Singular Solutions to the Bethe Ansatz Equations and Rigged Configurations

Abstract

We provide a conjecture for the following two quantities related with the spin-$\frac{1}{2}$ isotropic Heisenberg model defined over rings of even lengths: (i) the number of the solutions to the Bethe ansatz equations which correspond to non-zero Bethe vectors; (ii) the number of physical singular solutions of the Bethe ansatz equations in the sense of Nepomechie-Wang. The conjecture is based on a natural relationship between the solutions to the Bethe ansatz equations and the rigged configurations.

arXiv comment24 pages, final version, elucidated the relationship between the rigged configurations and string solutions (Section 3.1)

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Cited by in corpus (14)

• Completeness of the Bethe states for the rational, spin-1/2 Richardson--Gaudin system
• Algebraic geometry and Bethe ansatz (I) the quotient ring for BAE
• Twisting singular solutions of Bethe's equations
• Non Self-conjugate Strings, Singular Strings and Rigged Configurations in the Heisenberg Model
• A pedagogical introduction to quantum integrability, with a view towards theoretical high-energy physics
• Exact quantum numbers of collapsed and non-collapsed 2-string solutions in the Heisenberg spin chain
• Persistent currents in a strongly interacting multicomponent Bose gas on a ring
• Singular eigenstates in the even(odd) length Heisenberg spin chain
• Heisenberg model and Rigged Configurations
• Exact regimes of collapsed and extra two-string solutions in the two down-spin sector of the spin-1/2 massive XXZ spin chain
• Rigged Configurations Approach For The Spin-1/2 Isotropic Heisenberg Model
• Bethe's Quantum Numbers And Rigged Configurations
• Necklace Ansatz for strongly repulsive spin mixtures on a ring
• Tunable Hilbert space fragmentation and extended critical regime