Simons Collaboration on the Many Electron Problem Annual Meeting 2021 (Online)

Many Electrons Collaboration
Annual Report
Feb 02, 2021

Summary: The Simons Collaboration on the Many Electron Problem was renewed for an additional four-year period starting March 1, 2019. Several of the original Collaboration members moved to the Flatiron Institute as Founding Members of the Center for Computational Quantum Physics (CCQ). It was agreed that the departing members would not be replaced and that in the renewal period Collaboration funding would be at a lower level, while Collaboration research would emphasize topics not currently emphasized at CCQ, in particular (a) new directions in quantum embedding methods, and (b) diagrammatic Monte Carlo. Research in these directions has been very successful and the Collaboration plans to continue to emphasize these directions in the coming years. The Collaboration’s “Benchmark” papers have changed the intellectual direction of the field, introducing new standards for collaboration and reproducibility of results.

The COVID-induced cancellation of the summer school, the 2021 in-person annual meeting and the usual in person working group meetings, as well as greatly reduced travel, has freed up funds that we would like to use to support James LeBlanc (University of Newfoundland) who has been making increasingly important contributions to the Diagrammatic Monte Carlo effort, and to add an investigator (yet to be determined) to the embedding effort.

Science: 2020. The past COVID-dominated year saw no formal collaboration activities after the 2020 Annual Meeting, but informal collaborations and work on ongoing projects continued.

Electron density in hydrogen chain demonstrating dimerization>

Highlights include the development of the “all electron” embedding scheme (Chan,[1]), significant progress on the self energy embedding theory (Zgid, Gull [2]), the completion of the Hydrogen chain [3] and transition metal [4] benchmarking projects (Chan, Millis (also CCQ), Sorella, Wagner, White, Zhang (now CCQ)); pathbreaking studies of the Hubbard model including a magesterial multi-messenger study of many physical properties (Ferrero, Georges (CCQ), Kozik, Prokofeev, Svistunov, Zhang [5]) further evidence that the model is not superconducting at high temperatures for parameters relevant to experimentally observed high Tc superconducting materials (White, Zhang [6]) and development of the diagrammatic Monte Carlo method both theoretically (Svistunov [7]) and for the electron gas and real materials {Haule [8]).

2021 plans:

• Reuniting the collaboration: we are introducing a student/postdoc on-line seminar (organizers I. Tupitsyn, Amherst and Sergei Isakov, Michigan), that will be a combination or research presentation, methods tutorial and on-line coffee hour. We are scheduling a Diagrammatic Monte Carlo internal meeting (Ferrero) for early march, to be repeated at two month intervals as needed and an in person (COVID permitting) meeting on next steps in the hydrogen benchmarking (Millis, White) (fall 2021, at CCQ); conference on superconductivity in model systems (White) to be preceded by a zoom conference in late spring. Summer schools will not resume until in-person gatherings are practicable.
• 
  Schematic of all electron embedding, from [1]

  Embedding: further development of SEET Joint investigation of target systems via SEET (Gull, Zgid)and all electron DMFT (Chan) with comparison (where possible) to d-QMC (Wagner): transition metal monoxides and `infinite layer’ nickelate superconductors,. Relation of DMET to rotationally invariant slave boson methods (Chan, Kotliar), Release of all electron DMFT software package (Chan). Further development of basis sets and representation of interactions (Chan, Gull, Haule, Kotliar, Wagner, White).

• Crossovers as a function of interaction and temperature computed by Diagrammatic Monte Carlo methods, from M. Ferrero

  Diagrammatic Monte Carlo. Integration of formal advances (Svistunov, Prokofeev) into working codes (Ferrero, Haule) (planned meeting, March 2021). Completing solution of Hubbard model: diagrammatic Monte Carlo and other method investigation of pseudogap physics of doped model (Ferrero, Georges, LeBlanc, White, Zhang). Multimessenger investiations of superconductivity (White, Zhang) (planned meetings, May 2021 and fall 2021); implementation of diagrammatic MC for mateials (Haule), electron-phonon coupling and superconductivity in metallic hydrogen (Haule, Sorella). Use of diagrammatic methods to gain insight to embedding methods: (Gull, Kotliar). Also development of diagrammatic Monte Carlo methods to compute experimentally relevant observables directly in real time/frequency, avoiding the imaginary time/analytic continuation process used in the standard methods. (Ferrero, Haule, Le Blanc, Prokofev).

• Benchmarking projects, next steps (Wagner, White, Millis). Planned collaboration meeting.
• Additional personnel: James LeBlanc (Halifax): crucial contributions to Diagrammatic Monte Carlo; Sandro Sorella (supported in 2019/20) crucial contributions to benchmarking and quantum Monte Carlo methodologies and results, one person to be named later for embedding effort.

