Twisting singular solutions of Bethe's equations

Abstract

The Bethe equations for the periodic XXX and XXZ spin chains admit singular solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to be physical, in which case they correspond to genuine eigenvalues and eigenvectors of the Hamiltonian.

arXiv comment10 pages; v2: references added; v3: introduction expanded, and more references added

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Cited by in corpus (18)

• Effects of interactions on periodically driven dynamically localized systems
• Excited state correlations of the finite Heisenberg chain
• On Generalized $Q$-systems
• Completeness of the Bethe states for the rational, spin-1/2 Richardson--Gaudin system
• On zero-remainder conditions in the Bethe ansatz
• Asymptotic Four Point Functions
• Duality Relations for Overlaps of Integrable Boundary States in AdS/dCFT
• Asymptotics for the norm of Bethe eigenstates in the periodic totally asymmetric exclusion process
• Bethe-State Counting and the Witten Index
• Spin-$s$ Rational $Q$-system
• The propagator of the finite XXZ spin-$\frac{1}{2}$ chain
• A novel class of translationally invariant spin chains with long-range interactions
• Completing the solution for the $OSp(1|2)$ spin chain
• The Yang-Baxter paradox
• Counting Bethe States in Twisted Spin Chains
• Flag Integrable Models and Generalized Graded Algebras
• Necklace Ansatz for strongly repulsive spin mixtures on a ring
• Spin-$s$ $Q$-systems: Twist and Open Boundaries