On the complete-spectrum characterization of quantum integrable spin chains via the inhomogeneous T-Q relation

Abstract

With the XXZ spin chains as examples, we prove two theorems: (1) the functional relations derived from the off-diagonal Bethe Ansatz scheme are the sufficient and necessary conditions to characterize the complete spectrum of the corresponding transfer matrix; (2) each eigenvalue of the transfer matrix can be parameterized by a minimal inhomogeneous T-Q relation. These statements hold for both with and without inhomogeneity. The proof can be generalized to other finite-dimensional quantum integrable models.

11 pages, no figure, new version

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Cited by in corpus (4)

• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Non-analytic behavior of the Loschmidt echo in XXZ spin chains: exact results
• Spectrum of the quantum integrable $D_2^{(2)}$ spin chain with generic boundary fields
• Exact surface energy of the $D_2^{(1)}$ spin chain with generic non-diagonal boundary reflections