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Degrees and signatures of broken<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="script">P</mml:mi><mml:mi mathvariant="script">T</mml:mi></mml:mrow></mml:math>symmetry in nonuniform lattices
We investigate the robustness of the parity- and time-reversal ($\mathcal{P}\mathcal{T}$) symmetric phase in an $N$-site lattice with a position-dependent, parity-symmetric hopping function and a pair of imaginary, $\mathcal{P}\mathcal{T}$-symmetric impurities. We find that the ``fragile'' $\mathcal{P}\mathcal{T}$-symmetric phase in these lattices is stronger than its counterpart in a lattice with constant hopping. …