Year: 2026
Type: preprint
Abstract: The spin-$1/2$ Heisenberg antiferromagnetic chain is the canonical example of an integrable quantum many-body model. Despite its exact solvability, explicit finite-size solutions are typically only accessible via numerical evaluation of the Bethe ansatz equations. Here, we analyse the algebraic structure of the exact, symbolic ground states for chains up to twelve sites using the Bethe ansatz. We find that the algebraic degree of the ground state magnon phases and Bethe roots scale with respect to system size at a different rate to the ground-state energy and wavefunction coefficients. The ground-state Bethe roots and energy are found to become Galois unsolvable for ten or more sites, thus demonstrating the lack of a symbolic analytical solution in a quantum integrable model due to algebraic complexity.
Source: arXiv (Cornell University)
Authors: Bellwood, Oliver R., Munro, William J.
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G424178383
OpenAlex ID: W7160618399