Non Relativistic Limit of Integrable QFT and Lieb-Liniger Models

TL;DR

This paper investigates the non-relativistic limit of certain integrable quantum field theories, revealing that they reduce to Lieb-Liniger models, thus highlighting their universality and potential completeness in describing local bosonic interactions.

Contribution

It demonstrates how Toda and O(N) sigma models simplify to Lieb-Liniger models in the non-relativistic limit, providing evidence for their universality among integrable bosonic theories.

Findings

Non-relativistic limit yields Lieb-Liniger models

Toda theories become decoupled Lieb-Liniger models

O(N) sigma model results in symmetrically coupled Lieb-Liniger models

Abstract

In this paper we study a suitable limit of integrable QFT with the aim to identify continuous non-relativistic integrable models with local interactions. This limit amounts to sending to infinity the speed of light c but simultaneously adjusting the coupling constant g of the quantum field theories in such a way to keep finite the energies of the various excitations. The QFT considered here are Toda Field Theories and the O(N) non-linear sigma model. In both cases the resulting non-relativistic integrable models consist only of Lieb-Liniger models, which are fully decoupled for the Toda theories while symmetrically coupled for the O(N) model. These examples provide explicit evidence of the universality and ubiquity of the Lieb-Liniger models and, at the same time, suggest that these models may exhaust the list of possible non-relativistic integrable theories of bosonic particles with local interactions.