Mixed-State Long-Range Entanglement from Dimensional Constraints

TL;DR

This paper introduces a new mechanism for long-range entanglement in many-body mixed states based on dimensional mismatch, demonstrated through a translation-invariant maximally mixed state on a 1D ring.

Contribution

It reveals a novel route to long-range entanglement in mixed states via dimensional constraints, independent of symmetry anomalies or long-range correlations.

Findings

Maximally mixed state on a 1D ring exhibits long-range entanglement.

Dimensional mismatch leads to polynomial versus exponential growth in subspace dimensions.

Constructed a non-local Lindbladian to stabilize the state as steady state.

Abstract

We present a new mechanism for long-range entanglement (LRE) in strongly symmetric many-body mixed states that does not rely on symmetry anomalies or long-range correlations. Our primary example is the maximally mixed state in the translation-invariant subspace on a one-dimensional ring. This state is LRE because translationally symmetric short-range entangled states span a subspace whose dimension grows only polynomially with system size, whereas the full translation-invariant subspace grows exponentially. We further discuss certain unconventional properties of this state, including logarithmically growing conditional mutual information, strong-to-weak spontaneous symmetry-breaking, and R\'enyi-index-dependent operator-space entanglement. We also construct a geometrically non-local Lindbladian to stabilize this state as the steady state. Our results identify dimensional mismatch as a novel route to LRE that is intrinsic to many-body mixed states.