Entanglement negativity between separated regions in quantum critical systems

TL;DR

This paper investigates how entanglement, measured by logarithmic negativity, behaves between separated regions in quantum critical systems across various dimensions, revealing universal decay patterns and differences between bosonic and fermionic systems.

Contribution

It provides a non-perturbative analysis of entanglement decay in quantum critical systems, including conformal field theories and lattice models, highlighting the absence of long-range bipartite entanglement for bosons and algebraic decay for fermions.

Findings

Logarithmic negativity is large at small separations and universal.

Decays faster than any power at large separations for bosonic systems.

Fermionic systems exhibit algebraic decay of entanglement.

Abstract

We study the entanglement between disjoint subregions in quantum critical systems through the lens of the logarithmic negativity. We work with systems in arbitrary dimensions, including conformal field theories and their corresponding lattice Hamiltonians, as well as resonating valence-bond states. At small separations, the logarithmic negativity is big and displays universal behavior, but we show non-perturbatively that it decays faster than any power at large separations. This can already be seen in the minimal setting of single-spin subregions. The corresponding absence of distillable entanglement at large separations generalizes the 1d result, and indicates that quantum critical groundstates do not possess long-range bipartite entanglement, at least for bosons. For systems with fermions, a more suitable definition of the logarithmic negativity exists that takes into account fermion parity, and we show that it decays algebraically. Along the way we obtain general results for the moments of the partially transposed density matrix.