On the completeness of solutions of Bethe's equations

Autor:	Hao, Wenrui, Nepomechie, Rafael I., Sommese, Andrew J.
Rok vydání:	2013
Předmět:	Mathematical Physics Condensed Matter - Strongly Correlated Electrons High Energy Physics - Theory
Zdroj:	Phys. Rev. E 88, 052113 (2013)
Druh dokumentu:	Working Paper
DOI:	10.1103/PhysRevE.88.052113
Popis:	We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain with periodic boundary conditions. We formulate a conjecture for the number of solutions with pairwise distinct roots of these equations, in terms of numbers of so-called singular (or exceptional) solutions. Using homotopy continuation methods, we find all such solutions of the Bethe equations for chains of length up to 14. The numbers of these solutions are in perfect agreement with the conjecture. We also discuss an indirect method of finding solutions of the Bethe equations by solving the Baxter T-Q equation. We briefly comment on implications for thermodynamical computations based on the string hypothesis. Comment: 17 pages; 85 tables provided as supplemental material; v2: clarifications and references added; v3: numerical results extended to N=14, M=7
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1308.4645 Zobrazit plný text záznamu View this record from Arxiv