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arXiv:1407.2242 · Journal of Physics A Mathematical and Theoretical

Recursive formulas for the overlaps between Bethe states and product states in XXZ Heisenberg chains

Lorenzo Piroli, Pasquale Calabrese

Published Sep 5, 2014• 54 citations
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Abstract

We consider the problem of computing the overlaps between the Bethe states of the XXZ spin-1/2 chain and generic states. We derive recursive formulas for the overlaps between some simple product states and off-shell Bethe states within the framework of the algebraic Bethe ansatz. These recursive formulas can be used to prove in a simple and straightforward way the recently obtained results for the overlaps of the Bethe states with the Néel state, the dimer state, and the q -deformed dimer state. However, these recursive formulas are derived for a broader class of states and represent a concrete starting point for the computation of rather general overlaps. Our approach can be easily extended to other one-dimensional Bethe ansatz integrable models.

DOI
10.1088/1751-8113/47/38/385003

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