Universal theory of nonlinear Luttinger liquids

TL;DR

This paper develops a universal nonlinear hydrodynamic theory for one-dimensional quantum fluids, extending traditional Luttinger liquid models by incorporating spectrum nonlinearity to better predict dynamic response functions.

Contribution

It introduces a comprehensive nonlinear theory applicable to various 1D quantum systems, improving upon the linear Luttinger liquid framework.

Findings

Nonlinearity causes qualitative changes in spectral functions.

Universal applicability to fermionic, bosonic, and spin systems.

Enhanced accuracy in dynamic response predictions.

Abstract

One-dimensional quantum fluids are conventionally described by using an effective hydrodynamic approach known as Luttinger liquid theory. As the principal simplification, a generic spectrum of the constituent particles is replaced by a linear one, which leads to a linear hydrodynamic theory. We show that to describe the measurable dynamic response functions one needs to take into account the nonlinearity of the generic spectrum and thus of the resulting quantum hydrodynamic theory. This nonlinearity leads, for example, to a qualitative change in the behavior of the spectral function. The universal theory developed in this article is applicable to a wide class of one-dimensional fermionic, bosonic, and spin systems.