Revealing fermionic quantum criticality from new Monte Carlo techniques. Zi Yang Meng ( 孟子杨 )
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1 Revealing fermionic quantum criticality from new Monte Carlo techniques Zi Yang Meng ( 孟子杨 )
2 Collaborators and References Xiao Yan Xu Zi Hong Liu Chuang Chen Gao Pei Pan Yang Qi FM-QCP, AFM-QCP PRX 7, (2017) PRB 98, (2018) Yoni Schattner Erez Berg Kai Sun Self-learning QMC, EMUS QMC PRB 96, (R) (2017) arxiv:
3 Monte Carlo Casino de Monte-Carlo, Since 1858 Widely used in statistical and quantum many-body physics Unbiased: statistical error
4 Monte Carlo Method Markov chain Monte Carlo is a way to do important sampling Distribution of converges to the Boltzmann distribution Observable can be measured from a Markov chain
5 Quantum Monte Carlo Determinantal QMC for fermions Hubbard model: Metal-Insulator transition Magnetic order Spectral properties Unconventional superconductivity... World-line QMC for bosons Heisenberg model: Quantum magnetism / Optical lattice Phase transition and critical phenomena Spectral properties Quantum spin liquids...
6 Quantum Monte Carlo Determinantal QMC for fermions Fermions couple to critical bosonic mode Itinerant quantum critical point Non-Fermi-liquid Self-Learning Monte Carlo methods Matter fields couple to gauge fields... World-line QMC for bosons Deep connections between different problems Quantum spin liquids (Symmetry protected) Topo. matter Deconfined quantum criticality Composite fermions, symmetric mass generation Duality between DQCP and bosonic SPT Deconfined quantum critical point Emergent continuous symmetry Fractionalization Topological order... Dynamical measurements bridging experiment and theory QMC+SAC...
7 Computing Resources GigaFLOPS: 10^9 Tianhe-1 TeraFLOPS: 10^12 PetaFLOPS: 10^15 ExaFLOPS: 10^18 Tianhe-1: 5PetaFLOPS K-computer: 10PetaFLOPS Tianhe-2: 50PetaFLOPS TaihuLight: 100PetaFLOPs Tianhe-3: 1000PetaFLOPS Tianhe-2
8 Itinerant quantum critical point Nature 424, (2003) Nature 518, 179 (2015) Phys. Rev. Lett. 117, (2016) FM / AFM / Nematic fluctuations of itinerant electron systems Non-Fermi liquid, fluctuation induced superconductivity, Itinerant QCP Hertz-Millis-Moriya, Varma, Kivelson, Fradkin, Abanov, Chubukov, Sachdev, Senthil, Metzner, Vojta, Schmalian, Qimiao Si, Sung-Sik Lee, M. Metlitski... E. Berg, S. Trebst, F. Assaad, Z. Y. M....
9 Model PRX 7, (2017)
10 Quantum Monte Carlo PRX 7, (2017) Self-learning Monte Carlo Method O(N) speedup, large lattice is possible
11 Self-learning Monte Carlo Machine-learning Self-Learning Monte Carlo Method PRB (R) (2017) Self-Learning Monte Carlo method and cumulative update in fermion systems PRB 95, (R) (2017) Self-Learning quantum Monte Carlo method in interacting fermion systems PRB 96, (R) (2017)
12 SLMC for DQMC Fermions coupled to bosonic mode Itinerant quantum critical point Non-Fermi-liquid Electron-phonon coupling Self-Learning Monte Carlo Method PRB (R) (2017) Self-Learning Monte Carlo method and cumulative update in fermion systems PRB 95, (R) (2017) Self-Learning quantum Monte Carlo method in interacting fermion systems PRB 96, (R) (2017) Complexity for getting an independent configuration:
13 SLMC for DQMC Self-Learning on electron-phonon model Phys. Rev. B 98, (R) (2018) Chuang Chen Xiao Yan Xu Richard Scalettar
14 Model PRX 7, (2017)
15 Non-Fermi liquid PRX 7, (2017)
16 FM-QCP Hertz-Millis-Moriya (2+1)d Ising model Our model PRX 7, (2017)
17 FM-QCP Hertz-Millis-Moriya (2+1)d Ising model Our model PRX 7, (2017)
18 FM-QCP Hertz-Millis-Moriya (2+1)d Ising model Our model PRX 7, (2017)
19 Triangle lattice: AFM-QCP PRB 98, (2018) S. V. Isakov and R. Moessner, PRB 68, (2003) Y.-C. Wang, Y. Qi, S. Chen, Z. Y. M., Phys. Rev. B 96, (2017)
20 Triangle lattice: AFM-QCP PRB 98, (2018) L=30, beta=30 (30x30x600)
21 AFM-QCP PRB 98, (2018) L=30, beta=30 (30x30x600)
22 AFM-QCP PRB 98, (2018) L=30, beta=30 (30x30x600)
23 Elective Momentum Ultra-Size QMC (EMUS) r-space k-space arxiv:
24 EMUS-QMC arxiv: Computational complexity Speedup Naturally integrated in SLMC Generic in models when
25 EMUS at AFM-QCP PRB 98, (2018) DQMC L=30, beta=30 (30x30x600) arxiv: EQMC L=48, beta=48 (48x48x960)
26 EMUS at AFM-QCP Z.H.Liu, G.P. Pan, X.Y. Xu, K. Sun, Z.Y.M, in preparison
27 EMUS at AFM-QCP A. Abanov, A. Chubukov, J. Schmalian, Adv. in Phys., 52, 119 (2003) Z.H.Liu, G.P. Pan, X.Y. Xu, K. Sun, Z.Y.M, in preparation
28 Fermionic QCPs with QMCs Ferromagnetic QCP Antiferromagnetic QCP emergent U(1) at QCP Z2 at QCP
29 Quantum Monte Carlo Determinantal QMC for fermions Fermions couple to critical bosonic mode Itinerant quantum critical point Non-Fermi-liquid Self-Learning Monte Carlo methods Matter fields couple to gauge field... World-line QMC for bosons Deep connections between different problems Quantum spin liquids (Symmetry protected) Topo. matter Deconfined quantum criticality Composite fermions, symmetric mass generation Duality between DQCP and bosonic SPT Deconfined quantum critical point Emergent continuous symmetry Fractionalization Topological order... Dynamical measurements bridging experiment and theory QMC+SAC...
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