### Wavefunction matching for solving quantum many-body problems.

Strongly interacting systems are central to the fields of quantum physics and quantum chemistry. Monte Carlo simulations, a type of stochastic method, are widely used to study these systems. However, they face challenges when dealing with sign swings. An international team of researchers from Germany, Turkey, the US, China, South Korea and France has tackled this issue by developing a new technique called wave function matching.

As an example, the masses and radii of all nuclei up to mass number 50 have been calculated using this method. The results agree with the measurements, the researchers report now in the journal *Nature*.

All matter on Earth is made up of tiny particles known as atoms. Each atom it contains even smaller particles: protons, neutrons and electrons. Each of these particles follows the rules of quantum mechanics. Quantum mechanics forms the basis of 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 starting from a description of their elementary components and their interactions. In the case of nuclear physics, the elementary components are protons and neutrons. Some key questions that ab initio calculations can answer are the binding energies and properties of atomic nuclei and the relationship between nuclear structure and the fundamental interactions between protons and neutrons.

#### Challenges and solutions in quantum simulations

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 wavefunction matching, aims to help solve such computational problems for ab initio methods. “This problem is solved by the new wavefunction matching method by mapping the complicated problem to a first approximation to a simple model system that does not have such sign oscillations and then treating the changes in 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 Center for Advanced Simulation and Analysis at 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 Interdisciplinary Research Areas Modeling and Matter at the University of Bonn.

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

#### Practical applications and future perspectives

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 calculable interaction. This transformation is done in a way that preserves all the important properties of the original realistic interaction. Since the new wavefunctions are similar to those of the easily calculable interaction, researchers can now perform calculations with the easily calculable interaction and apply a standard procedure for handling small corrections—called perturbation theory.

The research team applied this new method to lattice quantum Monte Carlo simulations of light nuclei, intermediate-mass nuclei, neutron matter and nuclear matter. Using accurate 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 by matching wave functions.

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

Reference: “Matching Wave Functions for Solving Quantum Many-Body Problems” by Serdar Elhatisari, Lukas Bovermann, Yuan-Zhuo Ma, Evgeny Epelbaum, Dillon Frame, Fabian Hildenbrand, Myungkuk Kim, Youngman Kim, Hermann Krebs, Timo A. Lean De, , Ning Li, Bing-Nan Lu, Ulf-G. Meißner, Gautam Rupak, Shihang Shen, Young-Ho Song, and Gianluca Stellin, 15 May 2024, *Nature*.

DOI: 10.1038/s41586-024-07422-z

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

The first author, Prof. Dr. Serdar Elhatisari, comes from the University of Bonn and Gaziantep Islamic University of Science and Technology (Turkey). Important contributions were also made at Michigan State University. Other participants include Ruhr University in Bochum, South China Normal University (China), Daejeon Institute for Basic Sciences (South Korea), Sun Yat-Sen University in Guangzhou (China), Graduate School of China Academy of Engineering Physics in Beijing (China), Mississippi State University (USA) and Université Paris-Saclay (France). The study was funded by the US Department of Energy, the US National Science Foundation, the German Research Foundation, the National Natural Science Foundation of China, the International Initiative of the President of the Chinese Academy of Sciences, the Volkswagen Foundation, the European Research Council, the Council of Scientific and Technological Research of Turkey, National Security Academic Fund, Rare Isotope Science Project of the Institute for Basic Science, Korea National Research Foundation, Institute for Basic Science and Espace de Structure et de Reactions Nucleaires Theorique.

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