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 Neel 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.

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

Piroli, Lorenzo;Calabrese, Pasquale
2014-01-01

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 Neel 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.
2014
47
38
1
18
385003
https://arxiv.org/abs/1407.2242
Piroli, Lorenzo; Calabrese, Pasquale
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/12754
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