References

[1] “Ab initio Full Cell GW+DMFT for Correlated Materials “, T. Zhu and. G. Chan, arXiv:2003.01349

[2] “Ab initio self-energy embedding for the photoemission spectra of NiO and MnO”, Sergei Iskakov, Chia-Nan Yeh, Emanuel Gull, and Dominika Zgid, Phys. Rev. B 102, 085105 (2020)

[3] “Ground-State Properties of the Hydrogen Chain: Dimerization, Insulator-to-Metal Transition, and Magnetic Phases”, Mario Motta, Claudio Genovese, Fengjie Ma, Zhi-Hao Cui, Randy Sawaya, Garnet Kin-Lic Chan, Natalia Chepiga, Phillip Helms, Carlos Jiménez-Hoyos, Andrew J. Millis, Ushnish Ray, Enrico Ronca, Hao Shi, Sandro Sorella, Edwin M. Stoudenmire, Steven R. White, and Shiwei Zhang (Simons Collaboration on the Many-Electron Problem), Phys. Rev. X 10, 031058 (2020)

[4] “Direct Comparison of Many-Body Methods for Realistic Electronic Hamiltonians”, Kiel T. Williams, Yuan Yao, Jia Li, Li Chen, Hao Shi, Mario Motta, Chunyao Niu, Ushnish Ray, Sheng Guo, Robert J. Anderson, Junhao Li, Lan Nguyen Tran, Chia-Nan Yeh, Bastien Mussard, Sandeep Sharma, Fabien Bruneval, Mark van Schilfgaarde, George H. Booth, Garnet Kin-Lic Chan, Shiwei Zhang, Emanuel Gull, Dominika Zgid, Andrew Millis, Cyrus J. Umrigar, and Lucas K. Wagner (Simons Collaboration on the Many-Electron Problem), Phys. Rev. X 10, 011041 (2020).

[5] “Tracking the Footprints of Spin Fluctuations: A Multi-Method, Multi-Messenger Study of the Two-Dimensional Hubbard Model”, Thomas Schäfer, Nils Wentzell, Fedor Šimkovic IV, Yuan-Yao He, Cornelia Hille, Marcel Klett, Christian J. Eckhardt, Behnam Arzhang, Viktor Harkov, François-Marie Le Régent, Alfred Kirsch, Yan Wang, Aaram J. Kim, Evgeny Kozik, Evgeny A. Stepanov, Anna Kauch, Sabine Andergassen, Philipp Hansmann, Daniel Rohe, Yuri M. Vilk, James P. F. LeBlanc, Shiwei Zhang, A.-M. S. Tremblay, Michel Ferrero, Olivier Parcollet, Antoine Georges, arXiv:2006:10769, PRX in press (2021).

[6] “Absence of Superconductivity in the Pure Two-Dimensional Hubbard Model”, Mingpu Qin, Chia-Min Chung, Hao Shi, Ettore Vitali, Claudius Hubig, Ulrich Schollwöck, Steven R. White, and Shiwei Zhang (Simons Collaboration on the Many-Electron Problem), Phys. Rev. X 10, 031016 (2020) and Jiang, White and Scalapino, in preparation.

[7] “Homotopic Action: A Pathway to Convergent Diagrammatic Theories”, Aram J, Kim, Nikolai V. Prokof’ev, Boris V. Svistunov, Evgeny Kozik, arXiv:2010.05301.

[8] “ Single-particle excitations in the uniform electron gas by diagrammatic Monte Carlo”, K. Haule and K. Chen, arXiv:2012.03146.

The Magic of Two-Dimensional Materials

Eva Andrei, Ph.D.
Board of Governors Professor, Department of Physics , Rutgers, The State University of New Jersey

Atomically-thin crystal sheets have transformed the way we think about materials. Starting with the surprising isolation of graphene from graphite, this family of materials has by now grown to include dozens of viable atomic sheets, with thousands more predicted theoretically. The 2D structure makes it possible to change a material’s properties without changing its chemical composition — like an alchemist’s conjury. For example, by tuning the twist between two superposed 2D crystals to certain magic angles, one can create correlated-electron states that alternate between superconducting, ferromagnetic or insulating phases at the turn of a knob. Recent advances in both experiment and theory have expanded the toolbox for tuning electronic properties and uncovered their connection to the topology of the electronic wave-function. In this lecture, Eva Andrei will describe the highlights of this rapidly evolving field from its serendipitous discovery to recent developments.

More information is available at the lecture’s page.

Andrew Millis
Collaboration Overview and Plans (PDF)

Emanuel Gull
Embedding Methods (PDF)

Nikolay Prokof’ev
Diagramatic Monte Carlo (PDF)