Topological transition caused by reconstruction of zero-mode Majorana fermions in XYZ spin chain

Kitaev chain model has attracted much attention as a possible play-ground of topologically-protected quantum computation (TPQC), based on zero-energy modes of Majorana fermions (ZM2Fs). This model can be realized in a 1/2-spin chain compound, which has an anisotropic XY exchange interaction between nearest-neighbor sites. However, real materials also have a non-zero Ising interaction necessarily. Here, we theoretically study effects of the Ising interaction in a XYZ spin chain, where a fully anisotropic exchange is introduced in neighboring bonds. The existence of ZM2Fs can be clarified with energy gaps of ground states between different $Z_2\times Z_2 \times Z_2$ sectors, defined by $Q^\alpha=\prod_i (2S_i^\alpha)=\pm 1$ where $\alpha=x,y,z$. By calculating the energy gaps with variational matrix-product state method, we find a topological transition, where a ZM2F in $Q^\alpha$ sectors changes into that in other $Q^\beta$ sectors. Thus, we conclude that the transition originates from a reconstruction, namely a global $SU(2)$ rotation, of the ZM2F. Our results are helpful not only for understanding effects of possible Ising interactions in real compounds but also for important knowledge on stability of TPQCs.