AI Insight
This study presents a new computational method using diagrammatic Monte Carlo to calculate how positrons (antimatter electrons) interact with molecules. The stochastic sampling approach dramatically reduces memory requirements by a factor of 100-1000 compared to previous exact methods, while maintaining quantitative accuracy as demonstrated through benchmark calculations on lithium hydride. The method systematically sums infinite series of quantum mechanical corrections that describe positron-molecule interactions.
Why it matters
This computational advance makes it feasible to study positron interactions with larger, more complex molecules that were previously beyond reach due to computational limitations. Such calculations are important for understanding positron annihilation spectroscopy, a technique used in materials science and medical imaging, and for developing our understanding of antimatter-matter interactions.
Understand the Science
arXiv:2606.02549v2 Announce Type: replace
Abstract: A diagrammatic Monte Carlo evaluation of the ladder series contributions to the correlation potential (self energy) of a positron in the field of a molecule is presented. The $GW$@TDHF, virtual-positronium ($T$-matrix), and positron-hole Goldstone ladder series contributions are stochastically sampled order-by-order within the Tamm-Dancoff approximation, which is exact for the latter two classes, with Ces{‘a}ro-Riesz resummation used to extrapolate to infinite order. Gaussian bases are employed and Coulomb matrix elements are represented via density fitting, with the three centre integrals the largest arrays required to be stored in memory. The stochastic approach thus realizes a reduction in memory of the largest arrays required on the order of the number of molecular orbitals in the basis $Nsim$10$^2$–10$^3$ compared to the exact deterministic solution of Bethe-Salpeter equations [J. Hofierka, B. Cunningham, C. M. Rawlins, C. H. Patterson and D. G. Green, Nature {bf 606}, {688} (2022)]. Benchmark results for lithium hydride show quantitative agreement with exact diagonalisation, notably demonstrating the successful stochastic summation of the virtual-positronium infinite electron-positron ladder series.
Source: Diagrammatic Monte Carlo for positron-molecule many-body theory