We note that the referee did not offer comments on the physical or theoretical aspects of our method. These are, however, the main focus of our Letter, in line with PRL's scope as a physics journal, not a numerical analysis journal. We intend to give more details on the implementation of DPT on parallel architectures and other computational aspects in a more suitable venue in due time. 
Moreover, we observe that some of the referee's comments (on "unphysical" solutions or "boundary conditions") appear to refer to algorithms other than DPT. We emphasize that our paper gives explicit conditions under which DPT provably converges to a complete set of eigenvectors, without any ambiguity or 
For  these two 

Response to specific comments

Comment 1

The proposed dynamic perturbation theory (D-PT) is not general. It is formulated only for matrices with non-degenerate (simple) eigenvalues. 
This comment suggests that the exclusion of degenerate eigenvalues is a peculiar deficiency of our method. This is misleading in several ways:
The reported illustrations are with highly specialized trivial real symmetric matrices (2 × 2 or 3 × 3) or with a still simple, small size 100 × 100 real non-symmetric matrix with random numbers (as the elements of M) distributed uniformly in the interval [-1,1].