Visualizing elusive phase transitions with geometric entanglement

We show that by examining the global geometric entanglement it is possible to identify elusive or hard to detect quantum phase transitions. We analyze several one-dimensional quantum spin chains and demonstrate the existence of nonanalyticities in the geometric entanglement, in particular, across a Kosterlitz-Thouless transition and across a transition for a gapped deformed Affleck-Kennedy-Lieb-Tasaki chain. The observed nonanalyticities can be understood and classified in connection to the nature of the transitions, and are in sharp contrast to the analytic behavior of all the two-body reduced density operators and their derived entanglement measures.