On Generalized $Q$-systems

Abstract

We formulate $Q$-systems for the closed XXZ, open XXX and open quantum-group-invariant XXZ quantum spin chains. Polynomial solutions of these $Q$-systems can be found efficiently, which in turn lead directly to the admissible solutions of the corresponding Bethe ansatz equations.

27 pages. New version: included code, modified sec 3.2, and a few minor changes

References in corpus (3)

• Deformed strings in the Heisenberg model
• On zero-remainder conditions in the Bethe ansatz
• Twisting singular solutions of Bethe's equations

Cited by in corpus (19)

• Rational $Q$-systems, Higgsing and Mirror Symmetry
• Geometric Algebra and Algebraic Geometry of Loop and Potts Models
• On zero-remainder conditions in the Bethe ansatz
• Q-systems with boundary parameters
• Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains
• 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
• The $A_m^{(1)}$ Q-system
• Quantum groups and functional relations for arbitrary rank
• Rational Q-systems at Root of Unity I. Closed Chains
• Wronskian-type formula for inhomogeneous TQ-equations
• Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry
• Truncated string state space approach and its application to nonintegrable spin-$\frac{1}{2}$ Heisenberg chain
• Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder II: rotated lattice
• Spectrum-preserving deformations of integrable spin chains with open boundaries
• On the Q operator and the spectrum of the XXZ model at root of unity
• Spin-$s$ $Q$-systems: Twist and Open Boundaries