  Long-range effects induce some interesting behavior and considered as a
gateway to understand the non-local behavior in the quantum systems.
Especially, the long-range topological models became a platform for the
realization of new quasi-particles, which are believed to be potential
candidates for the topological qubits. In this work, we consider non-Hermitian
Su-Schriffer-Heeger (SSH) model and discuss the interplay of non-Hermiticity
and long-range effects. We use the approach of momentum space characterization,
critical exponents and curvature renormalization group (CRG) method to
understand the aspects of interplay. The longer-range (finite neighbors) effect
produces higher winding numbers, where we observe a staircase of transitions
among the even-even and odd-odd winding numbers which depends on the number of
interacting neighbors. Here we also highlight the effect of multi-criticality
in the system and show that they belong to a different universality class. The
interplay of long-range (infinite neighbors) effect and non-Hermiticity
produces fractional topological invariants, and we analyze them from the
behavior of pseudo-spin vectors. We also determine the long-range and
short-range limit of the model through universality class of critical
exponents. Our work mainly showcases that how the study of criticality in
topological system is interesting in exploring the interplay of non-Hermiticity
and long-range effects.
