Rényi entropy and subsystem distances in finite size and thermal states in critical XY chains. (27th August 2020)

• Record Type: Journal Article
• Authors: Arias, Raúl; Zhang, Jiaju
• Is Part Of: Journal of statistical mechanics. (2020:Aug.)
• Publication Date: 2020-08-27
• Subjects: conformal field theory -- entanglement entropies -- integrable spin chains and vertex models; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/ababfd
• Languages: English
• ISSNs: 1742-5468

Abstract

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 conformal field theories and find perfect matches in the continuum limit.