Bundling of bipartite entanglement

TL;DR

This paper explores the structure of bipartite entanglement spectra in constrained energy subspaces, revealing that they are identical across multiple bipartitions and proposing methods to verify this efficiently.

Contribution

It introduces a novel analysis of entanglement spectra in constrained subspaces and provides algorithms to verify spectral equivalence across bipartitions.

Findings

Entanglement spectra are identical across bipartitions in constrained subspaces.

Bipartite entanglement entropy forms 'bundles' under unitary evolution.

Polynomial-time algorithm for parity-embedded subspaces.

Abstract

We investigate bipartite entanglement and prove that in constrained energy subspaces, the entanglement spectra of multiple bipartitions are the same across the whole subspace. We show that in quantum many-body systems the bipartite entanglement entropy is affected in such a way that it forms "bundles" under unitary time evolution. Leveraging the structure of the subspace, we present methods to verify whether the entanglement spectrum of two bipartitions is identical throughout the entire subspace. For the subspace defined by the parity embedding, we further provide an algorithm that can determine this in polynomial time.