Symmetry-resolved genuine multi-entropy: Haar random and graph states

TL;DR

This paper investigates the structure of genuine multi-partite entanglement in Haar random and graph states with a conserved quantity, deriving explicit formulas and analyzing their entanglement features.

Contribution

It provides explicit formulas for symmetry-resolved multi-entropy in Haar random states with a $U(1)$ symmetry and compares entanglement structures in graph states.

Findings

Genuine multi-entropy depends on subsystem sizes similarly to non-conserved Haar states.

Numerical analysis shows distinctive multi-partite entanglement features in graph states.

Comparison highlights differences between Haar random and graph states' entanglement structures.

Abstract

We study the symmetry-resolved genuine multi-entropy, a measure that captures genuine multi-partite entanglement, in Haar random states and random graph states in the presence of a conserved quantity. For Haar random states, we derive explicit formulae for the genuine multi-entropy under a global $U(1)$ symmetry in the thermodynamic limit, and find that its dependence on subsystem sizes closely resembles that of fully Haar random states without a conserved charge. We also perform numerical analyses, focusing on spin systems for both Haar random and graph states. For random graph states, our numerical analyses reveal distinctive features of their multi-partite entanglement structure and we contrast them with the Haar random case.