Scaling of Disorder Operator and Entanglement Entropy at Easy-Plane Deconfined Quantum Criticalities

TL;DR

This study explores how disorder operator and entanglement entropy scale at phase transitions in an easy-plane quantum model, revealing anomalous behaviors linked to the transition's order and Goldstone modes.

Contribution

It provides new insights into the scaling behaviors of disorder operator and entanglement entropy at easy-plane deconfined quantum critical points, highlighting the evolution from weak to first-order transitions.

Findings

Finite order parameters at transition points indicate a shift from weak to first-order transition with anisotropy.

Anomalous scaling behaviors of EE and disorder operator are observed at critical points, similar to Goldstone mode scaling.

Log-coefficients approach 0.5 for small anisotropy, consistent with Goldstone mode contributions.

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 $\Delta$ varies from the Heisenberg limit ($\Delta=1$) to the easy-plane limit ($\Delta=0$). 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 $\Delta \le 0.3$, the obtained log-coefficients converge to 0.5 which is the same as the contribution from one Goldstone mode in the N\'eel phase. For $\Delta > 0.3$, 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.