Automorphism-Induced Entanglement Bounds in Many-Body Systems

TL;DR

This paper establishes a new automorphism-based upper bound on entanglement entropy in many-body ground states, improving understanding of entanglement scaling in symmetric systems.

Contribution

It introduces a novel bound based on automorphism group representations, complementing existing degeneracy bounds, with significant improvements for complete graphs.

Findings

The bound is model-agnostic and depends on automorphism group representations.

For complete graphs, the bound improves entropy scaling from linear to logarithmic.

The bound aligns with the exact entanglement entropy for complete graphs.

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.