Mott-glass phase of a one-dimensional quantum fluid with long-range interactions

Abstract

We investigate the ground-state properties of quantum particles interacting via a long-range repulsive potential ${\mathcal{V}}_{\sigma }(x)\sim 1/|x{|}^{1+\sigma }$ ($-1<\sigma$) or ${\mathcal{V}}_{\sigma }(x)\sim -|x{|}^{-1-\sigma }$ ($-2\le \sigma <-1$) that interpolates between the Coulomb potential ${\mathcal{V}}_0(x)$ and the linearly confining potential ${\mathcal{V}}_{-2}(x)$ of the Schwinger model. In the absence of disorder the ground state is a Wigner crystal when $\sigma \le 0$. Using bosonization and the nonperturbative functional renormalization group we show that any amount of disorder suppresses the Wigner crystallization when $-3/2<\sigma \le 0$; the ground state is then a Mott glass, i.e., a state that has a vanishing compressibility and a gapless optical conductivity. For $\sigma <-3/2$ the ground state remains a Wigner crystal.

v2) 6+10 pages, 3+1 figures; v3) Supplemental Material updated

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• Flowing bosonization in the nonperturbative functional renormalization-group approach
• Superfluid--Bose-glass transition in a system of disordered bosons with long-range hopping in one dimension
• Mott-glass phase induced by long-range correlated disorder in a one-dimensional Bose gas
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• From Bose glass to many-body localization in a one-dimensional disordered Bose gas