Advances \textit{ab Initio} Prediction of Broad Nuclear Resonances with Gamow DMRG

Scientists are pushing the boundaries of nuclear physics with new techniques to understand exotic nuclei, but predicting the limits of stability remains a significant hurdle. A. Sehovic, K. Fossez, and H. Hergert, from their respective institutions, have now extended the ab initio Gamow Density Matrix Renormalization Group (G-DMRG) method to tackle broad nuclear resonances, unstable states crucial for locating the ‘drip lines’ of the periodic table. Their innovative approach, detailed in this paper, introduces a novel truncation scheme and orbital ordering based on entanglement, stabilising calculations in extreme conditions and allowing for the first direct ab initio calculation of the ground state of hydrogen-5. This work represents a major step forward in systematically testing nuclear forces within light, exotic nuclei and promises to refine our understanding of the heaviest elements possible.

Researchers successfully adapted the G-DMRG method, a powerful tool for solving the quantum many-body problem, to describe nuclei behaving as open quantum systems, systems coupled to an environment of scattering states and decay channels. The team introduced a novel truncation scheme within the reference space of the calculation, alongside an orbital ordering strategy based on entanglement considerations, to stabilise these complex calculations.

To overcome computational hurdles, the study focused on controlling entanglement, which increases significantly when accounting for continuum couplings in the many-body problem. A new truncation scheme was proposed to stabilise the renormalization process and accelerate calculations under extreme conditions, representing a key innovation in the field. Furthermore, the researchers demonstrated that natural orbitals, a specific way of describing electron or nucleon arrangements, can efficiently represent broad resonances by redefining the reference space based on orbital occupations. Leveraging these advancements, they developed a robust recipe for converging \textit{ab initio} G-DMRG calculations, applying it to the low-lying states of \isotope[5,6]{He} and \isotope{H} to validate their approach and demonstrate the emergence of convergence patterns.
Experiments show that this refined methodology allows for unprecedented control over the renormalization process, a critical step in ensuring the accuracy of \textit{ab initio} calculations. Notably, the research team obtained the first direct \textit{ab initio} calculation of the ground state of \isotope{H}, a significant milestone in understanding the structure of exotic hydrogen isotopes. The study establishes that entanglement arising from continuum couplings can be effectively managed even in extreme conditions, successfully extending the G-DMRG method to the challenging regime of broad many-body resonances. This innovative approach directly addresses the challenges of describing open quantum systems, crucial for understanding nuclei at the limits of stability. The study then demonstrated how continuum couplings amplify entanglement within the many-body problem, subsequently proposing a refined truncation scheme to bolster renormalization and accelerate computations under extreme conditions.

This method achieves greater computational efficiency by strategically reducing the complexity of the calculations without sacrificing accuracy. Furthermore, researchers harnessed natural orbitals to efficiently represent broad resonances, introducing a novel ordering scheme and redefining the reference space based on orbital occupations. This technique allows for a more compact and accurate description of the nuclear wave function, particularly in systems with significant resonance behaviour. Leveraging these methodological advances, the team proposed a robust recipe for converging ab initio G-DMRG calculations, applying it to the low-lying states of \isotope[5,6]{He} and \isotope{H}.

These calculations demonstrably controlled the renormalization process and revealed emerging convergence patterns, validating the effectiveness of the new techniques. Crucially, the work delivered the first direct ab initio calculation of the ground state of \isotope{H} with a Jπ = 1/2+ spin-parity, a significant breakthrough in the field. The research conclusively demonstrates that entanglement arising from continuum couplings can be effectively managed even in extreme conditions, successfully extending the G-DMRG method to encompass the regime of broad many-body resonances. To overcome computational challenges, they introduced a novel truncation scheme within the reference space, guided by principles of quantum entanglement  . Experiments revealed that continuum couplings substantially increase entanglement within the many-body problem, necessitating a refined truncation strategy to stabilize calculations under extreme conditions.

The team proposed a new ordering scheme based on natural orbitals, redefining the reference space based on orbital occupations to efficiently describe these broad resonances. Leveraging these advancements, scientists proposed a robust recipe for converging ab initio G-DMRG calculations, applying it to the low-lying states of \isotope[5,6]{He} and \isotope{H}. Measurements confirm control of the renormalization process and demonstrate the emergence of clear convergence patterns, a crucial step towards reliable predictions. Results demonstrate the first direct ab initio calculation of the ground state of \isotope{H}, specifically determining a Jπ = 1/2+ spin-parity, a landmark achievement in nuclear physics.

Data shows that entanglement arising from continuum couplings can be effectively managed even in extreme conditions, allowing for a successful extension of the G-DMRG approach to regimes dominated by broad many-body resonances. The breakthrough delivers a powerful tool for exploring the drip lines, the boundaries of nuclear existence, and understanding the exotic phenomena occurring at the edge of stability. Tests prove the efficacy of the new truncation scheme, enabling calculations previously inaccessible due to computational complexity. Researchers introduced a new truncation scheme and orbital ordering, guided by entanglement considerations, to stabilise calculations in extreme conditions and accelerate convergence. The findings demonstrate control over entanglement arising from continuum couplings, successfully broadening the applicability of the G-DMRG method to resonant many-body systems.

Specifically, the team achieved the first direct \textit{ab initio} calculation of the ground state of \isotope{H} and applied their refined method to low-lying states of \isotope[5,6]{He} and \isotope{H}, observing consistent convergence patterns. The authors acknowledge limitations related to the computational demands of \textit{ab initio} methods, particularly as system size increases. Future research could focus on applying this approach to heavier nuclei and exploring a wider range of exotic nuclei to further constrain nuclear forces and refine our understanding of nuclear stability.