Excited states in variational Monte Carlo using a penalty method

ORAL

Abstract

Finding excited states has been a long-standing challenge in variational Monte Carlo for interacting systems. While there has been notable progress on this front, existing algorithms either do not allow for optimization of all wave function parameters, can have trouble to converging to the correct state as recently shown by Filippi and coworkers, or miss degenerate states. We present an algorithm based on orthogonalization to the ground state that resolves these difficulties in the limit as the wave function parameterization becomes complete. We show an application to the benzene molecule, in which ~10,000 parameters are optimized for the first 12 excited states.

*This material is partially based upon work supported by the U.S. Department of Energy, Office of Science, Of- fice of Basic Energy Sciences, Computational Materials Sciences program under Award Number DE-SC-0020177. L.K.W. was supported by the Simons Collaboration on the Many-Electron Problem. This research is part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (awards OCI-0725070 and ACI-1238993) the State of Illinois, and as of December, 2019, the National Geospatial- Intelligence Agency.

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Presenters

  • Shivesh Pathak

    • University of Illinois at Urbana-Champaign

Authors

  • Shivesh Pathak

    • University of Illinois at Urbana-Champaign

  • Brian Busemeyer

    • Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, Simons Foundation
    • Flatiron Institute

  • Jo?o N. B. Rodrigues

    • University ABC
    • Federal University of ABC

  • Lucas Wagner

    • University of Illinois at Urbana-Champaign
    • University of Illinois Urbana-Champaign