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

R\'enyi entropy and subsystem distances in finite size and thermal states in critical XY chains