How universal is the one-particle Green's function of a Luttinger liquid?

TL;DR

This paper investigates the universality of the one-particle Green's function in Luttinger liquids, revealing that its asymptotic behavior depends on interaction details and is less universal than previously thought.

Contribution

The study demonstrates that the asymptotic form of the Green's function in Luttinger liquids depends on interaction specifics beyond the standard parameters, challenging the notion of universality.

Findings

Green's function exhibits direction-dependent power-law decay.

Exponents depend on interaction smoothness and asymptotic behavior.

Universality is limited to specific interaction forms and directions.

Abstract

The one-particle Green's function of the Tomonaga-Luttinger model for one-dimensional interacting Fermions is discussed. Far away from the origin of the plane of space-time coordinates the function falls off like a power law. The exponent depends on the direction within the plane. For a certain form of the interaction potential or within an approximated cut-off procedure the different exponents only depend on the strength of the interaction at zero momentum and can be expressed in terms of the Luttinger liquid parameters $K_{\rho}$ and $K_{\sigma}$ of the model at hand. For a more general interaction and directions which are determined by the charge velocity $v_{\rho}$ and spin velocity $v_{\sigma}$ the exponents also depend on the smoothness of the interaction at zero momentum and the asymptotic behavior of the Green's function is not given by the Luttinger liquid parameters alone. This shows that the physics of large space-time distances in Luttinger liquids is less universal than is widely believed.