Critical Fermions are Universal Embezzlers

TL;DR

This paper demonstrates that ground states of certain one-dimensional quantum many-body systems act as universal embezzlers, enabling extraction of any entangled state with arbitrary precision using local operations.

Contribution

It proves that universal embezzlement is a common feature in ground states of critical free-fermionic and dual spin chain models, even at finite sizes.

Findings

Ground states are universal embezzlers for any finite error.

Universal embezzlement occurs in finite systems, not just in the thermodynamic limit.

Half-chain algebras are type III$_1$ factors, underpinning the embezzlement property.

Abstract

Universal embezzlers are bipartite quantum systems from which any entangled state may be extracted to arbitrary precision using local operations while perturbing the state of the system arbitrarily little. Here, we show that universal embezzlers are ubiquitous in many-body physics: The ground state sector of every local, translation-invariant, and critical free-fermionic many-body system on a one-dimensional lattice is a universal embezzler if bi-partitioned into two half-chains. The same property holds in locally-interacting, dual spin chains via the Jordan-Wigner transformation. Universal embezzlement manifests already for finite system sizes, not only in the thermodynamic limit: 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. 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 III$_1$ factors.