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H. Hergert

Publications and source records attributed to H. Hergert.

At least 19 recordsLinked to original sources
arXiv2026

Qcombo: A Python Package for Automated Commutator Calculations of Quantum Many-Body Operators

qcombo is a Python package for the symbolic evaluation of commutators between general quantum many-body operators expressed in normal-ordered form using the generalized Wick theorem. The package provides an automated and systematic framework for generating the corresponding algebraic expressions, significantly reducing the risk of human error in lengthy and complex analytical derivations. It is designed to assist the development and implementation of modern many-body methods in nuclear physics, quantum chemistry, and related fields. The functionality and workflow of the package are demonstrated through an application to the in-medium similarity renormalization group (IMSRG) method, which has been widely used for nuclear ab initio calculations. As a representative example, qcombo is employed to automatically generate the complete set of multi-reference IMSRG flow equations with operators truncated at the normal-ordered three-body level.

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arXiv2026

Ab initio mapping of the boundary of the $N=20$ island of inversion

Starting from a chiral two- plus three-nucleon interaction, we perform a systematic study of the low-lying states of neutron-rich nuclei around $N=20$ using the in-medium generator coordinate method (IM-GCM), which combines the multi-reference in-medium similarity renormalization group (MR-IMSRG) with the quantum-number projected generator coordinate method (PGCM) defined in a full single-particle space. The main features of the energy spectra and electromagnetic properties of low-lying states in both even-even and odd-mass nuclei of this mass region are reasonably reproduced. The boundary of the $N=20$ island of inversion (IOI) is investigated, and the results indicate that $^{30}$Ne, $^{29,31,33}$Na, $^{31-34}$Mg, and $^{35}$Al lie within the IOI, whereas $^{29}$F, $^{29}$Ne, $^{30}$Mg, $^{31, 33}$Al, $^{34,35}$Si, and $^{35}$P fall outside it.

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arXiv2026

\textit{Ab initio} Gamow density matrix renormalization group for broad nuclear many-body resonances

\textbf{Background} The reach of \textit{ab initio} theory has greatly increased in recent decades. However, predicting the location of the drip lines remains challenging due to uncertainties in nuclear forces and difficulties in describing nuclei that behave as open quantum systems. \textbf{Purpose} In this work, we extend the \textit{ab initio} Gamow Density Matrix Renormalization Group (G-DMRG) approach to the regime of broad many-body resonances to pave the way for systematic tests of nuclear forces in light exotic nuclei. \textbf{Methods} To stabilize calculations, we introduce a new truncation scheme in the reference space, and propose an orbital ordering based on entanglement considerations. We then show how continuum couplings increase entanglement in the many-body problem, and propose a new truncation scheme to stabilize the renormalization and accelerate calculations in extreme conditions. Finally, we demonstrate that natural orbitals can be used to efficiently describe broad resonances by introducing a new ordering scheme and by redefining the reference space based on occupations. \textbf{Results} Leveraging our findings, we propose a recipe to converge \textit{ab initio} G-DMRG calculations and apply it in low-lying states of \isotope[5,6]{He} and \isotope[4]{H}, demonstrating control of the renormalization and the emergence of convergence patterns. We also obtain the first direct \textit{ab initio} calculation of the $J^\pi = {1/2}^+$ ground state of \isotope[5]{H}. \textbf{Conclusions} We demonstrate that entanglement due to continuum couplings can be controlled in extreme conditions and successfully extend the G-DMRG approach in the regime of broad many-body resonances.

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arXiv2025

From spin to pseudospin symmetry: The origin of magic numbers in nuclear structure

Magic numbers lie at the heart of nuclear structure, reflecting enhanced stability in nuclei with closed shells. While the emergence of magic numbers beyond 20 is commonly attributed to strong spin-orbit coupling, the microscopic origin of the spin-orbit potential remains elusive, owing to its dependence on the resolution scale and renormalization scheme of nuclear forces. Here, we investigate the evolution of shell structure with varying momentum resolution in nuclear interactions derived from chiral effective field theory, using the similarity renormalization group to link different scales. We uncover a novel transition from spin symmetry to pseudospin symmetry as the resolution scale decreases, during which magic numbers emerge naturally. A similar pattern is found in calculations using relativistic one-boson-exchange potentials, underscoring the robustness of the phenomenon. This establishes a direct connection between realistic nuclear forces with a high resolution scale and effective nuclear forces at coarse-grained scales, offering a first-principles explanation for the origin of magic numbers and pseudospin symmetry in nuclear shell structure, and new insights into the structure of exotic nuclei far from stability.

