Symmetry-resolved genuine multientropy: Random Haar and graph states

We study the symmetry-resolved genuine multientropy, a measure that captures genuine multipartite entanglement, in Haar random states and random graph states in the presence of a conserved quantity. For Haar random states, we derive explicit formulas for the genuine multientropy under a global <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>1</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> 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 multipartite entanglement structure and we contrast them with the Haar random case.