Q-operator and T-Q relation from the fusion hierarchy

Wen Li Yang, Rafael I. Nepomechie, Yao Zhong Zhang

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


We propose that the Baxter Q-operator for the spin-1/2 XXZ quantum spin chain is given by the j→∞ limit of the transfer matrix with spin-j (i.e., (2j+1)-dimensional) auxiliary space. Applying this observation to the open chain with general (non-diagonal) integrable boundary terms, we obtain from the fusion hierarchy the T-Q relation for generic values (i.e., not roots of unity) of the bulk anisotropy parameter. We use this relation to determine the Bethe ansatz solution of the eigenvalues of the fundamental transfer matrix. This approach is complementary to the one used recently to solve the same model for the roots of unity case.

Original languageEnglish (US)
Pages (from-to)664-670
Number of pages7
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Issue number4-5
StatePublished - Feb 16 2006
Externally publishedYes


  • Bethe ansatz
  • Fusion hierarchy
  • Q-operator
  • Reflection equation
  • Spin chain

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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