We consider quantum integrable systems associated with reductive Lie algebra gl(n and Cartan-invariant non-skew-symmetric classical r-matrices. We show that under certain restrictions on the form of classical r-matrices “nested” or “hierarchical” Bethe ansatz usually based on a chain of subalgebras gl(n)⊃gl(n−1)⊃…⊃gl(1 is generalized onto the other chains or “hierarchies” of subalgebras. We show that among the r-matrices satisfying such the restrictions there are “twisted” or Zp-graded non-skew-symmetric classical r-matrices. We consider in detail example of the generalized Gaudin models with and without external magnetic field associated with Zp-graded non-skew-symmetric classical r-matrices and find the spectrum of the corresponding Gaudin-type hamiltonians using nested Bethe ansatz scheme and a chain of subalgebras gl(n)⊃gl(n−n1)⊃gl(n−n1−n2)⊃gl(n−(n1+…+np−1), where n1+n2+…+np=.
Skrypnyk, T. (2016). “Generalized” algebraic Bethe ansatz, Gaudin-type models and Zp-graded classical r-matrices. NUCLEAR PHYSICS. B, 913, 327-356 [10.1016/j.nuclphysb.2016.09.006].
“Generalized” algebraic Bethe ansatz, Gaudin-type models and Zp-graded classical r-matrices
Skrypnyk, T
2016
Abstract
We consider quantum integrable systems associated with reductive Lie algebra gl(n and Cartan-invariant non-skew-symmetric classical r-matrices. We show that under certain restrictions on the form of classical r-matrices “nested” or “hierarchical” Bethe ansatz usually based on a chain of subalgebras gl(n)⊃gl(n−1)⊃…⊃gl(1 is generalized onto the other chains or “hierarchies” of subalgebras. We show that among the r-matrices satisfying such the restrictions there are “twisted” or Zp-graded non-skew-symmetric classical r-matrices. We consider in detail example of the generalized Gaudin models with and without external magnetic field associated with Zp-graded non-skew-symmetric classical r-matrices and find the spectrum of the corresponding Gaudin-type hamiltonians using nested Bethe ansatz scheme and a chain of subalgebras gl(n)⊃gl(n−n1)⊃gl(n−n1−n2)⊃gl(n−(n1+…+np−1), where n1+n2+…+np=.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.