Matrix-product state approach to the generalized nuclear pairing Hamiltonian

TL;DR

This paper demonstrates that the ground state and excited states of nuclei with generalized pairing interactions can be efficiently computed using matrix-product states and DMRG, providing accurate results for large nuclei and complex configurations.

Contribution

It introduces a tensor network approach to nuclear pairing Hamiltonians, enabling efficient and precise calculations of nuclear properties beyond mean-field methods.

Findings

Accurately computed even-odd mass differences for lead isotopes.

Determined lowest excited states in full configuration space of one major shell.

Calculated first 100 excited states of $^{208}$Pb and two-neutron removal spectral function.

Abstract

We show that from the point of view of the generalized pairing Hamiltonian, the atomic nucleus is a system with small entanglement and can thus be described efficiently using a 1D tensor network (matrix-product state) despite the presence of long-range interactions. The ground state can be obtained using the density-matrix renormalization group (DMRG) algorithm, which is accurate up to machine precision even for large nuclei, is numerically as cheap as the widely used BCS (Bardeen-Cooper-Schrieffer) approach, and does not suffer from any mean-field artifacts. We apply this framework to compute the even-odd mass differences of all known lead isotopes from $^{178}$Pb to $^{220}$Pb in a very large configuration space of 13 shells between the neutron magic numbers 82 and 184 (i.e., two major shells) and find good agreement with the experiment. We also treat pairing with non-zero angular momentum and determine the lowest excited states in the full configuration space of one major shell, which we demonstrate for the $N=126$, $Z\geq 82$ isotones. To demonstrate the capabilities of the method beyond low-lying excitations, we calculate the first 100 excited states of $^{208}$Pb with singlet pairing and the two-neutron removal spectral function of $^{210}$Pb, which relates to a two-neutron pickup experiment.