Spin-charge separation in one-dimensional fermion systems beyond the Luttinger liquid theory

TL;DR

This paper presents a nonperturbative zero-temperature theory for the dynamic response of one-dimensional spin-1/2 fermions, accounting for dispersion nonlinearity, and extends the concept of spin-charge separation beyond the Luttinger liquid approximation.

Contribution

It introduces a novel approach that exactly incorporates dispersion nonlinearity, providing more accurate predictions for spectral functions and structure factors in 1D fermion systems.

Findings

Calculated power-law singularities for spectral functions and structure factors.

Exponents depend on momentum and differ from linear Luttinger liquid theory.

Generalized spin-charge separation to nonlinear spectra.

Abstract

We develop a nonperturbative zero-temperature theory for the dynamic response functions of interacting one-dimensional spin-1/2 fermions. In contrast to the conventional Luttinger liquid theory, we take into account the nonlinearity of the fermion dispersion exactly. We calculate the power-law singularities of the spectral function and the charge and spin density structure factors for arbitrary momenta and interaction strengths. The exponents characterizing the singularities are functions of momenta and differ significantly from the predictions of the linear Luttinger liquid theory. We generalize the notion of the spin-charge separation to the nonlinear spectrum. This generalization leads to phenomenological relations between threshold exponents and the threshold energy.