Entanglement negativity in a fermionic chain with dissipative defects: Exact results

TL;DR

This paper derives exact results for the dynamics of fermionic entanglement negativity in a chain with a dissipative defect, revealing linear growth, saturation, and volume-law scaling influenced by dissipation and initial criticality.

Contribution

It provides an exact analytical description of entanglement negativity dynamics in a dissipative free-fermion chain, highlighting the effects of localized loss and initial criticality.

Findings

Negativity grows linearly then saturates to volume law

Negativity differs from Rènyi mutual information with index 1/2

Logarithmic corrections appear at criticality

Abstract

We investigate the dynamics of the fermionic logarithmic negativity in a free-fermion chain with a localized loss, which acts as a dissipative impurity. The chain is initially prepared in a generic Fermi sea. In the standard hydrodynamic limit of large subsystems and long times, with their ratio fixed, the negativity between two subsystems is described by a simple formula, which depends only on the effective absorption coefficient of the impurity. The negativity grows linearly at short times, then saturating to a volume-law scaling. Physically, this reflects the continuous production with time of entangling pairs of excitations at the impurity site. Interestingly, the negativity is not the same as the R\'enyi mutual information with R\'enyi index $1/2$, in contrast with the case of unitary dynamics. This reflects the interplay between dissipative and unitary processes. The negativity content of the entangling pairs is obtained in terms of an effective two-state mixed density matrix for the subsystems. Criticality in the initial Fermi sea is reflected in the presence of logarithmic corrections. The prefactor of the logarithmic scaling depends on the loss rate, suggesting a nontrivial interplay between dissipation and criticality.