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Entanglement Dynamics after a Quench in Ising Field Theory: A Branch Point Twist Field Approach

Castro-Alvaredo, O. ORCID: 0000-0003-1876-7341, Lencsés, M., Szécsényi, I. M. and Viti, J. (2019). Entanglement Dynamics after a Quench in Ising Field Theory: A Branch Point Twist Field Approach. Journal of High Energy Physics, 2019(12), 79.. doi: 10.1007/JHEP12(2019)079

Abstract

We extend the branch point twist field approach for the calculation of entanglement entropies to time-dependent problems in 1+1-dimensional massive quantum field theories. We focus on the simplest example: a mass quench in the Ising field theory from initial mass m0 to final mass m. The main analytical results are obtained from a perturbative expansion of the twist field one-point function in the post-quench quasi-particle basis. The expected linear growth of the Rényi entropies at large times mt ≫ 1 emerges from a perturbative calculation at second order. We also show that the Rényi and von Neumann entropies, in infinite volume, contain subleading oscillatory contributions of frequency 2m and amplitude proportional to (mt)−3/2. The oscillatory terms are correctly predicted by an alternative perturbation series, in the pre-quench quasi-particle basis, which we also discuss. A comparison to lattice numerical calculations carried out on an Ising chain in the scaling limit shows very good agreement with the quantum field theory predictions. We also find evidence of clustering of twist field correlators which implies that the entanglement entropies are proportional to the number of subsystem boundary points.

Publication Type: Article
Additional Information: This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: https://openaccess.city.ac.uk/id/eprint/23414
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