Non relativistic limit of integrable QFT and Lieb–Liniger models. (30th December 2016)

• Record Type: Journal Article
• Authors: Bastianello, Alvise; De Luca, Andrea; Mussardo, Giuseppe
• Is Part Of: Journal of statistical mechanics. (2016:Dec.)
• Publication Date: 2016-12-30
• Subjects: 1 -- 16; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aa4f98
• Languages: English
• ISSNs: 1742-5468

Abstract

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.