Low lying excited states quantum entanglement and continuous quantum phase transitions.

From the perspective of entanglement in low-lying excited states, a profound analysis was carried out regarding the quantum phase transitions within three models that fall outside the Landau-Ginzburg-Wilson (LGW) paradigm. In the context of the deconfined quantum critical point (DQCP) in a one-dimensional quantum spin chain, our findings demonstrate a tight correlation between the reconstruction of low-lying excitation spectra and the DQCP. The precise location of the critical point and its continuous nature can be signaled by the singular behaviors of the entanglement of the first-excited state. Moreover, in comparison with two types of Berezinskii-Kosterlitz-Thouless (BKT) phase transitions, the entanglement presents three different singularity characteristics. These characteristics not only unveil the essence of diverse symmetry types on either side of the DQCP but also expose the disparate causes underlying the formation of the two BKT type phase transitions.