Entanglement entropy after a partial projective measurement in 1  +  1 dimensional conformal field theories: exact results. (29th June 2016)

• Record Type: Journal Article
• Authors: Rajabpour, M A
• Is Part Of: Journal of statistical mechanics. (2016:Jun.)
• Publication Date: 2016-06-29
• Subjects: Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2016/06/063109
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We calculate analytically the Rényi bipartite entanglement entropy S α of the ground state of 1 + 1 dimensional conformal field theories (CFT) after performing a projective measurement in part of the system. We show that the entanglement entropy in this setup is dependent on the central charge and the operator content of the system. When the measurement region A separates the two parts B and B ̄, the entanglement entropy between B and B ̄ decreases like a power-law with respect to the characteristic distance between the two regions with an exponent which is dependent on the rank α of the Rényi entanglement entropy and the smallest scaling dimension present in the system. We check our findings by making numerical calculations on the Klein–Gordon field theory (coupled harmonic oscillators) after fixing the position (partial measurement) of some of the oscillators. We also comment on the post-measurement entanglement entropy in the massive quantum field theories.