New wave function matching method helps solve many-body quantum problems

International research team solves a difficult physics problem

Wave function matching and the Tjon band. Credit: Nature (2024). DOI: 10.1038/s41586-024-07422-z

Strongly interacting systems play an important role in quantum physics and quantum chemistry. Stochastic methods such as Monte Carlo simulations are a proven method to investigate such systems. However, these methods reach their limits when so-called sign oscillations occur.

This problem has now been solved by an international team of researchers from Germany, Turkey, the US, China, South Korea and France using the new method of wave function matching. For example, with this method the masses and radii of all nuclei up to mass number 50 were calculated. The results correspond with the measurements, the researchers now report in the journal Nature.

All matter on Earth is made up of tiny particles known as atoms. Each atom contains even smaller particles: protons, neutrons and electrons. Each of these particles follows the rules of quantum mechanics. Quantum mechanics forms the basis of the quantum many-body theory, which describes systems with many particles, such as atomic nuclei.

One class of methods used by nuclear physicists to study atomic nuclei is the ab initio approach. It describes complex systems by beginning with a description of their elementary components and their interactions. In the case of nuclear physics, the elementary components are protons and neutrons. Some important questions that ab initio calculations can help answer are the binding energies and properties of atomic nuclei and the relationship between nuclear structure and the underlying interactions between protons and neutrons.

However, these ab initio methods have difficulties in performing reliable calculations for systems with complex interactions. One of these methods is quantum Monte Carlo simulations. Here quantities are calculated using random or stochastic processes.

Although quantum Monte Carlo simulations can be efficient and powerful, they have a significant weakness: the sign problem. It arises in processes with positive and negative weights, which cancel each other out. This cancellation leads to inaccurate final predictions.

A new approach, known as wave function matching, aims to help solve such computational problems for ab initio methods.

“This problem is solved by the new method of wave function matching by mapping the complicated problem in a first approximation onto a simple model system that does not have such sign oscillations and then dealing with the differences in the perturbation theory,” says Prof. Ulf- G. Meißner from the Helmholtz Institute for Radiation and Nuclear Physics at the University of Bonn and from the Institute for Nuclear Physics and the Center for Advanced Simulation and Analysis of Forschungszentrum Jülich.

“As an example, the masses and radii of all nuclei up to mass number 50 were calculated – and the results agree with the measurements,” reports Meißner, who is also a member of the Transdisciplinary Research Areas “Modeling” and “Matter” at the University of Bonn.

“In quantum many-body theory, we are often faced with the situation where we can perform calculations using a simple approximate interaction, but realistic high-fidelity interactions cause serious computational problems,” says Dean Lee, professor of physics at the Facility for Rare. Istope Beams and Department of Physics and Astronomy (FRIB) at Michigan State University and head of the Department of Theoretical Nuclear Sciences.

Wavefunction matching solves this problem by removing the short-range part of the high-fidelity interaction and replacing it with the short-range part of an easily computable interaction. This transformation is performed in a way that preserves all the important properties of the original realistic interaction.

Because the new wave functions are similar to those of the easily computable interaction, the researchers can now perform calculations with the easily computable interaction and apply a standard procedure for handling small corrections, called perturbation theory.

The research team applied this new method to quantum Monte Carlo simulations for light nuclei, intermediate-mass nuclei, neutron matter and nuclear matter. Using precise ab initio calculations, the results closely matched real-world data on nuclear properties such as size, structure and binding energy. Calculations that were once impossible due to the sign problem can now be performed with wave function matching.

Although the research team focused exclusively on quantum Monte Carlo simulations, wave function matching should be useful for many different ab initio approaches. “For example, this method can be used in both classical computing and quantum computing to better predict the properties of so-called topological materials, which are important for quantum computing,” says Meißner.

The first author is Prof. Dr. Serdar Elhatisari, who worked for two years as a Fellow on the ERC Advanced Grant EXOTIC of Prof. Meißner. According to Meißner, a large part of the work was carried out during this time. Part of the computing time on supercomputers at Forschungszentrum Jülich was provided by the IAS-4 institute, which Meißner heads.

More information:
Serdar Elhatisari et al., Wave function matching for solving quantum many-body problems, Nature (2024). DOI: 10.1038/s41586-024-07422-z

Offered by the University of Bonn

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