Matrix-Product State Approach to the Generalized Nuclear Pairing Hamiltonian

Abstract

It is shown 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 Bardeen-Cooper-Schrieffer (BCS) approach, and does not suffer from any mean-field artifacts. This framework is applied to compute the even-odd mass differences of all known lead isotopes from ${}^{178}\text{Pb}$ to ${}^{220}\text{Pb}$ 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. Pairing with non-zero angular momentum is also considered and the lowest excited states in the full configuration space of one major shell is determined, which is demonstrated for the $N=126$, $Z\ge 82$ isotones. To demonstrate the capabilities of the method beyond low-lying excitations, the first 100 excited states of ${}^{208}\text{Pb}$ with singlet pairing and the two-neutron removal spectral function of ${}^{210}\text{Pb}$ are calculated, which relate to a two-neutron pickup experiment.