We study the interplay between population imbalance in a two-component fermionic system and nearest-neighbor interaction using matrix product states method. Our analysis reveals the existence of a new type of Fulde-Ferrell-Larkin-Ovchinnikov phase in the presence of competing interactions. Furthermore, we find distinct evidence for the presence of hidden order in the system. We present an effective model to understand the emergent oscillations in the string correlations due to the imbalance, and show how they can become an efficient tool to investigate systems with imbalance.
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