Frustrated metallicity in the quasi-one-dimensional conductor PrBa$_2$Cu$_4$O$_8$

We have investigated the ground state of the extremely anisotropic quasi-one-dimensional metal PrBa$_2$Cu$_4$O$_8$ ($t_ {b}^2:t_{a}^2: t_{c}^2 \sim 4000: 2: 1$), the non- superconducting analogue of the high-T$_c$ cuprate YBa$_2$Cu$_4 $O$_8$, as a function of disorder content, introduced either through atomic-site substitution or electron irradiation. A common single disorder threshold is found to drive interchain and in-chain resistivities into a low temperature regime where they display $d\rho/dT<0$. The survival of a large magnetoresistance of orbital origin reveals the itinerancy of the electronic system not to be suppressed by the presence of disorder. We propose an interpretative scenario based on a microscopic fragmentation of the metallic chains, though in contrast to many previous theoretical proposals, coherent hopping between chains appears to remain a relevant perturbation within the disordered system.