Entanglement contour

TL;DR

The paper introduces the entanglement contour, a novel tool for analyzing the detailed structure of quantum entanglement in many-body systems, providing insights beyond traditional entanglement entropy measures.

Contribution

It presents the entanglement contour as a refined method to characterize entanglement, applicable to ground states and quenches, and demonstrates its ability to extract physical properties like central charge and phase distinctions.

Findings

Can determine the central charge from a single partition in 1D systems.

Distinguishes gapped and gapless phases in higher dimensions.

Tracks entanglement dynamics during quantum quenches.

Abstract

In the context of characterizing the structure of quantum entanglement in many-body systems, we introduce the entanglement contour, a tool to identify which real-space degrees of freedom contribute, and how much, to the entanglement of a region A with the rest of the system B. The entanglement contour provides a complementary, more refined approach to characterizing entanglement than just considering the entanglement entropy between A and B, with several concrete advantages. We illustrate this in the context of ground states and quantum quenches in fermionic quadratic systems. For instance, in a quantum critical system in $D = 1$ spatial dimensions, the entanglement contour allows us to determine the central charge of the underlying conformal field theory from just a single partition of the system into regions A and B, (using the entanglement entropy for the same task requires considering several partitions). In $D \geq 2$ dimensions, the entanglement contour can distinguish between gapped and gapless phases that obey a same boundary law for entanglement entropy. During a local or global quantum quench, the time-dependent contour provides a detailed account of the dynamics of entanglement, including propagating entanglement waves, which offers a microscopic explanation of the behavior of the entanglement entropy as a function of time.