# Simons Collaboration on the Many Electron Problem Annual Meeting 2017

Date & Time

A group of 55 researchers from the U.S., Canada and Europe gathered at the Simons Foundation on February 16 and 17 for the 2017 annual meeting of the Simons Collaboration on the Many Electron Problem. Talks by collaboration scientists and by distinguished external speakers were presented, along with poster sessions at which all of the collaboration-supported students and postdocs presented their work.

The collaboration’s goal is to develop new ways to solve the quantum mechanical behavior of systems comprising many interacting electrons, with the eventual goal of revolutionizing our ability to calculate and understand the properties of molecules and solids that are important in chemistry, physics and everyday life. The annual meeting is a venue for the collaboration members to meet, compare results, exchange ideas and hear about new ideas developed both by collaboration members and non-collaboration scientists.

• Meeting Report

Overview:

The 2017 meeting of the Simons Foundation Collaboration on the Many Electron Problem brought together members of the collaboration,  as well as  non-Collaboration scientists including Sandro Sorella (SISSA, Italy), Mike Zaletel (Princeton, Guest Speaker) and George Booth (Kings College London, Guest Speaker).

The main focus of the meeting was a review of Collaboration activities, with talks by Collaboration PIs summarizing progress and goals.  The relation between the Collaboration and the new Flatiron CCQ was also discussed.

The Scientific Advisory Board reported that the Collaboration is progressing well, with ample examples of important work that is unlikely to have taken place with the Collaboration. The benchmarking projects received particular praise.  The SAB endorsed the proposal to add a third benchmarking project, on dynamics and spectra, to be organized by Emanuel Gull and discussed ways to move forward on evaluating the real materials approaches. The discussion revealed difficulties with current proposals; more work is needed here.

The SAB argued that there was a strong case for continuing the Collaboration beyond the current funding period, and suggested that it should be viewed as a way to broaden the reach and the impact of the CCQ and that the collaboration research should be complementary to that of the CCQ.

Talks:

Michael Zaletel (Guest speaker, Princeton University) reported on recent studies of topological order using wave function (primarily DMRG) methods, including a theoretical characterization of the fractionally quantized Hall states of graphene. The methods may be useful in the next steps of wave functions group towards the complete solution of the Hubbard model.

Steven White (Group leader, wave functions).  Solving the Hubbard Model: Where do we stand? White reported recent Collaboration progress on the solution of the two dimensional Hubbard model, one of the fundamental models of quantum many-body physics, including an update on the Hubbard benchmarking project. A highlight was the recent determination (obtained jointly by collaboration PIs White, Chan and Zhang, along with external scientists) of the ground state of the Hubbard model at strong correlation and moderate doping. This collaboration work settled a decades old controversy and pointed the way to a deeper understanding of high transition temperature superconductivity.  Continuing this theme, Antoine Georges (Group leader, cluster embedding) showed that new developments in diagrammatic Monte Carlo (in particular an improved mathematical understanding of the convergence properties of the theory) now provide access to the pseudogap regime of the model.

Shiwei Zhang The Hydrogen Benchmarking Project reported progress in the next steps of moving methods from model to realistic systems. Zhang showed that methods are making progress in dealing with physically relevant (long ranged Coulomb) interactions and the complexities of working in the continuum. We now have a suite of methods that are accurate at the level of 5% of the binding energy per atom,  laying the foundation for progress on real materials. George Booth (Guest speaker) described a different approach, the FCIQMC’ method. Using previous collaboration benchmarking results he demonstrated accuracy for model systems. This methodology will likely be incorporated into the Collaboration going forward.

Mark van Schilfgaarde (Group Leader, Real materials) GW and beyond: realistic calculations for correlated materials summarized recent work of the real materials’ group, stressing the successes and challenges of the GW + DMFT approach.  Stimulated by this talk issues of benchmarking (or at least establishing the accuracy) of the X+DMFT/X+DMET methods for treating the complexities of real materials were discussed. The two key features of the GW+DMFT approach are the ability to treat interactions beyond the fully local on-site interactions, and to provide a systematic calculation of the interaction parameters and double counting.  An alternative approach to these issues was presented by new collaboration member Dominika Zgid  who presented first results from her Self Energy Embedding Theory.  These issues were also addressed by Nicolai Prokof’ev (Diagrammatic Monte Carlo) who summarized the current status of the program to systematically (stochastically) evaluate the diagram series of which GW is the first term.  Results are becoming available for the simplest model problem (“jellium’’; electrons in a uniform positive background).  The hydrogen benchmarking project is a first step towards incorporating the orbital structure of real materials into this methodology. Doing this in general is a significant challenge.

Emanuel Gull (Group Leader, Monte Carlo) identified the key challenge on the model system side as moving beyond the local physics/local interactions which dynamical mean field theory treats well. His talk, Dynamical Mean Field Theory and Beyond presented first results on GW, dual fermion and other approximations. Olivier Parcollet presented a closely related `Trilex’ approach.

Guifre Vidal presented a talk on Continuous tensor networks: recent results and a route map.

### Talks

• Agenda

#### THURSDAY, FEBRUARY 16TH

 A. Millis: Welcome and Collaboration Overview Poster Introductions S. White: Solving the Hubbard Model: Where do we stand? Poster Introductions M. van Schilfgaarde: GW and beyond: realistic calculations for correlated materials Lunch and Posters S. Zhang: The Hydrogen Benchmarking Project M. Zaletel: DMRG Studies of Graphene Quantum Hall Effects Break and Posters D. Zgid: Quantum Embedding Beyond DMFT G. Vidal: Continuous tensor networks: recent results and a route map

#### FRIDAY, FEBRUARY 17TH

 E. Gull: Dynamical Mean Field Theory and Beyond Break and Posters G. Booth: FCIQMC: Successes, issues and prospects O. Parcollet: Fiat Lex: nonlocality in dynamical mean field theory N. Prokof’ev: Diagrammatic Monte Carlo & the Fermionic Sign Problem A. Georges: The Pseudogap and the Simons Many Electron Collaboration
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