Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains

Abstract

We study the Rényi 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, Rényi 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.

arXiv commentv1, 32 pages, 15 figures; v2, 35 pages, 15 figures, published version

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• Symmetry resolved relative entropies and distances in conformal field theory
• Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory -- I. Single-particle states
• Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part II. Multi-particle states
• Subsystem distances between quasiparticle excited states
• Trace distance between fermionic Gaussian states from a truncation method
• Entanglement entropy of two disjoint intervals and spin structures in interacting chains in and out of equilibrium