2009/11/10 by V. E. Korepin, Vladimir E. Korepin, Korepin, Vladimir E.
Engineering · Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Geophysics and Sensor Technology #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #hep-th #math-ph #math.CO #math.MP
paper · pdf · doi:10.48550/arxiv.0911.1881
6 pages
arxiv created 2009/11/10 · openalex publication_date 2009/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a historical note. Bethe Ansatz solvable models are considered, for example XXZ Heisenberg anti-ferromagnet and Bose gas with delta interaction. Periodic boundary conditions lead to Bethe equation. The square of the norm of Bethe wave function is equal to a determinant of linearized system of Bethe equations (determinant of matrix of second derivatives of Yang action). The proof was first published in Communications in Mathematical Physics, vol 86, page 391 in l982. Also domain wall boundary conditions for 6 vertex model were discovered in the same paper [see Appendix D]. These play an important role for algebraic combinatorics: alternating sign matrices, domino tiling and plane partition. Many publications are devoted to six vertex model with domain wall boundary conditions.