Correlations and Coherence at Different Scales (CCDS25)

We report disorder-free localization of Majorana fermions on intermediate time scales in an emergent gapless non-integrable $Z_2$ quantum spin liquid. A large density of ground-state visons induced by an external magnetic field provides coherent flux disorder that (i) closes the Majorana fermion gap and (ii) localizes the fermions while preserving translation symmetry. The resulting Majorana metallic state is confirmed by the close agreement between the numerically obtained dynamical spin spectral function and the Majorana spectral function of an effective tight-binding model with coherent vison disorder. Compelling evidence of its localization is provided by the time evolution of the local energy density, which shows negligible spreading after a local quench on its ground state; and a vanishing energy current response despite the gapless energy spectrum. These results demonstrate that the disorder-free localization can also occur near equilibrium at low energy, and offer an explanation to the thermal paradox in recent experiments where a linear specific heat coexists with vanishing thermal transport in frustrated Mott insulators with neutral Fermi surfaces.