  Due to the interaction between topological defects of an order parameter and
underlying fermions, the defects can possess induced fermion numbers, leading
to several exotic phenomena of fundamental importance to both condensed matter
and high energy physics. One of the intriguing outcome of induced fermion
number is the presence of fluctuating competing orders inside the core of
topological defect. In this regard, the interaction between fermions and
skyrmion excitations of antiferromagnetic phase can have important consequence
for understanding the global phase diagrams of many condensed matter systems
where antiferromagnetism and several singlet orders compete. We critically
investigate the relation between fluctuating competing orders and skyrmion
excitations of the antiferromagnetic insulating phase of a half-filled
Kondo-Heisenberg model on honeycomb lattice. By combining analytical and
numerical methods we obtain exact eigenstates of underlying Dirac fermions in
the presence of a single skyrmion configuration, which are used for computing
induced chiral charge. Additionally, by employing this nonperturbative
eigenbasis we calculate the susceptibilities of different translational
symmetry breaking charge, bond and current density wave orders and
translational symmetry preserving Kondo singlet formation. Based on the
computed susceptibilities we establish spin Peierls and Kondo singlets as
dominant competing orders of antiferromagnetism. We show favorable agreement
between our findings and field theoretic predictions based on perturbative
gradient expansion scheme which crucially relies on adiabatic principle and
plane wave eigenstates for Dirac fermions. The methodology developed here can
be applied to many other correlated systems supporting competition between
spin-triplet and spin-singlet orders in both lower and higher spatial
dimensions.
