Walls, anomalies, and deconfinement in quantum antiferromagnets

Abstract

We consider the Abelian-Higgs model in 2+1 dimensions with instanton-monopole defects. This model is closely related to the phases of quantum anti-ferromagnets. In the presence of Z2 preserving monopole operators, there are two confining ground states in the monopole phase, corresponding to the Valence Bond Solid (VBS) phase of quantum magnets. We show that the domain-wall carries a 't Hooft anomaly in this case. The anomaly can be saturated by, e.g., charge-conjugation breaking on the wall or by the domain wall theory becoming gapless (a gapless model that saturates the anomaly is SU (2)1 WZW). Either way the fundamental scalar particles (i.e. spinons) which are confined in the bulk are deconfined on the domain-wall. This Z2 phase can be realized either with spin-1/2 on a rectangular lattice, or spin-1 on a square lattice. In both cases the domain wall contains spin-1/2 particles (which are absent in the bulk). We discuss the possible relation to recent lattice simulations of domain walls in VBS. We further generalize the discussion to Abrikosov-Nielsen-Olsen (ANO) vortices in a dual superconductor of the Abelian-Higgs model in 3+1 dimensions, and to the easy-plane limit of anti-ferromagnets. In the latter case the wall can undergo a variant of the BKT transition (consistent with the anomalies) while the bulk is still gapped. The same is true for the easy-axis limit of anti-ferromagnets. We also touch upon some analogies to Yang-Mills theory.

Intrinsic and emergent anomalies at deconfined critical points

“…While this paper was being completed, Ref. [33] appeared, which also discusses the implication of anomalies of 2+1D CP 1 model for lattice antiferromagnets. This paper is organized as follows.…”

Anomaly constraints on deconfinement and chiral phase transition

“…In [39], the authors obtained the inequality (8) for adjoint QCD by using the same anomaly as ours. In [40], the authors introduced the new order parameter for QCD by using the mixing of the center and flavor symmetry.…”

“…Note added.-Recently, we became aware of that two closely related papers [39,40] appeared. In [39], the authors obtained the inequality (8) for adjoint QCD by using the same anomaly as ours.…”

A symmetry breaking scenario for QCD3

“…In the case where the bosonic dual has a SO(2) = U(1) gauge symmetry, this enhanced π 2 is associated with an enhanced U(1) T magnetic symmetry. In this case this symmetry should be explicitly broken to Z 2 by adding monopole operators of charge two to the Lagrangian in order to preserve the duality (as was done recently in other models in [55,70]). These operators have a negligible effect in the Higgs phase, except that they allow Skyrmions to decay, while preserving the remaining Z 2 charge.…”