Norm of Bethe Wave Function as a Determinant - Mathematics > CombinatoricsReport as inadecuate

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Abstract: This is a historical note. Bethe Ansatz solvable models are considered, forexample XXZ Heisenberg anti-ferromagnet and Bose gas with delta interaction.Periodic boundary conditions lead to Bethe equation. The square of the norm ofBethe wave function is equal to a determinant of linearized system of Betheequations determinant of matrix of second derivatives of Yang action. Theproof was first published in Communications in Mathematical Physics, vol 86,page 391 in l982. Also domain wall boundary conditions for 6 vertex model werediscovered in the same paper see Appendix D. These play an important role foralgebraic combinatorics: alternating sign matrices, domino tiling and planepartition. Many publications are devoted to six vertex model with domain wallboundary conditions.

Author: Vladimir E. Korepin



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