Making Difficult Quantum Many-Body Calculations Possible

Solving quantum many-body problems with wavefunction matching.

Wavefunction matching replaces the short distance part of the two-body wavefunction for a realistic interaction with that of a simple easily computable interaction. The result is a new interaction that can be handled in quantum many-body calculations. — Image courtesy of Dean Lee

The Science

Quantum many-body systems are incredibly complex. This makes them difficult to study even with the most powerful computers. One of the methods scientists use to study quantum many-body systems is the ab initio approach, which describes complex systems in terms of elementary components and their interactions. However, some ab initio methods run into severe computational problems when using realistic interactions. Wavefunction matching is a new approach that solves this problem. It does so by changing the interactions of particles at short distances so that their quantum state wavefunctions match that of an easily computable interaction. This enables difficult calculations that were previously not possible.

The Impact

In this study, scientists introduced wavefunction matching and use it to perform lattice simulations with realistic interactions. They applied this approach to light nuclei, medium-mass nuclei, neutron matter, and nuclear matter. The theoretical results agree well with empirical data on properties such as nuclear size, structure, and binding energies. This approach allows scientists to make calculations that were once impossible. This approach is useful in many different applications, including both classical and quantum computing calculations.

Summary

Researchers using methods for quantum many-body systems that start from first principles frequently find that they can perform calculations using a simple approximate interaction, but realistic high-fidelity interactions are not possible due to computational problems. This research introduces a new approach called wavefunction matching that solves this problem by using surgery. Wavefunction matching removes the short-distance part of the high-fidelity interaction and replaces it with the short-distance part of an easily computable interaction.

This transformation is done in a way that preserves all the important properties of the original interaction. Since the new wavefunctions look like those of the easily computable interaction, calculations can now be performed using the easily computable interaction, together with a standard procedure for handling small corrections called perturbation theory. The researchers applied this new approach to lattice simulations for light nuclei, medium-mass nuclei, neutron matter, and nuclear matter.

Contact

Dean Lee
Facility for Rare Isotope Beams
[email protected]

Funding

This research was funded by the Department of Energy Office of Science and by an extensive array of German, Korean, Turkish, Chinese, and other organizations. For a complete list of funding sources, please see the paper in Nature.

Publications

Elhatisari, S., et al., Wavefunction matching for solving quantum many-body problems. Nature 630, 59–63 (2024). [DOI: 10.1038/s41586-024-07422-z]