Critical fermions are universal embezzlers

Universal embezzlers are bipartite quantum systems from which any entangled state may be extracted to arbitrary precision using local operations while perturbing the system arbitrarily little. Here we show that a universal embezzler can be created by bipartitioning any local, translation-invariant, critical free-fermionic many-body system on a one-dimensional lattice. The same property holds for locally interacting spin chains that are dual to the critical fermionic models by the Jordan–Wigner transformation. Furthermore, for any finite error and any targeted entangled state, a finite length of the chain is sufficient to embezzle said state within the given error. Hence, universal embezzlement is not restricted to the thermodynamic limit. As well as establishing the ubiquity of universal embezzlers in many-body physics, on a technical level, our main result establishes that the half-chain observable algebras associated with ground-state sectors of the given models are type III₁ factors.