Symmetric localization of ${\nu }_{\text{tot}}=4\mathrm{/}3$ fractional topological insulator edges

Motivated by the recent twisted MoTe${}_2$ experiment [arXiv:2601.18508], we develop a disordered interacting edge theory of a fractional topological insulator at ${\nu }_{\text{tot}}=4\mathrm{/}3$, consisting of two time-reversal-conjugated $\nu =2\mathrm{/}3$ fractional quantum Hall states. For an $S_z$-conserving edge, we uncover three distinct phases with two possible conductance values per edge in the long-edge limit: $\frac{2}{3}\frac{e^2}{h}$ and $\frac{4}{3}\frac{e^2}{h}$. In the presence of $S_z$-changing perturbations (e.g., Rashba spin-orbit coupling), an interaction-induced insulating edge state can emerge without breaking time-reversal or charge-conservation symmetry, corresponding to the absence of a topologically protected edge state. We further provide an exact mapping to a noninteracting fermionic theory exhibiting Anderson localization. Our results showcase an explicit, experimentally relevant example that the edge-state two-terminal transport is insufficient to identify the ${\nu }_{\text{tot}}=4\mathrm{/}3$ fractional topological insulators.