Multientropy and the dihedral measures at quantum critical points

The multientropy and dihedral measures are a class of tractable measures for multipartite entanglement, which are labeled by the Rényi index (or replica number) <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>n</a:mi> </a:math> as in the Rényi entanglement entropy. The purpose of this article is to demonstrate that these quantities are useful probes of quantum critical points by examining concrete examples. In particular, we compute the multientropy and dihedral measures in the ( <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mn>1</b:mn> <b:mo>+</b:mo> <b:mn>1</b:mn> </b:mrow> </b:math> )-dimensional massless free scalar field theory on a lattice and in the transverse-field Ising model. For <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>n</c:mi> <c:mo>=</c:mo> <c:mn>2</c:mn> </c:mrow> </c:math> , we find that the numerical results in both lattice theories quantitatively agree with those from conformal field theoretic calculations. For <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>n</d:mi> <d:mo>=</d:mo> <d:mn>3</d:mn> </d:mrow> </d:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>n</e:mi> <e:mo>=</e:mo> <e:mn>4</e:mn> </e:mrow> </e:math> , we provide predictions of these measures for the massless scalar field theory.