Intrinsic and emergent anomalies at deconfined critical points

TL;DR

This work casts Lieb-Schultz-Mattis-type constraints as quantum anomalies in the low-energy continuum and applies them to deconfined critical points in lattice antiferromagnets. By treating lattice symmetries as internal, it identifies intrinsic anomalies for the $S= frac{1}{2}$ square-lattice Neél–VBS transition and finds no such anomalies for the honeycomb lattice, while also unveiling emergent anomalies that can block weakly gapped symmetric states near criticality. It uses both bosonization and CP$^1$ descriptions, linking surface anomalies to bulk crystalline SPT phases and clarifying the role of vortices and domain walls. The paper also explores dynamics at rectangular and $S=1$ square-lattice cases, arguing for possible emergent $O(4)$/$SO(4)$-symmetric fixed points and outlining directions for further numerical and theoretical investigation of emergent phenomena near deconfined criticality.

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.

Figures (7)

• Figure 1: A staggering of bond strengths for an $S =1/2$ square lattice. Weakly perturbing the deconfined critical point with such a staggering cannot open a trivial gap, while preserving $T_xT_y$ and $SO(3)_s$ symmetry.
• Figure 2: Four domains of $S = 1/2$ square lattice VBS order with $V =1, i, -1, -i$ in a $Z^{rot}_4$ vortex configuration. Domain walls are marked in dashed orange. Top left and bottom: a $Z^{rot}_4$ symmetric vortex traps half-odd-integer spin. Top right: a vortex which does not preserve the $Z^{rot}_4$ symmetry need not trap a spin (see also appendix \ref{['app:vort']}).
• Figure 3: Three domains of $S = 1/2$ honeycomb lattice VBS order with $V =1, e^{2 \pi i/3}, e^{4 \pi i/3}$ in a $Z^{rot}_3$ vortex configuration. Domain walls are marked in dashed orange. A $Z^{rot}_3$ symmetric vortex may or may not trap $S =1/2$ depending on the details of the domain walls.
• Figure 4: $S =1$ square lattice VBS configurations. Red lines correspond to $S = 1$ spins locked into Haldane chains. Left: $Re(V) > 0, Im(V) = 0$. Right: $Re(V) = 0, Im(V) > 0$. Note that $Re(V)$ and $Im(V)$ are not related by any symmetry.
• Figure 5: A unit cell for the branching structure of the usual VBS convention. Edges occupied with a dimer are considered part of a domain associated with the direction labeling that edge.