Mott-Glass Phase Of A One-Dimensional Quantum Fluid With Long-Range Interactions

We investigate the ground-state properties of quantum particles interacting via a long-range repulsive potential V-sigma(x) similar to 1/vertical bar x vertical bar(1+sigma) (-1 < sigma) or V-sigma(x) similar to -vertical bar x vertical bar(1+sigma) (-2 <= sigma < -1) that interpolates between the Coulomb potential V-0(x) and the linearly confming potential V-2(x) of the Schwinger model. In the absence of disorder the ground state is a Wigner crystal when sigma < 0. Using bosonization and the nonperturbative functional renormalization group we show that any amount of disorder suppresses the Wigner crystallization when -3/2 < sigma <= 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.