Shape dependence of two-cylinder Rényi entropies for free bosons on a lattice

Chojnacki, L., Cook, C. Q., Dalidovich, D., Hayward Sierens, L. E., Lantagne-Hurtubise, É., Melko, R. G. and Vlaar, T. J. (2016) Shape dependence of two-cylinder Rényi entropies for free bosons on a lattice. Physical Review B, 94(16), 165136. (doi: 10.1103/PhysRevB.94.165136)

Abstract

Universal scaling terms occurring in Rényi entanglement entropies have the potential to bring new understanding to quantum critical points in free and interacting systems. Quantitative comparisons between analytical continuum theories and numerical calculations on lattice models play a crucial role in advancing such studies. In this paper, we exactly calculate the universal two-cylinder shape dependence of entanglement entropies for free bosons on finite-size square lattices, and compare to approximate functions derived in the continuum using several different Ansätze. Although none of these Ansätze are exact in the thermodynamic limit, we find that numerical fits are in good agreement with continuum functions derived using the anti–de Sitter/conformal field theory correspondence, an extensive mutual information model, and a quantum Lifshitz model. We use fits of our lattice data to these functions to calculate universal scalars defined in the thin-cylinder limit, and compare to values previously obtained for the free boson field theory in the continuum.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Vlaar, Dr Tiffany
• Authors: Chojnacki, L., Cook, C. Q., Dalidovich, D., Hayward Sierens, L. E., Lantagne-Hurtubise, É., Melko, R. G., and Vlaar, T. J.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Physical Review B
• Publisher: American Physical Society
• ISSN: 2469-9950
• ISSN (Online): 2469-9969