Automorphism-Induced Entanglement Bounds in Many-Body Systems

• URL: http://arxiv.org/abs/2604.11059v1
• Date: Mon, 13 Apr 2026 06:35:58 GMT
• Title: Automorphism-Induced Entanglement Bounds in Many-Body Systems
• Abstract summary: We derive an upper bound on the maximum balanced bipartite entanglement entropy of ground states of many-body Hamiltonians defined on a graph.<n>For the complete graph $K_n$, the new bound yields an exponential improvement from linear to logarithmic scaling in the system size.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We derive an upper bound on the maximum balanced bipartite entanglement entropy of ground states of many-body Hamiltonians defined on a graph, agnostic to any particular model, that possesses a nontrivial automorphism group. We show that the entropy is bounded by the logarithm of a weighted sum of multiplicities of irreducible representations of the bipartition-preserving automorphism subgroup. This bound complements the known degeneracy-based bound, with neither universally dominating the other. For the complete graph $K_n$, the new bound yields an exponential improvement from linear to logarithmic scaling in the system size, consistent with the exact value of the entropy.

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