Scaling of Disorder Operator and Entanglement Entropy at Easy-Plane Deconfined Quantum Criticalities
arxiv(2024)
Abstract
We systematically investigate the scaling behavior of the disorder operator
and the entanglement entropy (EE) of the easy-plane JQ (EPJQ) model at its
transition between the antiferromagnetic XY ordered phase (AFXY) and the
valence bond solid (VBS) phase. We find (1) there exists a 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
Δ varies from the Heisenberg limit (Δ=1) to the easy-plane limit
(Δ=0); (2) Both EE and disorder operator with smooth boundary
cut exhibit anomalous scaling behavior at the transition points, resembling the
scaling inside the Goldstone model phase, and the anomalous scaling becomes
strengthened as the transition becomes more first order; (3) First
put forward in Ref. [arXiv:2401.12838], with the finite-size corrections in EE
for Goldstone phase is properly considered in the fitting form, the anomalous
scaling behavior of EE can be adapted with emergent SO(5) symmetry breaking at
the Heisenberg limit (Δ=1). We extend this method in the EPJQ model and
observe similar results, which may indicate emergent SO(4) symmetry breaking in
the easy-plane regime (Δ<1) or emergent SO(5) symmetry breaking in the
Heisenberg limit (Δ=1). These observations provide evidence that the
Néel-VBS transition in the JQ model setting evolves from weak to prominent
first-order transition as the system becomes anisotropic, and the non-local
probes such as EE and disorder operator, serve as the sensitive tool to detect
such salient yet fundamental features.
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