  We study the R\'enyi entropy and subsystem distances on one interval for the
finite size and thermal states in the critical XY chains, focusing on the
critical Ising chain and XX chain with zero transverse field. We construct
numerically the reduced density matrices and calculate the von Neumann entropy,
R\'enyi entropy, subsystem trace distance, Schatten two-distance, and relative
entropy. As the continuum limit of the critical Ising chain and XX chain with
zero field are, respectively, the two-dimensional free massless Majorana and
Dirac fermion theories, which are conformal field theories, we compare the spin
chain numerical results with the analytical results in CFTs and find perfect
matches in the continuum limit.
