Entanglement entropy and deconfined criticality: emergent SO(5) symmetry and proper lattice bipartition

TL;DR

This paper investigates the entanglement entropy in a 2D quantum spin model at a deconfined critical point, revealing how lattice bipartition details affect observed critical behavior and supporting emergent SO(5) symmetry.

Contribution

It demonstrates the importance of lattice bipartition choice in observing logarithmic entanglement entropy contributions and supports the emergent SO(5) symmetry at the critical point.

Findings

Logarithmic corner contributions scale with system size.

Proper bipartition reveals critical behavior consistent with SO(5) symmetry.

Lattice bipartition details significantly influence entanglement entropy observations.

Abstract

We study the R\'enyi entanglement entropy (EE) of the two-dimensional $J$-$Q$ model, the emblematic quantum spin model of deconfined criticality at the phase transition between antiferromagnetic and valence-bond-solid ground states. State-of-the-art quantum Monte Carlo calculations of the EE reveal critical corner contributions that scale logarithmically with the system size, with a coefficient in remarkable agreement with the form expected from a large-$N$ conformal field theory with SO($N=5$) symmetry. However, details of the bipartition of the lattice are crucial in order to observe this behavior. If the subsystem for the reduced density matrix does not properly accommodate valence-bond fluctuations, logarithmic contributions appear even for corner-less bipartitions. We here use a $45^\circ$ tilted cut on the square lattice. Beyond supporting an SO($5$) deconfined quantum critical point, our results for both the regular and tilted cuts demonstrate important microscopic aspects of the EE that are not captured by conformal field theory.