Universal divergence of the Renyi entropy of a thinly sliced torus at the Ising fixed point

• Published in: arXiv.org
• Main Authors: Kulchytskyy, Bohdan, Hayward Sierens, Lauren E, Melko, Roger G
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 18.04.2019
• Subjects: Computer simulation; Cylinders; Divergence; Embedded systems; Entanglement; Entropy (Information theory); Ising model; Physics - Strongly Correlated Electrons; Toruses
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1904.08955

The entanglement entropy of a quantum critical system can provide new universal numbers that depend on the geometry of the entangling bipartition. We calculate a universal number called \(\kappa\), which arises when a quantum critical system is embedded on a two-dimensional torus and bipartitioned into two cylinders. In the limit when one of the cylinders is a thin slice through the torus, \(\kappa\) parameterizes a divergence that occurs in the entanglement entropy sub-leading to the area law. Using large-scale Monte Carlo simulations of an Ising model in 2+1 dimensions, we access the second Renyi entropy, and determine that, at the Wilson-Fisher (WF) fixed point, \(\kappa_{2,\text{WF}} = 0.0174(5)\). This result is significantly different from its value for the Gaussian fixed point, known to be \(\kappa_{2,\text{Gaussian}} \approx 0.0227998\).