Quench dynamics of the Tomonaga-Luttinger model with momentum dependent interaction

TL;DR

This paper investigates the relaxation dynamics of the one-dimensional Tomonaga-Luttinger model after an interaction quench, emphasizing the effects of momentum-dependent interactions on universal Luttinger liquid behavior and steady-state properties.

Contribution

It provides a detailed analysis of how momentum-dependent interactions influence the quench dynamics and steady-state distributions in the Tomonaga-Luttinger model, revealing universal decay laws.

Findings

Steady-state fermionic momentum distribution exhibits universal Luttinger liquid behavior.

Large time decay follows a power law with an exponent depending only on zero-momentum interaction.

A factor of two difference is observed between steady-state and equilibrium momentum distributions.

Abstract

We study the relaxation dynamics of the one-dimensional Tomonaga-Luttinger model after an interaction quench paying particular attention to the momentum dependence of the two-particle interaction. Several potentials of different analytical form are investigated all leading to universal Luttinger liquid physics in equilibrium. The steady-state fermionic momentum distribution shows universal behavior in the sense of the Luttinger liquid phenomenology. For generic regular potentials the large time decay of the momentum distribution function towards the steady-state value is characterized by a power law with a universal exponent which only depends on the potential at zero momentum transfer. A commonly employed ad hoc procedure fails to give this exponent. Besides quenches from zero to positive interactions we also consider abrupt changes of the interaction between two arbitrary values. Additionally, we discuss the appearance of a factor of two between the steady-state momentum distribution function and the one obtained in equilibrium at equal two-particle interaction.