One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm

Understand

For many years, the Luttinger liquid theory has served as a useful paradigm for the description of one-dimensional (1D) quantum fluids in the limit of low energies.

• This theory is based on a linearization of the dispersion relation of the particles constituting the fluid.
• We review the recent progress in understanding 1D quantum fluids beyond the low-energy limit, where the nonlinearity of the dispersion relation becomes essential.
• The novel methods which have been developed to tackle such systems combine phenomenology built on the ideas of the Fermi edge singularity and the Fermi liquid theory, perturbation theory in the interaction strength, and a new way of treating finite-size integrable models.