distribution defined by the first two cumulants obtained for the particular case. The minimization procedure we applied is the simulated annealing technique [@Kirkpatrick83]. Below our reconstructions are based on calculating the first six GIMs in all cases.

Su-Schrieffer-Heeger and Rice-Mele models {#sec:SSH}
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The SSH model was first introduced [@Su79] to understand the properties of one-dimensional polyacetylene. The RM model is an extension of the SSH model, it includes an additional term, consisting of an alternating on-site potential, added in order to extend the SSH model to diatomic polymers. In recent decades it has been studied extensively due to the wealth of interesting physical phenomena it displays: topological soliton excitation, fractional charge, and non-trivial edge states[@Takayama80; @Su80; @Jackiw76; @Heeger88; @Ruostekoski02; @Li14]. It was also realized as a system of cold atoms trapped in an optical lattice in one dimension recently [@Atala13]. The Berry phase in the RM model was studied by Vanderbilt and King-Smith [@Vanderbilt93]. In that study the point of the model in parameter space of the model which is metallic (and which is responsible for the topologically nontrivial behavior) was encircled in parameter space. This leads to the increase of $C_1$ (the Berry phase, or the polarization) by 