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arXiv2024

Ab initio nuclear shape coexistence and emergence of island of inversion around $N=20$

We extend a nuclear ab initio framework based on chiral two- and three-nucleon interactions to investigate shape coexistence and the degradation of the $N=20$ magic number in both even-even and odd-even magnesium isotopes. The quantum-number projected generator coordinate method, combined with the in-medium similarity renormalization group (IMSRG), is employed to compute their low-lying states. This approach reasonably reproduces the coexistence of weakly and strongly deformed states at comparable energies, and allows us to track the emergence of the $N=20$ island of inversion through the continuous IMSRG evolution of the chiral Hamiltonian. Our results indicate that the ground state of $^{33}$Mg with spin-parity $3/2^-$ is predominantly a strongly deformed configuration with $K^\pi = 3/2^-$, while the lowest $7/2^-$ state is predicted to be a shape isomer, consisting of a mixture of weakly deformed configurations with different $K$ values. The results highlight the essential roles of both dynamical and static collective correlations in reproducing the ordering of nuclear states with distinct shapes.

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arXiv2024

Quantum-number projected generator coordinate method for $^{21}$Ne with a chiral two-nucleon-plus-three-nucleon interaction

We report a study of the low-lying states of deformed $^{21}$Ne within the framework of quantum-number projected generator coordinate method (PGCM), starting from a chiral two-nucleon-plus-three-nucleon (NN+3N) interaction. The wave functions of states are constructed as a linear combination of a set of axially-deformed Hartree-Fock-Bogliubov (HFB) wave functions with different quadrupole deformations. These HFB wave functions are projected onto different angular momenta and the correct neutron and proton numbers for $^{21}$Ne. The results of calculations based on the effective Hamiltonians derived by normal-ordering the 3N interaction with respect to three different reference states, including the quantum-number projected HFB wave functions for $^{20}$Ne, $^{22}$Ne, and an ensemble of them with equal weights, are compared. This study serves as a key step towards ab initio calculations of odd-mass deformed nuclei with the in-medium GCM.

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arXiv2023

Ab initio uncertainty quantification of neutrinoless double-beta decay in $^{76}$Ge

The observation of neutrinoless double-beta ($0\nu\beta\beta$) decay would offer proof of lepton number violation, demonstrating that neutrinos are Majorana particles, while also helping us understand why there is more matter than antimatter in the Universe. If the decay is driven by the exchange of the three known light neutrinos, a discovery would, in addition, link the observed decay rate to the neutrino mass scale through a theoretical quantity known as the nuclear matrix element (NME). Accurate values of the NMEs for all nuclei considered for use in $0\nu\beta\beta$ experiments are therefore crucial for designing and interpreting those experiments. Here, we report the first comprehensive ab initio uncertainty quantification of the $0\nu\beta\beta$-decay NME, in the key nucleus $^{76}$Ge. Our method employs nuclear strong and weak interactions derived within chiral effective field theory and recently developed many-body emulators. Our result, with a conservative treatment of uncertainty, is an NME of $2.60^{+1.28}_{-1.36}$, which, together with the best-existing half-life sensitivity and phase-space factor, sets an upper limit for effective neutrino mass of $187^{+205}_{-62}$ meV. The result is important for designing next-generation germanium detectors aiming to cover the entire inverted hierarchy region of neutrino masses.

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arXiv2023

Fundamental Symmetries, Neutrons, and Neutrinos (FSNN): Whitepaper for the 2023 NSAC Long Range Plan

This whitepaper presents the research priorities decided on by attendees of the 2022 Town Meeting for Fundamental Symmetries, Neutrons and Neutrinos, which took place December 13-15, 2022 in Chapel Hill, NC, as part of the Nuclear Science Advisory Committee (NSAC) 2023 Long Range Planning process. A total of 275 scientists registered for the meeting. The whitepaper makes a number of explicit recommendations and justifies them in detail.

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arXiv2023

Nuclear $\beta$ decay as a probe for physics beyond the Standard Model

This white paper was submitted to the 2022 Fundamental Symmetries, Neutrons, and Neutrinos (FSNN) Town Hall Meeting in preparation for the next NSAC Long Range Plan. We advocate to support current and future theoretical and experimental searches for physics beyond the Standard Model using nuclear $\beta$ decay.

