one polarization quantum, consistent with the quantization of charge transport [@Thouless83; @King-Smith93].

The hopping part of the SSH Hamiltonian reads: $$\hat{H}_{SSH} = -J \sum_{i=1}^{N/2}  c_{i,A}^\dagger c_{i,B}
               -J' \sum_{i=1}^{N/2}  c_{i,B}^\dagger c_{i+1,A} + \mbox{H.c.},$$ where $N$ denotes the number of sites, the on-site potential has the form $$\hat{H}_{\Delta} = -\Delta \sum_{i=1}^{N/2}  c_{i,A}^\dagger c_{i,A}
               + \Delta \sum_{i=1}^{N/2}  c_{i,B}^\dagger c_{i,B}.$$ The model is shown schematically in Fig. \[fig:model\]. This figure shows the one-dimensional lattice, including sublattices, the alternating hoppings, and the on-site potential. The unit cell is indicated in shaded yellow. Also shown is the continuous variable $x$, which runs from $-\infty$ to $\infty$, and will serve as the axis for the reconstructed probability distributions of the polarization calculated below.

The hoppings can also be expressed in terms of the average hopping $t$ and the deviation $\delta$ as $$\label{eqn:tdelta}
J = \frac{t}{2} + \frac{\delta}{2}, J' = \frac{t}{2} - \frac{\delta}{2}.$$ The total Hamiltonian we consider is $$\hat{H} = \hat{H}_{SSH} + \hat{H}_{\Delta}.$$ The parameters $J$ and $J'$ are hopping parameters corresponding to hopping along alternating bonds. We take the lattice constant to be unity (the unit cell is two lattice constants). The parameter $\Delta$ denotes the on-site potential, whose sign alternates from site to site. This 