NuLattice: Ab initio computations of atomic nuclei on lattices

TL;DR

NuLattice introduces a Python-based toolkit for ab initio nuclear structure calculations on spatial lattices, employing Hartree-Fock, CCSD, IMSRG(2), and full configuration interaction with leading-order pion-less EFT interactions. By embedding the problem on a lattice, the code exploits sparsity and locality to keep data and computations tractable on standard hardware, enabling detailed studies of light nuclei such as $^2$H, $^3$He, $^4$He, $^8$Be, $^{12}$C, and $^{16}$O. The results show that Hartree-Fock and CCS capture most of the binding energy for compact nuclei, while heavier nuclei composed of multiple $\ ext{\alpha}$ particles are not bound within this LO framework, highlighting the need for finite-range or chiral interactions for binding beyond $ ext{alpha}$ clusters. The package is modular, open-source, and demonstrated through extensive benchmarks and educational use, with clear paths toward future extensions (finite-range interactions, excited states, sparse IMSRG) to broaden applicability and accuracy.

Abstract

We introduce NuLattice, a Python software package for ab initio computations of atomic nuclei on lattices. The computational tools consist of Hartree Fock, the coupled cluster method, the in-medium similarity renormalization group, and full configuration interaction. At present, the employed interactions are from pion-less effective field theory at leading order and consist of two-body and three-body contacts. We present results for light nuclei $^{2}$H, $^{3,4}$He, $^{8}$Be, $^{12}$C, and $^{16}$O. NuLattice algorithms exploit the sparsity and locality of lattice interactions, and as a result computations can be run on laptops.

Figures (5)

• Figure 1: Ground-state energy of $^2$H as a function of the lattice size $L$ for a spacing $a=2$ fm, computed via coupled-cluster with singles (CCS) and coupled-cluster with singles and doubles (CCSD), which yields the same result as full configuration interaction (FCI). The energy of the reference state is $E_{\rm ref}$.
• Figure 2: Ground-state energy of $^4$He on a lattice with $L=4$ and $a=2.5$ fm, as a function of the three-body strength $w$, from coupled cluster with singles (CCS), coupled cluster with singles and doubles (CCSD), Hartree Fock (HF), and compared to full configuration interaction (FCI). The energy of the reference state is $E_{\rm ref}$. The vertical dashed line marks the physical point.
• Figure 3: Absolute ratio of the missing energy $E_{\rm FCI}-E$ and the correlation energy $E_{\rm FCI}-E_{\rm ref}$ in computations of $^4$He on a lattice with $L=4$ and $a=2.5$ fm, as a function of the three-body strengths $w$, from coupled cluster with singles (CCS), coupled cluster with singles and doubles (CCSD), and Hartree Fock (HF). The vertical dashed line marks the physical point.
• Figure 4: Ground state energy per nucleon for $^4$He, $^8$Be, $^{12}$C, and $^{16}$O for three difference lattice spacings done with a lattice size $L=5$, computed with coupled cluster with singles and doubles.
• Figure 5: Ground-state energies of $^8$Be, $^{12}$C, and $^{16}$O as a function of lattice size $L$ for the spacing $a=2$ fm, computed with Hartree Fock (HF), coupled cluster with singles and doubles (CCSD) based on a lattice reference state, and IMSRG(2) based on a Hartree-Fock reference state.