On zero-remainder conditions in the Bethe ansatz

Abstract

We prove that physical solutions to the Heisenberg spin chain Bethe ansatz equations are exactly obtained by imposing two zero-remainder conditions. This bridges the gap between different criteria, yielding an alternative proof of a recently devised algorithm based on $QQ$ relations, and solving its minimality issue.

14 pages. New version: corrected typos, modified abstract and added references

References in corpus (5)

• A Shortcut to the Q-Operator
• Deformed strings in the Heisenberg model
• Low-Temperature Dynamical Structure Factor of the Two-Leg Spin-1/2 Heisenberg Ladder
• On Generalized $Q$-systems
• Twisting singular solutions of Bethe's equations

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• Lattice regularisation of a non-compact boundary conformal field theory
• The action of the Virasoro algebra in quantum spin chains. I. The non-rational case
• Cylinder partition function of the 6-vertex model from algebraic geometry
• Spin-$s$ Rational $Q$-system
• Wronskian-type formula for inhomogeneous TQ-equations
• Rational Q-systems at Root of Unity I. Closed Chains
• Analytic continuation of Bethe energies and application to the thermodynamic limit of the $SL(2,\mathbb{C})$ non-compact spin chains
• Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry
• On the Q operator and the spectrum of the XXZ model at root of unity
• Spectrum-preserving deformations of integrable spin chains with open boundaries
• Spin-$s$ $Q$-systems: Twist and Open Boundaries