Time evolution of entanglement negativity across a defect

Understand

We consider a quench in a free-fermion chain by joining two homogeneous half-chains via a defect.

• The time evolution of the entanglement negativity is studied between adjacent segments surrounding the defect.
• In case of equal initial fillings, the negativity grows logarithmically in time and essentially equals one-half of the R\'enyi mutual information with index $\alpha = 1/2$ in the limit of large segments.
• In sharp contrast, in the biased case one finds a linear increase followed by the saturation at an extensive value for both quantities, which is due to the backscattering from the defect and can be reproduced in a quasiparticle picture.