The Luttinger liquid in superlattice structures: atomic gases, quantum dots and the classical Ising chain

Abstract

We study the physical properties of a Luttinger liquid in a superlattice that is characterized by alternating two tunneling parameters. Using the bosonization approach, we describe the corresponding Hubbard model by the equivalent Tomonaga–Luttinger model. We analyze the spin–charge separation and transport properties of the superlattice system. We suggest that cold Fermi gases trapped in a bichromatic optical lattice and coupled quantum dots offer the opportunity to measure these effects in a convenient manner. We also study the classical Ising chain with two tunneling parameters. We find that the classical two-point correlator decreases as the difference between the two tunneling parameters increases.