# Glassy properties of the Bose-glass phase of a one-dimensional disordered Bose fluid

## TL;DR

This paper investigates the glassy phase of a disordered one-dimensional Bose fluid, revealing a cuspy disorder correlator and quantum tunneling effects that influence low-frequency conductivity, using advanced theoretical methods.

## Contribution

It introduces a nonperturbative functional renormalization-group analysis of the Bose-glass phase, highlighting the cuspy disorder correlator and quantum tunneling effects.

## Key findings

- Identification of a cuspy disorder correlator in the Bose-glass phase
- Quantum tunneling causes rounding of nonanalyticities at finite momentum
- Low-frequency conductivity exhibits an $$ behavior due to rare superfluid regions

## Abstract

We study a one-dimensional disordered Bose fluid using bosonization, the replica method and a nonperturbative functional renormalization-group approach. The Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale, quantum tunneling between these metastable states leads to a rounding of the nonanalyticity in a quantum boundary layer that encodes the existence of rare superfluid regions responsible for the $\omega^2$ behavior of the (dissipative) conductivity in the low-frequency limit. These results can be understood within the "droplet" picture put forward for the description of glassy (classical) systems.