS 116 (34), 16760-16767 (2019)

  37. Fermion QCPs with QMC ➢ PRX 7, 031101 (2017) ➢ PRB 98, 045116 (2018) ➢ PNAS 116 (34), 16760 (2019)

  38. What we talk about ● Fermions couple to critical bosonic modes ● Itinerant quantum critical point ● Non-Fermi-liquid ● Self-learning Monte Carlo methods ● Matter fields couple to guage fields ● Alegbraic spin liquid, orthogonal metal …... ● Designer spin/boson models QMC ● DQCP & Gauge and matter fields ● Emergent continuous symmetry ● Dynamical signatures of topological order and spin liquids ● Duality between SPT transitions and DQCP …...

  40. U1 gauge field couple to matter field

  41. U1 gauge field couple to matter field

  42. U1 gauge field couple to matter field ➢ Wei Wang, et. al. PRB 100, 085123 (2019)

  43. U1 gauge field couple to matter field

  44. Z2 gauge field couple to matter field ➢ Chuang Chen et al., arXiv:1904.12872 ➢ Gazit, Assaad, Sachdev, arXiv:1906.11250 ➢ Hohenadler, Assaad, PRL 121, 086601 (2018) ➢ Hohenadler, Assaad, PRB 100, 125133 (2019)

  45. Z2 gauge field couple to matter field

  46. Z2 gauge field couple to matter field

  47. Z2 gauge field couple to matter field

  48. Designer Hamiltonian for Chiral Ising GN ➢ PRB 97, 081110 (2018) 3 times larger linear dispersion area ➢ Yuzhi Liu, Kai Sun, ZYM, arXiv:1910.07430

  49. ➢ Yuzhi Liu, Kai Sun, ZYM, arXiv:1910.07430

  50. Learning in many-body physics Learning in model ➢ PRX 7, 031101 (2017) ➢ PRB 98, 045116 (2018) ➢ PNAS 116 (34), 16760 (2019) ➢ arXiv:1910.07430 Learning in methodology ➢ PRB 95, 041101 (R) (2017) ➢ PRB 96, 041119 (R) (2017) ➢ PRB 98, 041102 (R) (2018) ➢ PRL 122, 077601 (2019) ➢ PRB 99, 085114 (2019) ➢ arXiv:1910.07430 Learning in new paradigms quantum matter ➢ PRX 9, 021022 (2019) ➢ PRB 100, 085123 (2019) ➢ arXiv: 1904.12872

  51. Metropolis – Hastings: local 2D Ising simulation https://mattbierbaum.github.io/ising.js/

  52. Metropolis – Hastings: cluster

  53. Metropolis – Hastings: critical slowing down

  54. Determinant quantum Monte Carlo

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