Superfluid--Bose-glass transition in a system of disordered bosons with long-range hopping in one dimension

We study the superfluid--Bose-glass transition in a one-dimensional lattice boson model with power-law decaying hopping amplitude $t_{i-j}\sim 1/|i-j|^\alpha$, using bosonization and the nonperturbative functional renormalization group (FRG). When $\alpha$ is smaller than a critical value $\alpha_c<3$, the U(1) symmetry is spontaneously broken, which leads to a density mode with nonlinear dispersion and dynamical exponent $z=(\alpha-1)/2$; the superfluid phase is then stable for sufficiently weak disorder, contrary to the case of short-range hopping where the superfluid phase is destabilized by an infinitesimal disorder when the Luttinger parameter is smaller than $3/2$. In the presence of disorder, long-range hopping has however no effect in the infrared limit and the FRG flow eventually becomes similar to that of a boson system with short-range hopping. This implies that the superfluid phase, when stable, exhibits a density mode with linear dispersion ($z=1$) and the superfluid--Bose-glass transition remains in the Berezinskii-Kosterlitz-Thouless universality class, while the Bose-glass fixed point is insensitive to long-range hopping. We compare our findings with a recent numerical study.