Analytic continuation of Bethe energies and application to the thermodynamic limit of the SL(2, ℂ) non-compact spin chains

• Published in: The journal of high energy physics Vol. 2020; no. 8; pp. 1 - 55
• Main Authors: Granet, Etienne, Jacobsen, Jesper Lykke, Saleur, Hubert
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2020; Springer; SpringerOpen
• Subjects: Bethe Ansatz; Classical and Quantum Gravitation; Conformal Field Theory; Elementary Particles; General Physics; High Energy Physics - Theory; Lattice Integrable Models; Mathematical Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Lattice Integrable Models; Conformal Field Theory; Bethe Ansatz; spin: chain; energy levels; scaling; integrability; noncompact; twist; thermodynamical; ground state
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP08(2020)069

A bstract We consider the problem of analytically continuing energies computed with the Bethe ansatz, as posed by the study of non-compact integrable spin chains. By introducing an imaginary extensive twist in the Bethe equations, we show that one can expand the analytic continuation of energies in the scaling limit around another ‘pseudo-vacuum’ sitting at a negative number of Bethe roots, in the same way as around the usual pseudo-vacuum. We show that this method can be used to compute the energy levels of some states of the SL(2, ℂ) integrable spin chain in the infinite-volume limit, and as a proof of principle recover the ground-state value previously obtained in [ 1 ] (for the case of spins s = 0 , s ¯ = − 1) by extrapolating results in small sizes. These results represent, as far as we know, the first (partial) description of the spectrum of SL(2, ℂ) non-compact spin chains in the thermodynamic limit.