Magnetic field induced tunability of spin Hamiltonians: Resonances and Efimov states in Yb 2 Ti 2 O 7
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For a considerable time, large datasets containing problem instances have proven valuable for analyzing computer hardware, software, and algorithms. One notable example of the value of large datasets is ImageNet [1], a vast repository of images that has been instrumental in testing numerous deep learning packages. Similarly, in the domain of computational chemistry and materials science, the availability of extensive datasets such as the Protein Data Bank [2], the Materials Project [3], and QM9 [4] has greatly facilitated the evaluation of new algorithms and software approaches, while also promoting standardization within the field. These well-defined datasets and problem instances, in turn, serve as the foundation for creating benchmarking suites like MLPerf [5] and LINPACK [6], [7]. These suites enable fair and rigorous comparisons of different methodologies and solutions, fostering continuous advancements in various areas of computer science and beyond.
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Deep learning can provide a better complementary link between the theoretical models and experimental results in magnetism.
The 3α phenomenological model describes the structure of the carbon-12 nucleus as a cluster of three alpha particles. This model includes a pairwise α–α interaction and a three-body force. To fit the three-body potential, the 12 C data are used, while ensuring that the pair potential reproduces the α–α scattering data. Alternatively, the mass-energy compensation (MEC) effect can be used to simulate the effect of the three-body potential by adjusting the mass of the α particle within the effective-mass approach. We demonstrate the MEC effect for the 3α ground state by numerically solving the differential Faddeev equation, in which the α–α interaction is described by the Ali-Bodmer potential. The effective masses of α particles are evaluated for the ground and excited 0 + and bound 2 + states. Here, we demonstrate a coupling between the ground and first excited 0 + states, indicated by an anti-crossing of these energy levels in the energy–mass coordinates. A correspondence between the effective mass and a three-body potential is demonstrated. We discuss the results of the 0$^{+}_{2}$ calculations for various models of the α–α interaction.
Short and revised version of SAND2024-14806O, to be published in the Proceedings of the ACM STOC 2025