The negativity contour: a quasi-local measure of entanglement for mixed states

TL;DR

This paper introduces the negativity contour, a local measure of entanglement for mixed states in quantum many-body systems, enabling detailed analysis of entanglement structure and its dynamics.

Contribution

It develops an explicit negativity contour function for Gaussian states and generalizes it to complex many-body systems, providing a practical tool for entanglement analysis.

Findings

Positivity for holographic states and quasi-particle systems

Distinct entanglement structures in Fermi liquids and non-Fermi liquids

Temperature-dependent negativity dynamics after a quantum quench

Abstract

In this paper, we study the entanglement structure of mixed states in quantum many-body systems using the $\textit{negativity contour}$, a local measure of entanglement that determines which real-space degrees of freedom in a subregion are contributing to the logarithmic negativity and with what magnitude. We construct an explicit contour function for Gaussian states using the fermionic partial-transpose. We generalize this contour function to generic many-body systems using a natural combination of derivatives of the logarithmic negativity. Though the latter negativity contour function is not strictly positive for all quantum systems, it is simple to compute and produces reasonable and interesting results. In particular, it rigorously satisfies the positivity condition for all holographic states and those obeying the quasi-particle picture. We apply this formalism to quantum field theories with a Fermi surface, contrasting the entanglement structure of Fermi liquids and holographic (hyperscale violating) non-Fermi liquids. The analysis of non-Fermi liquids show anomalous temperature dependence of the negativity depending on the dynamical critical exponent. We further compute the negativity contour following a quantum quench and discuss how this may clarify certain aspects of thermalization.