self-learning quantum monte carlo method in interacting...
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Xiao Yan Xu
(许霄琰 )
IOP, CAS
7/7/2017
Self-Learning quantum Monte Carlo method
in interacting fermion systems
Serials works on SLMC
IOP: Zi Hong Liu, Zi Yang MengMIT: Junwei Liu, Yang Qi, Huitao Shen, Yuki Nagai, Liang FuUM: Kai Sun
arXiv:1610.03137arXiv:1611.09364arXiv:1612.03804 arXiv:1705.06724 arXiv:1706.10004
Similar work from Li Huang, Yi-feng Yang, Lei WangarXiv:1610.02746arXiv:1612.01871
The power of SLMC
● Reduce the time cost per sweepFor 100×100×20 latticeDQMC ~ 150000 seconds/sweepSLMC ~ 500 seconds/sweep
● Reduce the auto-correlation timeDQMC ~ may scale with system size at critical pointSLMC ~ constants ideally, model dependent
Determinantal QMC (DQMC)
DQMC(BSS algorithm)
DQMC(BSS algorithm)
~(ßN)3
~ßN3
DQMC basics
Slater determinant and its properties
Occupation number representationNe particle states
operator with form
overlap of slater determinant
DQMC basics
Hubbard-Stratonovich transformationdeal with interaction termA continuous form
Other examples
DQMC
Trotter decomposition
HS transformation
Trace out fermions (trace over all Ne particle basis, Ne=1,...,N)
DQMC
partition function
Importance sampling of configurations
Application of DQMC
Coupled Fermion-boson lattice systems ● Interacting systems after HS transformation
Hubbard like modelsMott transition, chiral Ising and chiral Heisenberg transition, bosonic SPT etc.
● build-in coupled fermion-bosonAFM in metal, SDW, nematic QCP, FM QCP, Z2 deconfined phase transtion
Issues of DQMC
● Local update is level 1 BLAS algorithmSize limited, L=20 is the typical size
● (critical) slowing down in some modelsbuild-in coupled fermion-boson problem
Slowing down for some models in DQMC
Complexity for getting an independent configuration:
Self-learning DQMC
arXiv:1612.03804arXiv:1706.10004
Self-Learning Monte Carlo
L
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arXiv:1612.03804
Self-Learning Determinantal Quantum Monte Carlo
Complexity
● Cumulative update:
● Detail balance:
● Sweep Green's function:
Complexity speed up
Self-Learning Determinantal Quantum Monte Carlo
Autocorrelation time
Institute of Physics, Chinese Academy of Sciences
Self-Learning Determinantal Quantum Monte Carlo
Institute of Physics, Chinese Academy of Sciences
Using SLDQMC to attack hard problems
arXiv:1706.10004
Itinerant quantum critical point with frustration
Institute of Physics, Chinese Academy of Sciences
Itinerant quantum critical point with frustration
Non-fermi liquid behavior on hot spots
Itinerant quantum critical point with frustration
dynamical exponents z=2
Itinerant quantum critical point with frustration
Linear T dependence in spin susceptibility
L=30, beta=30(30×30×600)
Itinerant quantum critical point with frustration
Hertz-Millis-Moriya theory on finite momentum QCP
Summary and outlook
SLMC can be used to attack some hard problems
How general can it be is still a question
Self-Learning Monte Carlo
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arXiv:1612.03804