Multi-entropy and the Dihedral Measures at Quantum Critical Points

TL;DR

This paper introduces multi-entropy and dihedral measures as new tools for probing quantum critical points, demonstrating their effectiveness through calculations in scalar field theory and Ising models, with results aligning with conformal field theory.

Contribution

It presents multi-entropy and dihedral measures as novel, tractable probes for quantum criticality, with explicit calculations and predictions in lattice models and conformal field theory.

Findings

Quantitative agreement of n=2 measures with conformal field theory

New predictions for n=3 and n=4 measures in scalar field theory

Demonstration of measures as effective probes of quantum critical points

Abstract

The multi-entropy and dihedral measures are a class of tractable measures for multi-partite entanglement, which are labeled by the R\'enyi index (or replica number) $n$ as in the R\'enyi entanglement entropy. The purpose of this article is to demonstrate that these quantities are new useful probes of quantum critical points by examining concrete examples. In particular, we compute the multi-entropy and dihedral measures in the $1+1$ dimensional massless free scalar field theory on a lattice and in the transverse-field Ising model. For $n=2$, we find that the numerical results in both lattice theories quantitatively agree with those from conformal field theoretic calculations. For $n=3$ and $n=4$, we provide new predictions of these measures for the massless scalar field theory.