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arXiv:math-ph/0012042

Direct proof for the Scalar Product with Bethe eigenstate in Spin chains

А. А. Овчинников

Published Dec 22, 2000• 0 citations
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Abstract

We present the simple and direct proof of the determinantal formula for the scalar product of Bethe eigenstate with an arbitrary dual state. We briefly review the direct calculation of the general scalar product with the help of the factorizing operator and the construction of the factorizing operator itself. We also comment on the previous determination of the scalar product of Bethe eigenstate with an arbitrary dual state.

DOI
10.48550/arxiv.math-ph/0012042

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We present the simple and direct proof of the determinantal formula for the scalar product of Bethe eigenstate with an arbitrary dual state. We briefly review the direct calculation of the general scalar product with the help of the factorizing operator and the construction of the factorizing operator itself. We also comment on the previous determination of the scalar product of Bethe eigenstate with an arbitrary dual state.
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We consider an XYZXYZXYZ spin chain within the framework of the generalized algebraic Bethe ansatz. We study scalar products of the transfer matrix eigenvectors and arbitrary Bethe vectors. In the particular case of free fermions, we obtain explicit expressions for the scalar products with different number of parameters in two Bethe vectors.
The scalar product of XXZ spin chain revisited. Application to the ground state at Δ=−1/2Δ=-1/2Δ=−1/2
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