The Simons Collaboration on the Many Electron Problem held its first working meeting September 4 and 5 at the Simons Foundation. 29 scientists attended, including five guest speakers in addition to the collaboration’s members.
Organized by group directors Steven White of the University of California, Irvine and Emanuel Gull of the University of Michigan, the meeting focused on model systems that capture the essential difficulties of many-particle quantum mechanics while omitting much of the complexity of actual materials. Despite their simplicity, the models have resisted analytical solution and bringing them under numerical control has been a long-standing goal of the field.
Collaboration scientists and guest speakers presented and compared findings from a diverse spectrum of methods ranging from auxiliary field Monte Carlo and diagrammatic Monte Carlo to density matrix renormalization group and tensor network, also including multireference symmetry-projected variational calculations, conventional and enhanced dynamical mean field theory, density matrix embedding theory and linked cluster expansions. Intensive discussions before and during the meeting led to new insights into the strengths and limitations of the various theoretical approaches and have catalyzed new interactions between research groups.
The cross-comparison of results demonstrated at the meeting provides a firm base of understanding that will guide the collaboration’s development of next-generation methods for more realistic problems.
Thursday, September 4
9:10 - 9:45 AM Auxiliary-field calculations: progress, issues, and opportunities | S. Zhang View Slides 9:45 - 10:25 AM The Numerical Linked Cluster Expansion and Entanglement at Quantum Critical Points |R. Melko View Slides 10:45 - 11:20 AM Combing QMC and Tensor Networks to Approach the Hubbard Model | B. Clark View Slides 11:20 AM - 12:00 PM Short talks| M. Ferrero; B. Verstichel
- View Ferrero Slides
- View Verstichel Slides
1:00 - 1:25 PM Benchmarks: how well do our methods work? | E. Gull View Slides 1:25 - 2:15 PM Short Talks | J. LeBlanc; G. Chan View Slides 2:15 - 2:45 PM Dynamical cluster approximation with continuous self- energy: Superconductivity in the Hubbard model |T. Maier View Slides 2:45 - 3:30 PM Short Talks | G. Evenbly; Y. Deng
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- View Deng Slides
3:45 - 4:10 PM Stripes and pairing in t-J and Hubbard models | S. White View Slides 4:10 - 5:00 PM Short Talks | N. Prokofiev; A. Go; Z. Zhu
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- View Go Slides
- View Zhu Slides
Friday, September 5
9:00 - 9:25 AM Quantum algorithms for the Hubbard Model | M.Troyer View Slides 9:25 - 10:30 AM Short talks | E. Kozik; B. Zheng; M. Troyer
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- View Zheng Slides
- View Troyer Slides
10:45 - 11:25 AM Symmetry breaking and restoration applied to the Hubbard model | G. Scuseria View Slides 11:25 AM - 12:30 PM Short talks | H. Shi; M. Qin
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- View Qin Slides
12:30 - 2:00 PM Working Lunch: Summary, Goals and Future Plans | A. Millis