Algebraic Bethe ansatz for singular solutions

Abstract

The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with N sites have solutions containing i/2, -i/2 that are singular: both the corresponding energy and the algebraic Bethe ansatz vector are divergent. Such solutions must be carefully regularized. We consider a regularization involving a parameter that can be determined using a generalization of the Bethe equations. These generalized Bethe equations provide a practical way of determining which singular solutions correspond to eigenvectors of the model.

10 pages; v2: refs added; v3: new section on general singular solutions, and more references

References in corpus (1)

• Low-Temperature Dynamical Structure Factor of the Two-Leg Spin-1/2 Heisenberg Ladder

Cited by in corpus (30)

• Onsager's Scars in Disordered Spin Chains
• On the completeness of solutions of Bethe's equations
• Dissipative quantum Ising chain as a non-Hermitian Ashkin-Teller model
• Excited state correlations of the finite Heisenberg chain
• Bethe Ansatz for Yangian Invariants: Towards Super Yang-Mills Scattering Amplitudes
• Slavnov and Gaudin-Korepin Formulas for Models without $\mathrm{U}(1)$ Symmetry: the Twisted XXX Chain
• Singular solutions, repeated roots and completeness for higher-spin chains
• On Generalized $Q$-systems
• On zero-remainder conditions in the Bethe ansatz
• Singular Solutions to the Bethe Ansatz Equations and Rigged Configurations
• 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
• Duality Relations for Overlaps of Integrable Boundary States in AdS/dCFT
• Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains
• Cylinder partition function of the 6-vertex model from algebraic geometry
• Bethe-State Counting and the Witten Index
• Spin-$s$ Rational $Q$-system
• The propagator of the finite XXZ spin-$\frac{1}{2}$ chain
• Persistent currents in a strongly interacting multicomponent Bose gas on a ring
• Estimating Bethe roots with VQE
• Completing the solution for the $OSp(1|2)$ spin chain
• Exact regimes of collapsed and extra two-string solutions in the two down-spin sector of the spin-1/2 massive XXZ spin chain
• Torus partition function of the six-vertex model from algebraic geometry
• Asymptotic analysis of the form-factors of quantum spin chains
• Flag Integrable Models and Generalized Graded Algebras
• Bethe's Quantum Numbers And Rigged Configurations
• Counting Bethe States in Twisted Spin Chains
• Spin-$s$ $Q$-systems: Twist and Open Boundaries
• Necklace Ansatz for strongly repulsive spin mixtures on a ring
• On the Integrable Structure of Super Yang-Mills Scattering Amplitudes