It is well known that the standard bulk-boundary correspondence does not hold for non-Hermitian systems in which also new phenomena such as exceptional points occur. Here, we study, mostly by analytical means, a paradigmatic one-dimensional non-Hermitian model with dimerization, asymmetric hopping, and imaginary staggered potentials. We present analytical solutions for the singular value and the eigensystem of this model with both open and closed boundary conditions. We explicitly demonstrate that the proper bulk-boundary correspondence is between topological winding numbers in the periodic case and singular values, not eigenvalues, in the open case. These protected singular values are connected to hidden edge modes that only become exact zero-energy eigenmodes in the semi-infinite chain limit. We also show that a nontrivial topology leads to protected eigenvalues in the entanglement spectrum. In the $\mathcal{PT}$-symmetric case, we find that the model has a previously overlooked phase where exceptional points become dense in the thermodynamic limit. This phase shows unusual hyper-ballistic transport properties with a dynamical critical exponent $z=1/2$.

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• Entanglement entropy
• Topological phase transition
• Exceptional points
• Non-Hermitian systems
• Su-Schrieffer-Heeger model