One dimensional Bose-Hubbard model with long range hopping

Abstract

Interacting one-dimensional bosons with long range hopping decaying as a power law $r^{-\alpha }$ with distance $r$ are considered with the renormalization group and the self-consistent harmonic approximation. For $\alpha \ge 3$, the ground state is always a Tomonaga-Luttinger liquid, whereas for $\alpha <3$, a ground state with long range order breaking the continuous global gauge symmetry becomes possible for sufficiently weak repulsion. At positive temperature, continuous symmetry breaking becomes restricted to $\alpha <2$, and for $2<\alpha <3$, a Tomonaga-Luttinger liquid with the Tomonaga-Luttinger exponent diverging at low temperature is found.

RevTex 4, 17 pages, 5 figures (v2) added one reference, minor corrections, hyperref enabled

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