1D Quantum Liquids with Power-Law Interactions: a Luttinger Staircase with Polar Molecules

Abstract

We study one dimensional fermionic and bosonic gases with repulsive power-law interactions $1/|x{|}^{\beta }$, with $\beta >1$, in the framework of Tomonaga-Luttinger liquid (LL) theory. We obtain an accurate analytical expression linking the LL parameter to the microscopic Hamiltonian, for arbitrary $\beta$ and strength of the interactions. In the presence of a small periodic potential, power-law interactions make the LL unstable towards the formation of a cascade of lattice solids with fractional filling, thus forming a "Luttinger staircase". Several of these quantum phases and phase transitions are realized with groundstate polar molecules and weakly-bound magnetic Feshbach molecules.

4 pages, 3 figures, one table, updated discussions in Pag 2, 4

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• Bound states of Dipolar Bosons in One-dimensional Systems
• Quantum phases of attractive bosons on a Bose-Hubbard ladder with three-body constraint
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• Fractal ground state of ion chains in periodic potentials
• Bose-Hubbard model with power-law hopping in one dimension