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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 bedescribed efficiently using a one-dimensional tensor network (matrix-productstate) despite the presence of long-range interactions. The ground state can beobtained using the density-matrix renormalization group (DMRG) algorithm, whichis accurate up to machine precision even for large nuclei, is numerically ascheap as the widely used BCS approach, and does not suffer from any mean-fieldartefacts.  We apply this framework to compute the even-odd mass differences of all knownlead isotopes from $^{178}$Pb to $^{220}$Pb in a very large configuration spaceof 13 shells between the neutron magic numbers 82 and 184 (i.e., two majorshells) and find good agreement with the experiment.  To go beyond the ground state, we calculate the first 100 excited states, aswell as the two-neutron removal spectral function of $^{210}$Pb which relatesto a two-neutron pickup experiment. Finally, we treat pairing with non-zeroangular momentum and determine the lowest excited states in the fullconfiguration space of one major shell, which we demonstrate for the $N=126$,$Z\geq 82$ isotones.

Matrix-product state approach to the generalized nuclear pairing Hamiltonian