Frame et al. (Frame D, He R Z, Ipsen I, Lee D, Lee D, Rrapaj E 2018 Phys. Rev. Lett. 121032501 ) proposed to use eigenvector continuation to solve high-dimensional many-body wavefunctions of relevant quantum models. When a model’s Hamiltonian matrix includes smoothly varying parameters, the corresponding eigenvector trajectory spans only a low-dimensional subspace. Therefore, it is possible to simplify the calculations by projecting the Hamiltonian onto a set of basis vectors of this subspace. However, the dimension of the trajectory subspace and its relationship with the size of the model are still unclear. In this paper, we study the antiferromagnetic Heisenberg chain models of different sizes systematically; their exchange interactions change with parameters smoothly. We first use principal component analysis to determine the subspaces of ground state many-body wavefunction vector trajectories of a 4-spin model and a 6-spin model, and plot the trajectories in the subspaces, respectively; we then analyze the principal components of ground state vector trajectories of models including $8,\cdots ,14$ spins, and reveal that when using eigenvector continuation to solve the ground state of an antiferromagnetic Heisenberg chain model, the number of basis vectors required increases with the number of spins in the model increasing. Our study can guide the application of eigenvector continuation in solving the Hamiltonian of a Heisenberg chain model containing more spins.