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Sublattice signatures of transitions in a $\mathcal{PT}$-symmetric dimer lattice

Lattice models with non-hermitian, parity and time-reversal ($\mathcal{PT}$) symmetric Hamiltonians, realized most readily in coupled optical systems, have been intensely studied in the past few years. A $\mathcal{PT}$-symmetric dimer lattice consists of dimers with intra-dimer coupling $ν$, inter-dimer coupling $ν'$, and balanced gain and loss potentials $\pm iγ$ within each dimer. This model undergoes two independent transitions, namely a $\mathcal{PT}$-breaking transition and a topological transition. We numerically and analytically investigate the signatures of these transitions in the time-evolution of states that are initially localized on the gain-site or the loss-site.