Topological terms on topological defects: a quantum Monte Carlo study
Abstract
Dirac fermions in 2+1 dimensions with dynamically generated anticommuting SO(3) antiferromagnetic (AFM) and Z2 Kekul\'e valence-bond solid (KVBS) masses map onto a field theory with a topological θ-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 θ-term implies that a domain wall of the Z2 KVBS order parameter harbors a spin-1/2 Heisenberg chain, as described by a 1+1 dimensional SO(3) non-linear sigma model with θ-term at θ = π. 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-1/2 chain at the Z2 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.