Response functions in multicomponent Luttinger liquids

Abstract

We derive an analytic expression for the zero temperature Fourier transform of the density-density correlation function of a multicomponent Luttinger liquid with different velocities. By employing Schwinger identity and a generalized Feynman identity exact integral expressions are derived, and approximate analytical forms are given for frequencies close to each component singularity. We find power-like singularities and compute the corresponding exponents. Numerical results are shown for N = 3 components and implications for experiments on cold atoms are discussed.

Exact density profiles and symmetry classification for strongly interacting multi-component Fermi gases in tight waveguides

“…The homogeneous system may also be described at low energy as a multi-component Luttinger liquid. This model has been extensively studied in the context of electronic multichannel systems [6,7] and exotic condensed matter materials [7][8][9][10][11].…”

Dimensional crossover in a Fermi gas and a cross-dimensional Tomonaga-Luttinger model

“…density-density) in an array of 1D wires. Some analytical results are already available for two [49] or three [50] coupled Tomonaga-Luttinger liquids, but most challenging is the limit of an infinite number of components [51] as compared with higherdimensional interacting systems. This may give new insights on the conditions to observe a transition from a 1D Luttinger liquid to a 2D Fermi liquid, studied in [46], and more generally, on the huge differences between the low-dimensional and the 3D systems, for instance in the appearance of vortices or solitons.…”

Correlations in low-dimensional quantum gases

“…This case will be the subject of a later publication. A few results concerning dynamical correlations are even already available for a few components [446,447], and a general formalism based on generalized hypergeometric series has been developped to deal with an arbitrary number of components [448].…”