Solving Quantum Many-Body Problems with Wavefunction Matching

According to the journal Nature, an international team of researchers from Germany, Turkey, the United States, China, South Korea, and France has suggested a novel approach for exploring strongly interacting systems using wavefunction matching.

Quantum physics and quantum chemistry both rely heavily on strongly interacting systems. Monte Carlo simulations, for example, are a well-established approach for studying complex systems. However, these approaches have limitations when so-called sign oscillations occur.

For example, this approach was used to compute the masses and radii of all nuclei up to mass 50. The results are consistent with the measurements.

All matter on Earth comprises atoms, each containing smaller particles: protons, neutrons, and electrons. These particles are governed by the rules of quantum mechanics. Quantum mechanics serves as the foundation for quantum many-body theory, which delves into systems with numerous particles like atomic nuclei.

Nuclear physicists employ various methods to explore atomic nuclei, including the ab initio approach, which tackles complex systems by beginning with a description of their elementary components and interactions. In nuclear physics, these components are protons and neutrons. Ab initio calculations aim to address fundamental questions such as atomic nuclei's binding energies, properties, and the correlation between nuclear structure and proton-neutron interactions.

Yet, ab initio methods encounter challenges when dealing with systems featuring intricate interactions. Quantum Monte Carlo simulations, a subset of these methods, calculate quantities using random or stochastic processes. While efficient and potent, they have a major weakness: the sign problem. This issue arises due to the presence of positive and negative weights that cancel each other out, resulting in inaccurate predictions.

Wavefunction matching is a novel method designed to assist in resolving such calculation issues for ab initio techniques.

This problem is solved by the new method of wavefunction matching by mapping the complicated problem in a first approximation to a simple model system that does not have such sign oscillations and then treating the differences in perturbation theory. As an example, the masses and radii of all nuclei up to mass number 50 were calculated - and the results agree with the measurements.

Ulf-G. Meißner, Professor, Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn

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

Wavefunction matching tackles this challenge by eliminating the short-distance component of the high-fidelity interaction and substituting it with the short-distance component of a readily calculable interaction. This substitution is executed in a manner that conserves all essential properties of the original, realistic interaction.

As the new wavefunctions closely resemble those of the easily computable interaction, researchers can now conduct calculations with the latter and employ standard procedures, such as perturbation theory, to manage minor corrections.

This innovative method was applied by the research team to lattice quantum Monte Carlo simulations for various scenarios, including light nuclei, medium-mass nuclei, neutron matter, and nuclear matter.

Through precise ab initio calculations, the outcomes closely mirrored real-world data on nuclear properties like size, structure, and binding energy. What were once deemed impossible calculations due to the sign problem are now achievable with wavefunction matching.

Although the research team primarily focused on quantum Monte Carlo simulations, wavefunction matching holds promise for a wide array of ab initio approaches.

Meißner stated, “This method can be used in both classical computing and quantum computing, for example, to better predict the properties of so-called topological materials, which are important for quantum computing.”

The first author, Prof. Dr Serdar Elhatisari, was a Fellow of Prof. Meißner’s ERC Advanced Grant EXOTIC for two years. Meißner states that a significant portion of the work was completed during this time. Part of the computing time on supercomputers at Forschungszentrum Jülich was provided by the IAS-4 institute, which Meißner heads.

Sponsorship

Prof. Dr. Serdar Elhatisari, the first author, is affiliated with Gaziantep Islam Science and Technology University (Turkey) and the University of Bonn. Michigan State University also made significant contributions. Université Paris-Saclay (France), Mississippi State University (USA), Sun Yat-Sen University in Guangzhou (China), Ruhr University Bochum, South China Normal University (China), the Institute for Basic Science in Daejeon (South Korea), and the Graduate School of China Academy of Engineering Physics in Beijing (China) are among the other participants.

The US Department of Energy, the US National Science Foundation, the German Research Foundation, the National Natural Science Foundation of China, the Chinese Academy of Sciences President's International Fellowship Initiative, the Volkswagen Foundation, the European Research Council, the Scientific and Technological Research Council of Turkey, the National Security Academic Fund, the Rare Isotope Science Project of the Institute for Basic Science, the National Research Foundation of Korea, the Institute for Basic Science and the Espace de Structure et de reactions Nucleaires Theorique all provided funding for the study.

Journal Reference:

Elhatisari, S., et. al. (2024) Wavefunction matching for solving quantum many-body problems. Nature. doi:10.1038/s41586-024-07422-z