The scalar product of XXZ spin chain revisited. Application to the ground state at Δ=-1/2

2014/11/11 by Garbali, Alexander
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1411.2938

Abstract

For the scalar product S_n of the XXZ s=1/2 spin chain we derive a new determinant expression which is symmetric in the Bethe roots. We consider an application of this formula to the inhomogeneous groundstate of the model with Δ=-1/2 with twisted periodic boundary conditions. At this point the ground state eigenvalue τ_n of the transfer matrix is known and has a simple form that does not contain the Bethe roots. We use the knowledge of τ_n(μ) to obtain a closed expression for the scalar product. The result is written in terms of Schur functions. The computations of the normalization of the ground state and the expectation value of σ^z are also presented.

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