![Open SSH chain in the limit $w=0$ and $v\ne 0$[]{data-label="openssh1"}](fig2.pdf)

This seems like a repetitive problem of a dimer which is, of course, easy to solve. We know the solutions should be the superposition of the $A$ site and $B$ site for each dimer. We can even guess that this should correspond to an insulating state as the chain is now broken and no particle can hop from one end of the chain to the other.

Let us now look at the other extreme case of $v=0$.

![Open SSH chain in the limit $v=0$ and $w\ne 0$[]{data-label="openssh2"}](fig3.pdf)

Similar to the previous case, we get a few dimers but since the chain has open boundaries, we now have two single sites at the end of the chain, see FIG. \[openssh2\]. If these two sites, one at each end, carry an electron the energy should be zero because, in the SSH model, there is no energy contribution for an electron to be held fixed at one site. So we should expect two zero energy states in the system localised at the edges of the chain. Again going by the same argument as in the previous case we expect this case to describe 