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

TL;DR

This paper analyzes one-dimensional quantum gases with power-law interactions, deriving an analytical relation for the Luttinger parameter and revealing a cascade of quantum phases called the Luttinger staircase, observed in polar molecules.

Contribution

It provides an exact analytical expression linking the Luttinger parameter to microscopic interactions for arbitrary power-law exponents and interaction strengths.

Findings

Power-law interactions induce a cascade of lattice solid phases.

The Luttinger staircase involves fractional filling phases.

Quantum phases are realizable with polar molecules and Feshbach 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.