Abstract
We propose a method to determine the quantum numbers, which we call the rigged configurations, for the solutions to the Bethe ansatz equations for the spin-1/2 isotropic Heisenberg model under the periodic boundary condition. Our method is based on the observation that the sums of Bethe's quantum numbers within each string behave particularly nicely. We confirm our procedure for all solutions for length 12 chain (totally 923 solutions).
Highlights
Bethe’s seminal solution to the isotropic Heisenberg model under the periodic boundary condition [3] in 1931 is one of the prototypical theories on the quantum integrable systems
In the analysis of the solutions to the Bethe ansatz equations, it has been customary to assume that roots of the solutions take a particular form called the strings
We introduce the deformation of singular solutions i λ1 (θ ) = + + c(reiθ )N, i λ2 (θ ) = − +
Summary
Bethe’s seminal solution to the isotropic Heisenberg model under the periodic boundary condition [3] in 1931 is one of the prototypical theories on the quantum integrable systems. In the analysis of the solutions to the Bethe ansatz equations, it has been customary to assume that roots of the solutions take a particular form called the strings This idea was already apparent in the original Bethe’s paper. As a continuation of a previous work [19], we propose a method to assign quantum numbers to strings of roots. For this purpose, we start from the so-called Bethe’s quantum numbers (see Section 3). Our basic observation is that the sum of Bethe’s quantum numbers associated with all roots of a given string behaves in a simple manner. There are supplementary tables (see remarks after Conjecture 3).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
