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 topological $\theta$-term. This term provides mechanism for continuous phase transitions between different symmetry-broken states: defects of one carry the charge other proliferate at transition. The $\theta$-term implies that domain wall KVBS order parameter harbors spin-$1/2$ Heisenberg chain, as described by $1+1$ dimensional non-linear sigma model $\theta = \pi$. Using pinning fields to stabilize wall, we show our auxiliary-field quantum Monte Carlo simulations indeed support emergence chain defect. concept can be generalized higher where SO(4) or SO(5) theories terms are realized wall.