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  • Bringing people and ideas together to fund, conduct, and share transformative science.

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  • Founded by Jim and Marilyn Simons, we’re a private philanthropy advancing mathematics and basic science.

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Bringing people and ideas together to fund, conduct, and share transformative science.

Our grants advance knowledge and strengthen connections between science and society.

Discover the latest news, research, and updates.

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We convene scientists, mathematicians, and thinkers to share ideas and explore new questions.

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Founded by Jim and Marilyn Simons, we’re a private philanthropy advancing mathematics and basic science.

Work with us on the frontier of basic science research.

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The Flatiron Institute is a research center that uses computational science to advance fields like physics, biology, and astronomy.

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Featured

Dissecting mechanisms of hyperarousal in autism and related disorders using the Simons Sleep Project

Funded Work

Gravity Follows Newton’s and Einstein’s Rules, Even at Cosmic Scales

April 15, 2026

Scientists Capture Superconductivity’s ‘Dancing Pairs’ for First Time, Filling Gap in Decades-Old Theory

April 15, 2026

How SURFiN Fellowships Jump-Started These 3 Neuroscience Students’ STEM Careers

March 18, 2026

Results

  1. Interfacing Branching Random Walks with Metropolis Sampling: Constraint Release in Auxiliary-Field Quantum Monte Carlo

    Publication
  2. Solving 2D and 3D lattice models of correlated fermions -- combining matrix product states with mean field theory

    Publication
  3. Solving 2D and 3D lattice models of correlated fermions -- combining matrix product states with mean field theory

    Publication
  4. Ab initio Calculations in Atoms, Molecules, and Solids, Treating Spin-Orbit Coupling and Electron Interaction on Equal Footing

    Publication
  5. Pseudo-BCS wave function from density matrix decomposition: Application in auxiliary-field quantum Monte Carlo

    Publication
    We present a method to construct pseudo-BCS wave functions from the one-body density matrix. The resulting many-body wave function, which can be produced for any …
  6. Precision Many-Body Study of the Berezinskii-Kosterlitz-Thouless Transition and Temperature-Dependent Properties in the Two-Dimensional Fermi Gas

    Publication
  7. Stripes and spin-density waves in the doped two-dimensional Hubbard model: ground state phase diagram

    Publication
  8. Absence of superconductivity in the pure two-dimensional Hubbard model

    Publication
    We study the superconducting pairing correlations in the ground state of the doped Hubbard model -- in its original form without hopping beyond nearest neighbor or other perturbing parameters …
  9. Direct comparison of many-body methods for realistic electronic Hamiltonians

    Publication
    A large collaboration carefully benchmarks 20 first-principles many-body electronic structure methods on a test set of seven transition metal atoms and their ions and monoxides. Good …
  10. Metal-Insulator and Magnetic Phase Diagram of Ca2RuO4 from Auxiliary Field Quantum Monte Carlo and Dynamical Mean Field Theory

    Publication
    Layered perovskite ruthenium oxides exhibit a striking series of metal-insulator and magnetic-nonmagnetic phase transitions easily tuned by temperature, pressure, epitaxy, and nonlinear drive. In this work …
  11. Ground-state properties of the hydrogen chain: insulator-to-metal transition, dimerization, and magnetic phases

    Publication
    Accurate and predictive computations of the quantum-mechanical behavior of many interacting electrons in realistic atomic environments are critical for the theoretical design of materials with desired properties …
  12. Reaching the continuum limit in finite-temperature ab initio field-theory computations in many-fermion systems

    Publication
    Finite-temperature, grand-canonical computations based on field theory are widely applied in areas including condensed matter physics, ultracold atomic gas systems, and lattice gauge theory. However, these …
  13. Auxiliary Field Quantum Monte Carlo for Multiband Hubbard Models: Controlling the Sign and Phase Problems to Capture Hund's Physics

    Publication
    In the study of strongly-correlated, many-electron systems, the Hubbard Kanamori (HK) model has emerged as one of the prototypes for transition metal oxide physics. The model …
  14. Finite-temperature auxiliary-field quantum Monte Carlo: Self-consistent constraint and systematic approach to low temperatures

    Publication
    We describe an approach for many-body calculations with a finite-temperature, grand canonical ensemble formalism using auxiliary-field quantum Monte Carlo (AFQMC) with a self-consistent constraint …
  15. Auxiliary Field Quantum Monte Carlo for Multiband Hubbard Models: Controlling the Sign and Phase Problems to Capture Hund's Physics

    Publication
  16. Metal-insulator transition in the ground-state of the three-band Hubbard model at half-filling

    Publication
    The three-band Hubbard model is a fundamental model for understanding properties of the Copper-Oxygen planes in cuprate superconductors. We use cutting-edge auxiliary-field quantum Monte …
  17. Magnetic orders in the hole doped three-band Hubbard model: spin spirals, nematicity, and ferromagnetic domain walls

    Publication
    The copper-oxygen planes in cuprates have been at the center of the search for a theory of high-temperature superconductivity. We conduct an extensive study of the …
  18. Accurate computations of Rashba spin-orbit coupling in interacting systems: from the Fermi gas to real materials

    Publication
    We describe the treatment of Rashba spin-orbit coupling (SOC) in interacting many-fermion systems within the auxiliary-field quantum Monte Carlo framework, and present a set of …

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