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Solutions of the Yang-Baxter equation for isotropic quantum spin chains

T Kennedy

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The author considers solutions of the Yang-Baxter equation such that the logarithmic derivative of the transfer matrix yields a quantum spin Hamiltonian which is isotropic in spin space, i.e. SU(2)-invariant. Four such solutions are known for each value of the spin S. (For S=1/2 they degenerate into the same solution, and for S=1 they only give three different solutions). For S<or=6 he shows that these are the only solutions which are SU(2)-invariant, except for S=3 when there is a fifth solution.


PACS

02.20.Qs General properties, structure, and representation of Lie groups

02.10.Yn Matrix theory

02.10.Ud Linear algebra

MSC

15A90 Applications of matrix theory to physics

22Exx Lie groups (For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis thereon, see 43A80, 43A85, 43A90)

Subjects

Mathematical physics

Dates

Issue 10 (21 May 1992)



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