Circuit Complexity in presence of a defect

We study circuit complexity for the ground state of a harmonic chainwith defect in 1+1 dimensions, choosing as a reference state, the ground state of the homogeneous chain. By employing the covariance matrix for-malism, we compute numerically C2 complexity and extract its divergence pattern in the continuum limit. We find that, upon a suitable choice of the coordinates, C2 complexity displays a logarithmic divergence. Finally, we compare our results with the existing ones for the entanglement entropy of half chain and the holographic complexity in the presence of a defect.