Genuine Multipartite Entanglement Trends in Gapless-gapped Transitions of Quantum Spin Systems

We investigate the behavior of genuine multiparticle entanglement, as quantified by the generalized geometric measure, in gapless-to-gapped quantum transitions of one- and two-dimensional quantum spin models. The investigations are performed in the exactly solvable one-dimensional $XY$ models, as well as two-dimensional frustrated $J_{1}-J_{2}$ models, including the Shastry-Sutherland model. The generalized geometric measure shows non-monotonic features near such transitions in the frustrated quantum systems. We also compare the features of the generalized geometric measure near the quantum critical points with the same for measures of bipartite quantum correlations. The multipartite quantum correlation measure turns out to be a better indicator of quantum critical points than the bipartite measures, especially for two-dimensional models.