Spin-charge separation in a nodal antiferromagnetic insulator

Abstract

In this Brief Report, by using two-dimensional Hubbard models with $\ensuremath{\pi}$-flux phase and that on a hexagonal lattice as examples, we explore spin-charge-separated solitons in nodal antiferromagnetic (AF) insulator---an AF order with massive Dirac fermionic excitations (see details in text). We calculated fermion zero modes and induced quantum numbers on solitons (half skyrmions) in the continuum limit, which are similar to that in the quasi-one-dimensional conductor polyacetylene ${(\text{CH})}_{x}$ and that in topological band insulator. In particular, we find some different phenomena: thanks to an induced staggered spin moment, a mobile half skyrmion becomes a fermionic particle; when a hole or an electron is added, the half skyrmion turns into a bosonic particle with charge degree of freedom only. Our results imply that nontrivial induced quantum number on solitons may be a universal feature of spin-charge separation in different systems.