Scaling of disorder operator and entanglement entropy at easy-plane deconfined quantum criticalities

Abstract

We systematically investigate the scaling behaviors of the disorder operator and the entanglement entropy (EE) of the easy-plane JQ (EPJQ) model at its transitions between the antiferromagnetic XY ordered phase (AFXY) and the valence bond solid (VBS) phase. We find there exists a tiny yet finite value of the order parameters at the AFXY-VBS phase transition points of the EPJQ model, and the finite order parameter is strengthened as anisotropy $\mathrm{\ensuremath{\Delta}}$ varies from the Heisenberg limit ($\mathrm{\ensuremath{\Delta}}=1$) to the easy-plane limit ($\mathrm{\ensuremath{\Delta}}=0$). This observation provides evidence that the N\'eel-VBS transition in the JQ model setting evolves from weak to prominent first-order transition as the system becomes anisotropic. Furthermore, both EE and disorder operator with smooth boundary cut exhibit anomalous scaling behavior at the transition points, resembling the scaling inside the Goldstone mode (AFXY) phase, and the anomalous scaling becomes strengthened as the transition becomes more first order. In particular, for $\mathrm{\ensuremath{\Delta}}\ensuremath{\le}0.3$, the obtained log-coefficients of EE converge to 0.5 which is the same as the contribution from one Goldstone mode in the N\'eel phase. For $\mathrm{\ensuremath{\Delta}}>0.3$, the log-coefficients are smaller and our findings might suffer from strong finite-size effects due to the fact that the remaining N\'eel order here is quite tiny.