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

TL;DR

This work extends ab initio Gamow DMRG to broad nuclear resonances by integrating the Berggren basis with a non-Hermitian, complex-symmetric framework. It introduces a truncation scheme at reference-space construction, an entanglement-aware orbital ordering strategy, a density-matrix stabilization method, and the use of natural orbitals to efficiently describe broad resonances. The authors demonstrate controlled renormalization, convergence trends, and physically meaningful resonance states in light systems such as $^{5}$He, $^{6}$He, $^{4}$H, and $^{5}$H, including the first direct ab initio calculation of the $J^{\pi}=1/2^+$ ground state of $^{5}$H. Collectively, these advances enable systematic ab initio tests of nuclear forces in exotic, open quantum systems and pave the way for extending predictive power toward drip-line regions.

Abstract

\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 $J^π= {1/2}^+$ 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.

Figures (44)

• Figure 1: Illustration of the different types of poles of the single-particle $S$ matrix in the complex momentum plane. The continuum of scattering states is represented by a thick blue line on the positive side of the real axis.
• Figure 2: Illustration of the Berggren basis in the complex momentum plane. Poles of the $S$ matrix that are excluded are marked in red, while those included are marked in blue. Two valid deformations of the continuum of scattering states $\mathcal{L}^+$ are indicated by blue contours in the 4 quadrant.
• Figure 3: Illustration of the Wilsonian renormalization of the Hamiltonian in the original formulation of DMRG. The Hamiltonian is originally built in the reference space, and then the effect of the environment is "absorbed" by the renormalization. The Hamiltonian obtained, expressed in a renormalized space, approximates the full Hamiltonian.
• Figure 4: Ground-state energy of [3]He as a function of the DMRG truncation $\epsilon$. The horizontal lines denote the extrapolated G-DMRG energies. The relative energy difference with the exact NCGSM result (in percent) is shown on the right panel.
• Figure 5: Blue: Binding energy of [4]He in an increasingly larger reference space ($2 \leq N \leq 10$ orbitals) and without any p-h truncation (4p4h). Red: Binding energy of [4]He in a reference space built upon $N=10$ orbitals, with a 2p2h truncation at construction applied at orbital $i$, and none otherwise. The exact result for $N=10$ and no p-h truncation is shown as a horizontal line.