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arXiv2022

Neutrinoless Double Beta Decay

This White Paper, prepared for the Fundamental Symmetries, Neutrons, and Neutrinos Town Meeting related to the 2023 Nuclear Physics Long Range Plan, makes the case for double beta decay as a critical component of the future nuclear physics program. The major experimental collaborations and many theorists have endorsed this white paper.

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arXiv2022

Optimization of generator coordinate method with machine-learning techniques for nuclear spectra and neutrinoless double-beta decay: ridge regression for nuclei with axial deformation

The generator coordinate method (GCM) is an important tool of choice for modeling large-amplitude collective motion in atomic nuclei. The computational complexity of the GCM increases rapidly with the number of collective coordinates. It imposes a strong restriction on the applicability of the method. In this work, we propose a subspace-reduction algorithm that employs optimal statistical ML models as surrogates for exact quantum-number projection calculations for norm and Hamiltonian kernels. The model space of the original GCM is reduced to a subspace relevant for nuclear low energy spectra and the NME of ground state to ground state $0\nu\beta\beta$ decay based on the orthogonality condition (OC) and the energy-transition-orthogonality procedure (ENTROP), respectively. For simplicity, the polynomial ridge regression (RR) algorithm is used to learn the norm and Hamiltonian kernels of axially deformed configurations. The efficiency and accuracy of this algorithm are illustrated for 76Ge and 76Se by comparing results obtained using the optimal RR models to direct GCM calculations. The low-lying energy spectra of $^{76}$Ge and $^{76}$Se, as well as the $0\nu\beta\beta$-decay NME between their ground states, are computed. The results show that the performance of the GCM+OC/ENTROP+RR is more robust than that of the GCM+RR alone, and the former can reproduce the results of the original GCM calculation accurately with a significantly reduced computational cost.

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arXiv2022

Modewise Johnson-Lindenstrauss Embeddings for Nuclear Many-Body Theory

In this work, we explore modewise Johnson-Lindenstrauss embeddings (JLEs) as a tool to reduce the computational cost and memory requirements of nuclear many-body methods. JLEs are randomized projections of high-dimensional data tensors onto low-dimensional subspaces that preserve key structural features. Such embeddings allow for the oblivious and incremental compression of large tensors, e.g., the nuclear Hamiltonian, into significantly smaller random sketches that still allow for the accurate calculation of ground-state energies and other observables. Their oblivious character makes it possible to compress a tensor without knowing in advance exactly what observables one might want to approximate at a later time. This opens the door for the use of tensors that are much too large to store in memory, e.g., complete two-plus three-nucleon Hamiltonians in large, symmetry-unrestricted bases. Such compressed Hamiltonians can be stored and used later on with relative ease. As a first step, we analyze the JLE's impact on the second-order Many-Body Perturbation Theory (MBPT) corrections for nuclear ground-state observables. Numerical experiments for a wide range of closed-shell nuclei, model spaces and state-of-the-art nuclear interactions demonstrate the validity and potential of the proposed approach: We can compress nuclear Hamiltonians hundred- to thousand-fold while only incurring mean relative errors of 1\% or less in ground-state observables. Importantly, we show that JLEs capture the relevant physical information contained in the highly structured Hamiltonian tensor despite their random characteristics. In addition to the significant storage savings, the achieved compressions imply multiple order-of magnitude reductions in computational effort when the compressed Hamiltonians are used in higher-order MBPT or nonperturbative many-body methods.

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arXiv2022

Rooting the EDF method into the ab initio framework. PGCM-PT formalism based on MR-IMSRG pre-processed Hamiltonians

Recently, ab initio techniques have been successfully connected to the traditional valence-space shell model. In doing so, they can either explicitly provide ab initio shell-model effective Hamiltonians or constrain the construction of empirical ones. In the present work, the possibility to follow a similar path for the nuclear energy density functional (EDF) method is analyzed. For this connection to be actualized, two theoretical techniques are instrumental: the recently proposed ab initio PGCM-PT many-body formalism and the MR-IMSRG pre-processing of the nuclear Hamiltonian. Based on both formal arguments and numerical results, possible new lines of research are briefly discussed, namely to compute ab initio EDF effective Hamiltonians at low computational cost, to constrain empirical ones or to produce them directly via an effective field theory that remains to be invented.

