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 Vσ(x) ∼ 1/|x| 1+σ (−1 < σ) or Vσ(x) ∼ −|x| −1−σ (−2 ≤ σ < −1) that interpolates between the Coulomb potential V0(x) and the linearly confining potential V−2(x) of the Schwinger model. In the absence of disorder the ground state is a Wigner crystal when σ ≤ 0. Using bosonization and the nonperturbative functional renormalization group we show that any amount of disorder suppresses the Wigner crystallization when −3/2 < σ ≤ 0; the ground state is then a Mott glass, i.e., a state that has a vanishing compressibility and a gapless optical conductivity. For σ < −3/2 the ground state remains a Wigner crystal.