SciPost Phys. 3, 009 (2017) ·
published 4 August 2017
In this work we demonstrate a simple way to implement the quantum inverse
scattering method to find eigenstates of spin-1/2 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 non-trivial in the rotated system approach.