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Due to the interaction between topological defects of an order parameter andunderlying fermions, the defects can possess induced fermion numbers, leadingto several exotic phenomena of fundamental importance to both condensed matterand high energy physics. One of the intriguing outcome of induced fermionnumber is the presence of fluctuating competing orders inside the core oftopological defect. In this regard, the interaction between fermions andskyrmion excitations of antiferromagnetic phase can have important consequencefor understanding the global phase diagrams of many condensed matter systemswhere antiferromagnetism and several singlet orders compete. We criticallyinvestigate the relation between fluctuating competing orders and skyrmionexcitations of the antiferromagnetic insulating phase of a half-filledKondo-Heisenberg model on honeycomb lattice. By combining analytical andnumerical methods we obtain exact eigenstates of underlying Dirac fermions inthe presence of a single skyrmion configuration, which are used for computinginduced chiral charge. Additionally, by employing this nonperturbativeeigenbasis we calculate the susceptibilities of different translationalsymmetry breaking charge, bond and current density wave orders andtranslational symmetry preserving Kondo singlet formation. Based on thecomputed susceptibilities we establish spin Peierls and Kondo singlets asdominant competing orders of antiferromagnetism. We show favorable agreementbetween our findings and field theoretic predictions based on perturbativegradient expansion scheme which crucially relies on adiabatic principle andplane wave eigenstates for Dirac fermions. The methodology developed here canbe applied to many other correlated systems supporting competition betweenspin-triplet and spin-singlet orders in both lower and higher spatialdimensions.

Skyrmion defects and competing singlet orders in a half-filled antiferromagnetic Kondo-Heisenberg model on the honeycomb lattice