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arXiv2022

Ab initio studies of double Gamow-Teller transition and its correlation with neutrinoless double beta decay

We use chiral interactions and several {\em ab initio} methods to compute the nuclear matrix elements (NMEs) for ground-state to ground-state double Gamow-Teller transitions in a range of isotopes, and explore the correlation of these NMEs with those for neutrinoless double beta decay produced by the exchange of a light Majorana neutrino. When all the NMEs of both isospin-conserving and isospin-changing transitions from the {\em ab initio} calculations are considered, the correlation is strong. For the experimentally relevant isospin-changing transitions by themselves, however, the correlation is weaker and may not be helpful for reducing the uncertainty in the NMEs for neutrinoless double-beta decay.

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arXiv2022

Towards Precise and Accurate Calculations of Neutrinoless Double-Beta Decay: Project Scoping Workshop Report

We present the results of a National Science Foundation (NSF) Project Scoping Workshop, the purpose of which was to assess the current status of calculations for the nuclear matrix elements governing neutrinoless double-beta decay and determine if more work on them is required. After reviewing important recent progress in the application of effective field theory, lattice quantum chromodynamics, and ab initio nuclear-structure theory to double-beta decay, we discuss the state of the art in nuclear-physics uncertainty quantification and then construct a road map for work in all these areas to fully complement the increasingly sensitive experiments in operation and under development. The road map contains specific projects in theoretical and computational physics as well as an uncertainty-quantification plan that employs Bayesian Model Mixing and an analysis of correlations between double-beta-decay rates and other observables. The goal of this program is a set of accurate and precise matrix elements, in all nuclei of interest to experimentalists, delivered together with carefully assessed uncertainties. Such calculations will allow crisp conclusions from the observation or non-observation of neutrinoless double-beta decay, no matter what new physics is at play.

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arXiv2021

Singular Value Decomposition and Similarity Renormalization Group Evolution of Nuclear Interactions

One of the main challenges for ab initio nuclear many-body theory is the growth of computational and storage costs as calculations are extended to heavy, exotic, and structurally complex nuclei. Here, we investigate the factorization of nuclear interactions as a means to address this issue. We perform Singular Value Decompositions of nucleon-nucleon interactions in partial wave representation and study the dependence of the singular value spectrum on interaction characteristics like regularization scheme and resolution scales. We develop and implement the Similarity Renormalization Group (SRG) evolution of the factorized interaction, and demonstrate that this SVD-SRG approach accurately preserves two-nucleon observables. We find that low-resolution interactions allow the truncation of the SVD at low rank, and that a small number of relevant components is sufficient to capture the nuclear interaction and perform an accurate SRG evolution, while the Coulomb interaction requires special consideration. The rank is uniform across all partial waves, and almost independent of the basis choice in the tested cases. This suggests an interpretation of the relevant singular components as mere representations of a small set of abstract operators that can describe the interaction and its SRG flow. Following the traditional workflow for nuclear interactions, we discuss how the transformation between the center-of-mass and laboratory frames creates redundant copies of the partial wave components when implemented in matrix representation, and we discuss strategies for mitigation. Finally, we test the low-rank approximation to the SRG-evolved interactions in many-body calculations using the In-Medium SRG. By including nuclear radii in our analysis, we verify that the implementation of the SRG using the singular vectors of the interaction does not spoil the evolution of other observables.

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arXiv2021

Ab initio calculation of the contact operator contribution in the standard mechanism for neutrinoless double beta decay

Starting from chiral nuclear interactions, we evaluate the contribution of the leading-order contact transition operator to the nuclear matrix element (NME) of neutrinoless double-beta decay, assuming a light Majorana neutrino-exchange mechanism. The corresponding low-energy constant (LEC) is determined by fitting the transition amplitude of the $nn\to ppe^-e^-$ process to a recently proposed synthetic datum. We examine the dependence of the amplitude on similarity renormalization group (SRG) scale and chiral expansion order of the nuclear interaction, finding that both dependences can be compensated to a large extent by readjusting the LEC. We evaluate the contribution of both the leading-order contact operator and standard long-range operator to the neutrinoless double-beta decays in the light nuclei $^{6,8}$He and the candidate nucleus $^{48}$Ca. Our results provide the first clear demonstration that the contact term enhances the NME by 43(7)% in $^{48}$Ca, where the uncertainty is propagated from the synthetic datum.

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