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We study a one-dimensional disordered Bose fluid using bosonization, thereplica method and a nonperturbative functional renormalization-group approach.We find that the Bose-glass phase is described by a fully attractivestrong-disorder fixed point characterized by a singular disorder correlatorwhose functional dependence assumes a cuspy form that is related to theexistence of metastable states. At nonzero momentum scale $k$, quantumtunneling between the ground state and low-lying metastable states leads to arounding of the cusp singularity into a quantum boundary layer (QBL). The widthof the QBL depends on an effective Luttinger parameter $K_k\sim k^\theta$ thatvanishes with an exponent $\theta=z-1$ related to the dynamical criticalexponent $z$. The QBL encodes the existence of rare "superfluid" regions,controls the low-energy dynamics and yields a (dissipative) conductivityvanishing as $\omega^2$ in the low-frequency limit. These results reveal theglassy properties (pinning, "shocks" or static avalanches) of the Bose-glassphase and can be understood within the "droplet" picture put forward for thedescription of glassy (classical) systems.

Bose-glass phase of a one-dimensional disordered Bose fluid: metastable states, quantum tunneling and droplets