What we talk about when we talk about
Learning in many-body physics
StoriesZi Yang Meng
孟 子 杨

Raymond Carver
Anton Chekhov of American literature“I was going to tell you about something. Imean, I was going to prove a point. Yousee, this happened a few months ago, but
it’s still going on right now, and it ought tomake us feel ashamed when we talk like
we know what we’re talking about when wetalk about love.”➢ Rich analytic literature, sum particularseries of diagrams➢ The ultimate desire is to obtain theexact forms of fermionic and bosonicpropagators 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)

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

Monte Carlo – Ising Model● Metropolis – Hastings

Metropolis – Hastings: cluster

Metropolis – Hastings: autocorrelation

Modified Ising with four spin interaction

Quantum rotor (2+1)D XYMonte CarloQuantum many-body system - Bosons/Spins➢➢➢Nature 518, 179 (2015)

CPL 34, 077502 (2017)

PRL 119, 227208 (2017)➢Science, under review

Quantum many-body system - Fermions

Twisted double bilayer Graphene
Ferromagnetic fluctuations
ArXiv:1903.06952
Nature under review● FM / AFM / Nematicfluctuations of itinerant
electron systems● Non-Fermi liquid, fluctuationinduced superconductivity● Fermionic QCP
Ce-based heavy fermion metal, arXiv:1907.10470
Huiqiu Yuan’s group at Zhejiang University

Quantum Monte CarloQuantum Monte CarloComputing facilities

Determinant quantum Monte CarloDeterminant quantum Monte CarloDeterminant quantum Monte CarloDeterminantal quantum Monte Carlo● Hubbard-Stratonovich Transformation● Measurements➢PRX 7, 031052 (2017)

SACSAC➢PRL 123, 157601 (2019)

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 topologicalorder and spin liquids●Duality between SPT transitions andDQCP●…...

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

ModelModel➢ PRX 7, 031101 (2017)

SLMC

Metropolis – Hastings: Self-learning

Xiao Yan Xu IOP, HKUST, UCSD
Junwei Liu IOP, MIT, HKUSTQi Yang
MIT, Fudan
Liang Fu
MITYuki 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)

…...

SLMC

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

SLMC

SLMC

Non-Fermi-liquid

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

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

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

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

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

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

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

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 topologicalorder and spin liquids●
Duality between SPT transitions andDQCP●…...

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

U1 gauge field couple to matter field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)

Z2 gauge field couple to matter fieldZ2 gauge field couple to matter fieldZ2 gauge field couple to matter fieldDesigner Hamiltonian for Chiral Ising GN➢

PRB 97, 081110 (2018)

3 times larger linear dispersion area
➢ Yuzhi Liu, Kai Sun, ZYM, arXiv:1910.07430

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

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

Metropolis – Hastings: local

2D Ising simulation
https://mattbierbaum.github.io/ising.js/

Metropolis – Hastings: cluster

Metropolis – Hastings: critical slowing downDeterminant quantum Monte Carlo