SciPost Phys. 4, 030 (2018) ·
published 15 June 2018

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The distribution of Bethe roots, solution of the inhomogeneous Bethe equations, which characterize the ground state of the periodic XXX Heisenberg spin$\frac{1}{2}$ chain is investigated. Numerical calculations show that, for this state, the new inhomogeneous term does not contribute to the Baxter TQ equation in the thermodynamic limit. Different families of Bethe roots are identified and their large N behaviour are conjectured and validated.
SciPost Phys. 3, 009 (2017) ·
published 4 August 2017

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In this work we demonstrate a simple way to implement the quantum inverse scattering method to find eigenstates of spin1/2 XXX Gaudin magnets in an arbitrarily oriented magnetic field. The procedure differs vastly from the most natural approach which would be to simply orient the spin quantisation axis in the same direction as the magnetic field through an appropriate rotation. Instead, we define a modified realisation of the rational Gaudin algebra and use the quantum inverse scattering method which allows us, within a slightly modified implementation, to build an algebraic Bethe ansatz using the same unrotated reference state (pseudovacuum) for any external field. This common framework allows us to easily write determinant expressions for certain scalar products which would be highly nontrivial in the rotated system approach.