Walls, Anomalies, and (De)Confinement in Quantum Anti-Ferromagnets

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 ${\mathbb{Z}}_2$ 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 ${\mathbb{Z}}_2$ 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.

13 pages, 8 figures

References in corpus (13)

• Generalized Global Symmetries
• "Deconfined" quantum critical points
• Theta, Time Reversal, and Temperature
• Deconfined quantum critical points: symmetries and dualities
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Comments on Global Symmetries, Anomalies, and Duality in (2+1)d
• Anomalies of discrete symmetries in three dimensions and group cohomology
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Construction of bosonic symmetry-protected-trivial states and their topological invariants via $G\times SO(\infty )$ non-linear $\sigma$-models
• Topological Model for Domain Walls in (Super-)Yang-Mills Theories
• Phase structure of the N=1 supersymmetric Yang-Mills theory at finite temperature
• Lattice realization of a bosonic integer quantum Hall state - trivial insulator transition and relation to the self-dual line in the easy-plane NCCP1 model

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