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What we talk about when we talk about Learning in many-body physics - - PowerPoint PPT Presentation
What we talk about when we talk about Learning in many-body physics - - PowerPoint PPT Presentation
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
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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.”
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➢ Rich analytic literature, sum particular
series of diagrams
➢ The ultimate desire is to obtain the
exact forms of fermionic and bosonic propagators in NFL in D>1
➢ Alternative numerical approaches QMC ➢ Lattice models, large sizes and low T ➢ Numerics and Analytics would converge
➢ PNAS 116 (34), 16760-16767 (2019)
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Monte Carlo
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Monte Carlo
Calculation of Pi
➢ Optimization ➢ Numerical integration ➢ Generate probability distributions
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Monte Carlo – Ising Model
- Metropolis – Hastings
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Metropolis – Hastings: cluster
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Metropolis – Hastings: autocorrelation
Modified Ising with four spin interaction Quantum rotor (2+1)D XY
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Monte Carlo
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Quantum many-body system - Bosons/Spins
➢ Nature 518, 179 (2015) ➢ PRL 119, 227208 (2017) ➢
CPL 34, 077502 (2017)
➢
Science, under review
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Quantum many-body system - Fermions
Twisted double bilayer Graphene Ferromagnetic fluctuations ArXiv:1903.06952 Nature under review Ce-based heavy fermion metal, arXiv:1907.10470 Huiqiu Yuan’s group at Zhejiang University
- FM / AFM / Nematic
fluctuations of itinerant electron systems
- Non-Fermi liquid, fluctuation
induced superconductivity
- Fermionic QCP
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Quantum Monte Carlo
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Quantum Monte Carlo
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Computing facilities
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Determinant quantum Monte Carlo
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Determinant quantum Monte Carlo
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Determinant quantum Monte Carlo
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Determinantal quantum Monte Carlo
- Hubbard-Stratonovich Transformation
➢ PRX 7, 031052 (2017) ➢ PRL 123, 157601 (2019)
- Measurements
SAC SAC
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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
- rder and spin liquids
- Duality between SPT transitions and
DQCP
…...
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People
Revealing Fermionic Quantum Criticality from New Monte Carlo Techniques Topical Review, J. Phys.: Condens. Matter 31, 463001 (2019)
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Model
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Model
➢ PRX 7, 031101 (2017)
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SLMC
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Metropolis – Hastings: Self-learning
➢ PRB 95, 041101(R) (2017) ➢ PRB 95, 041101(R) (2017) ➢ PRB 96, 041119(R) (2017) ➢ PRL 122, 077601 (2019)
…...
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 …...
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SLMC
➢ PRB 95, 041101 (2017) ➢ PRB 96, 041119 (2017) ➢ PRL 122, 077601 (2019)
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SLMC
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SLMC
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Non-Fermi-liquid
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FM-QCP
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AFM-QCP
➢ PNAS 116 (34), 16760-16767 (2019)
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EMUS (elective momentum ultra-size) QMC
➢ PRB 99, 085114 (2019)
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EMUS
- Computational complexity
- Naturally integrated in SLMC
- Generic in finite Q models
➢ PRB 99, 085114 (2019)
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AFM-QCP
➢ PNAS 116 (34), 16760-16767 (2019)
Bare boson (2+1)D Ising
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AFM-QCP
➢ PNAS 116 (34), 16760-16767 (2019)
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AFM-QCP
➢ PNAS 116 (34), 16760-16767 (2019)
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Fermion QCPs with QMC
➢ PRX 7, 031101 (2017) ➢ PRB 98, 045116 (2018) ➢ PNAS 116 (34), 16760 (2019)
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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
- rder and spin liquids
- Duality between SPT transitions and
DQCP
…...
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U1 gauge field couple to matter field
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U1 gauge field couple to matter field
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U1 gauge field couple to matter field
➢ Wei Wang, et. al. PRB 100, 085123 (2019)
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U1 gauge field couple to matter field
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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)
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Z2 gauge field couple to matter field
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Z2 gauge field couple to matter field
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Z2 gauge field couple to matter field
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Designer Hamiltonian for Chiral Ising GN
3 times larger linear dispersion area
➢ Yuzhi Liu, Kai Sun, ZYM, arXiv:1910.07430
➢ PRB 97, 081110 (2018)
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➢ Yuzhi Liu, Kai Sun, ZYM, arXiv:1910.07430
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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
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Metropolis – Hastings: local
2D Ising simulation https://mattbierbaum.github.io/ising.js/
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Metropolis – Hastings: cluster
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Metropolis – Hastings: critical slowing down
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