  We present a study of the size--mass relation for local post-starburst (PSB)
galaxies at $z\lesssim0.33$ selected from the Sloan Digital Sky Survey Data
Release 8. We find that PSB galaxies with stellar mass ($M_*$) at
$10^9~M_{\odot}<M_*<10^{12}~M_{\odot}$ have their galaxy size smaller than or
comparable with those of quiescent galaxies (QGs). After controlling redshift
and stellar mass, the sizes of PSBs are $\sim 13\%$ smaller on average than
those of QGs, such differences become larger and significant towards the
low-$M_*$ end, especially at $10^{9.5}~M_{\odot} \lesssim M_*\lesssim
10^{10.5}~M_{\odot}$ where PSBs can be on average $\sim 19\%$ smaller than QGs.
In comparison with predictions of possible PSB evolutionary pathways from
cosmological simulations, we suggest that a fast quenching of star formation
following a short-lived starburst event (might be induced by major merger)
should be the dominated pathway of our PSB sample. Furthermore, by
cross-matching with group catalogs, we confirm that local PSBs at
$M_*\lesssim10^{10}~M_{\odot}$ are more clustered than more massive ones. PSBs
resided in groups are found to be slightly larger in galaxy size and more
disk-like compared to field PSBs, which is qualitatively consistent with and
thus hints the environment-driven fast quenching pathway for group PSBs. Taken
together, our results support multiple evolutionary pathways for local PSB
galaxies: while massive PSBs are thought of as products of fast quenching
following a major merger-induced starburst, environment-induced fast quenching
should play a role in the evolution of less massive PSBs, especially at
$M_*\lesssim 10^{10}~M_{\odot}$.
