Intrinsic and emergent anomalies at deconfined critical points

TL;DR

This paper explores how quantum anomalies related to Lieb-Schultz-Mattis theorems influence the nature of deconfined critical points in antiferromagnets, revealing constraints on trivial gapped states near criticality.

Contribution

It demonstrates the presence of quantum anomalies at deconfined critical points and identifies new anomalies that prevent trivial gapped phases near these critical points.

Findings

Quantum anomalies manifest at deconfined critical points in certain antiferromagnets.

No trivial gapped state can be realized near the critical points due to these anomalies.

Anomalies can emerge independently of microscopic Lieb-Schultz-Mattis constraints.

Abstract

It is well known that theorems of Lieb-Schultz-Mattis type prohibit the existence of a trivial symmetric gapped ground state in certain systems possessing a combination of internal and lattice symmetries. In the continuum description of such systems the Lieb-Schultz-Mattis theorem is manifested in the form of a quantum anomaly afflicting the symmetry. We demonstrate this phenomenon in the context of the deconfined critical point between a Neel state and a valence bond solid in an $S =1/2$ square lattice antiferromagnet, and compare it to the case of $S=1/2$ honeycomb lattice where no anomaly is present. We also point out that new anomalies, unrelated to the microscopic Lieb-Schultz-Mattis theorem, can emerge prohibiting the existence of a trivial gapped state in the immediate vicinity of critical points or phases. For instance, no translationally invariant weak perturbation of the $S = 1/2$ gapless spin chain can open up a trivial gap even if the spin-rotation symmetry is explicitly broken. The same result holds for the $S =1/2$ deconfined critical point on a square lattice.