Topological terms on topological defects: a quantum Monte Carlo study

Dirac fermions in $2+1$ dimensions with dynamically generated anticommuting SO(3) antiferromagnetic (AFM) and Z${}_2$ Kekul'e valence-bond solid (KVBS) masses map onto a field theory with a topological $\theta$-term. This term provides a mechanism for continuous phase transitions between different symmetry-broken states: topological defects of one phase carry the charge of the other and proliferate at the transition. The $\theta$-term implies that a domain wall of the Z${}_2$ KVBS order parameter harbors a spin-$1\mathrm{/}2$ Heisenberg chain, as described by a $1+1$ dimensional SO(3) non-linear sigma model with $\theta$-term at $\theta =\pi$. Using pinning fields to stabilize the domain wall, we show that our auxiliary-field quantum Monte Carlo simulations indeed support the emergence of a spin-$1\mathrm{/}2$ chain at the Z${}_2$ topological defect. This concept can be generalized to higher dimensions where $2+1$ dimensional SO(4) or SO(5) theories with topological terms are realized at a domain wall.