Quench dynamics of negativity Hamiltonians

TL;DR

This paper studies the dynamics of negativity Hamiltonians in free fermionic systems after a quench, revealing their structure and equivalence in certain limits through analytic and numerical methods.

Contribution

It generalizes a quasiparticle picture to tripartite geometries and analytically compares negativity Hamiltonians, highlighting their structural differences and equivalence in the scaling limit.

Findings

Negativity Hamiltonian includes non-local and four-fermion terms

Fermionic negativity Hamiltonian is purely quadratic

Logarithmic negativity is identical for both Hamiltonians in the ballistic limit

Abstract

In this paper, we investigate the quench dynamics of the negativity and fermionic negativity Hamiltonians in free fermionic systems. We do this by generalizing a recently developed quasiparticle picture for the entanglement Hamiltonians to tripartite geometries. We obtain analytic expressions for these quantities which are then extensively checked against previous results and numerics. In particular, we find that the standard negativity Hamiltonian contains both non-local hopping terms and four fermion interactions, whereas the fermionic version is purely quadratic. However, despite their marked difference, we show that the logarithmic negativity obtained from either are identical in the ballistic scaling limit, as are their symmetry resolution.