  We present a detailed analysis of the X-ray luminosity (Lx) dependence of the
cyclotron absorption line energy (Ecyc) for the X-ray binary pulsar 1A 0535+262
during its 2020 giant outburst based on pulse-to-pulse analysis. By applying
this technique to high cadence observations of Insight-HXMT, we reveal the most
comprehensive Ecyc-Lx correlation across a broad luminosity range of
~(0.03-1.3)*10^38 erg/s. Apart from the positive and negative correlations
between cyclotron line energy and luminosity at Lx~(1-3)*10^37 erg/s and
~(7-13)*10^37 erg/s, which are expected from the typical subcritical and
supercritical accretion regimes, respectively, a plateau in the correlation is
also detected at ~(3-7)*10^37 erg/s^-1. Moreover, at the lowest luminosity
level (Lx<10^37 erg/s), the positive Ecyc-Lx correlation seems to be broken,
and the pulse profile also occurs a significant transition. These discoveries
provide the first complete view on the correlation between luminosity and the
centriod energy of the cyclotron line, and therefore are relevant for
understanding how accretion onto magnetized neutron stars depends on
luminosity.
