Jason Kaye

I am an Associate Research Scientist, joint between the Center for Computational Mathematics and the Center for Computational Quantum Physics at the Flatiron Institute, Simons Foundation. My research focuses on the development of robust, high-order, and scalable numerical algorithms for problems in computational quantum physics. I work with high-order and adaptive methods, fast algorithms for the compression of structured operators, and efficient methods for the numerical solution of integral and differential equations. These algorithms have been applied to many-body Green's function methods, quantum embedding, diagrammatics, electronic structure, and other approaches to the quantum many-body problem. Nearly all of my projects involve close collaborations with computational physicists and chemists, and cover algorithm development, implementation, and software.

Download my CV (Feb '24)

Publications/Preprints

(ordered by first appearance)
If no arXiv link is given, journal publication is open access.

  1. L. Van Muñoz, S. Beck, J. Kaye, "AutoBZ.jl: Automatic, adaptive Brillouin zone integration using Wannier interpolation", J. Open Source Softw., 9 (102), 7080 (2024). journal
  2. L. Van Muñoz, J. Kaye, A. Barnett, S. Beck, "High-order and adaptive optical conductivity calculations using Wannier interpolation", arXiv:2406.15466 (2024). arXiv
  3. D. Kiese, H. U. R. Strand, K. Chen, N. Wentzell, O. Parcollet, J. Kaye, "Discrete Lehmann representation of three-point functions", arXiv:2405.06716 (2024). arXiv
  4. J. Kaye, H. U. R. Strand, N. Wentzell, "cppdlr: Imaginary time calculations using the discrete Lehmann representation", J. Open Source Softw., 9 (100), 6297 (2024). journal
  5. T. Blommel, J. Kaye, Y. Murakami, E. Gull, D. Golež, "Chirped amplitude mode in photo-excited superconductors", arXiv:2403.01589 (2024). arXiv
  6. H. LaBollita, J. Kaye, A. Hampel, "Stabilizing the calculation of the self-energy in dynamical mean-field theory using constrained residual minimization", arXiv:2310.01266 (2023). arXiv
  7. J. Kaye, Z. Huang, H. U. R. Strand, D. Golež, "Decomposing imaginary time Feynman diagrams using separable basis functions: Anderson impurity model strong coupling expansion", Phys. Rev. X, 14, 031034 (2024). journal
  8. N. Sheng, A. Hampel, S. Beck, O. Parcollet, N. Wentzell, J. Kaye, K. Chen, "Low-rank Green's function representations applied to dynamical mean-field theory", Phys. Rev. B, 107, 245123 (2023). journal arXiv
  9. J. Kaye, S. Beck, A. Barnett, L. Van Muñoz, O. Parcollet, "Automatic, high-order, and adaptive algorithms for Brillouin zone integration", SciPost Phys., 15 (2), 062 (2023). journal
  10. J. Kaye, A. Barnett, L. Greengard, U. De Giovannini, A. Rubio, "Eliminating artificial boundary conditions in time-dependent density functional theory using Fourier contour deformation", J. Chem. Theory Comput., 19 (5), 1409-1420 (2023). journal arXiv
  11. Y. Núñez-Fernández, M. Jeannin, P. T. Dumitrescu, T. Kloss, J. Kaye, O. Parcollet, X. Waintal, "Learning Feynman diagrams with tensor trains", Phys. Rev. X, 12, 041018 (2022). journal
  12. J. Hoskins, J. Kaye, M. Rachh, J. C. Schotland, "Analysis of single-excitation states in quantum optics", arXiv:2110.07049 (2021). arXiv
  13. J. Kaye, K. Chen, H. U. R. Strand, "libdlr: Efficient imaginary time calculations using the discrete Lehmann representation", Comput. Phys. Commun., 280, 108458 (2022). journal
  14. J. Kaye, H. U. R. Strand, "A fast time domain solver for the equilibrium Dyson equation", Adv. Comput. Math., 49, 63 (2023). journal
  15. J. Hoskins, J. Kaye, M. Rachh, J. C. Schotland, "A fast, high-order numerical method for the simulation of single-excitation states in quantum optics", J. Comput. Phys., 473, 111723 (2023). journal arXiv
  16. J. Kaye, K. Chen, O. Parcollet, "Discrete Lehmann representation of imaginary time Green's functions", Phys. Rev. B, 105, 235115 (2022). journal arXiv
  17. J. Kaye, D. Golež, "Low rank compression in the numerical solution of the nonequilibrium Dyson equation", SciPost Phys., 10 (4), 091 (2021). journal
  18. J. Kaye, A. Barnett, L. Greengard, "A high-order integral equation-based solver for the time-dependent Schrödinger equation", Comm. Pure Appl. Math., 75, 1657-1712 (2022). journal arXiv
  19. J. Kaye, L. Greengard, "A fast solver for the narrow capture and narrow escape problems in the sphere", J. Comput. Phys. X, 5, 100047 (2020). journal
  20. J. Kaye, L. Greengard, "Transparent boundary conditions for the time-dependent Schrödinger equation with a vector potential", arXiv:1812.04200 (2018). arXiv
  21. Y. Bao, J. Kaye, C. S. Peskin, "A Gaussian-like immersed-boundary kernel with three continuous derivatives and improved translational invariance", J. Comput. Phys., 316, 139-144 (2016). journal arXiv
  22. J. Kaye, L. Lin, C. Yang, "A posteriori error estimator for adaptive local basis functions to solve Kohn-Sham density functional theory", Commun. Math. Sci., 13 (7), 1741-1773 (2015). journal arXiv
  23. S. E. Field, C. R. Galley, J. S. Hesthaven, J. Kaye, M. Tiglio, "Fast prediction and evaluation of gravitational waveforms using surrogate models", Phys. Rev. X, 4 (3), 031006 (2014). journal
Dissertation: Integral equation-based numerical methods for the time-dependent Schrödinger equation (Courant Institute of Mathematical Sciences, New York University, Adviser: Leslie Greengard)


Software

cppdlr C++ library implementing the discrete Lehmann representation of imaginary time Green's functions (with Nils Wentzell & Hugo U. R. Strand) (paper)
libdlr Python & Fortran libraries implementing the discrete Lehmann representation of imaginary time Green's functions (with Hugo U. R. Strand) (paper)
AutoBZ Julia package implementing algorithms for automatic, high-order, and adaptive Brillouin zone integration (code written primarily by Lorenzo van Muñoz) (paper)
adapol Python package for adaptive pole-fitting of Matsubara functions (code written primarily by Zhen Huang)

Contact