Quantum Monte Carlo investigations of correlated electron systems, present and future. Zi Yang Meng ( 孟子杨 )
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1 Quantum Monte Carlo investigations of correlated electron systems, present and future Zi Yang Meng ( 孟子杨 )
2 Collaborators Xiao Yan Xu Yoni Schattner Zi Hong Liu Erez Berg Chuang Chen Kai Sun Gao Pei Pan Cenke Xu Yang Qi Fakher Assaad
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 modes 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 SPT transitions Deconfined quantum critical point Emergent continuous symmetry... Dynamical measurements bridging experiment and theory QMC+SAC Dynamical Signatures of fractionalizations & topo. order...
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, Y. Schattner, 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 George Batrouni 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 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 SPT transitions Deconfined quantum critical point Emergent continuous symmetry... Dynamical measurements bridging experiment and theory QMC+SAC Dynamical Signatures of fractionalizations & topo. order...
30 U1 gauge fields coupled to Fermi surface arxiv:
31 U1 gauge fields coupled to Fermi surface arxiv:
32 U1 gauge fields coupled to Fermi surface arxiv:
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