Non Relativistic Limit of Integrable QFT and Lieb-Liniger Models

Alvise Bastianello 1 Andrea De Luca 2 Giuseppe Mussardo 3

Journal of Statistical Mechanics: Theory and Experiment, IOP Science, 2016, 2016 (12), pp.123104

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.

  • 1. SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies
  • 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 3. ICTP - International Center for Theoretical Physics [Trieste]