I have a 1D discrete, finite system that lacks translational invariance. It appears to have edge states, in much the same way as an SSH model has edge states. In the SSH model we can study the infinite version of the finite chain to calculate a topological index, the Zak phase. I am trying to think if I can define (or there already exists) some kind of topological index that captures the presence of these edge states. However my system lacks translational invariance. Any suggestions on how to approach this? I have found the Bott index, but it appears to only be defined for 2D systems.
EDIT
Let me give a specific example. I have a Hamiltonian
$$H = \sum_{n=1}^N (b_n^\dagger + b_n)[\Omega(a_n^\dagger + a_n)+\omega(a_{n+1}^\dagger + a_{n+1})]$$
which describes a dimerised chain with $N$ unit cells, each containing an A-site and B-site. $\Omega$ is the intra-cell interaction, and $\omega$ is the inter-cell interaction. I want to find a topological index for this specific system, with a finite $N$. I don't want to take any periodic boundary conditions or extend to infinity etc. I believe I can use one of the indices given by Terry Loring, but which one and how exactly? My Hamiltonian in matrix form is
$$H=\frac{1}{2}\hat{\mathbf{\Psi}}^\dagger \begin{pmatrix} \mathbf{0}_{2N} & \mathbf{h}^\dagger \\ \mathbf{h} & \mathbf{0}_{2N} \end{pmatrix}\hat{\mathbf{\Psi}} $$
where $\mathbf{h} = \mathbf{J}_2 \otimes \mathbf{W}$, with $\mathbf{J}_2$ a $2\times2$ matrix-of-ones, and $\mathbf{W}$ a $N\times N$ matrix with constant entries $\Omega$ along the main diagonal and $\omega$ along the 1-diagonal (first diagonal to the right of the main diagonal). The vector of operators is given by
$$\hat{\mathbf{\Psi}} = (a_1, a_2, \dots, a_N, a_1^\dagger, a_2^\dagger, \dots, a_N^\dagger, b_1, b_2, \dots, b_N, b_1^\dagger, b_2^\dagger, \dots, b_N^\dagger)^T$$
I am happy with either an analytic or numerical calculation of the topological index.