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

· pdf
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

· pdf
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.