2017/01/10 by Heinz-Jürgen Schmidt, Heinz–Jürgen Schmidt, Schmidt, Heinz-Jürgen · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Opinion Dynamics and Social Influence #Other Condensed Matter (cond-mat.other) #Quantum Mechanics and Applications #Quantum many-body systems #cond-mat.other #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1701.02489
The latest version contains an additional theorem on the existence of symmetric ground states (section IV)
openalex publication_date 2017/01/10 · arxiv created 2017/02/05 · arxiv updated 2017/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We formulate part I of a rigorous theory of ground states for classical, finite, Heisenberg spin systems. The main result is that all ground states can be constructed from the eigenvectors of a real, symmetric matrix with entries comprising the coupling constants of the spin system as well as certain Lagrange parameters. The eigenvectors correspond to the unique maximum of the minimal eigenvalue considered as a function of the Lagrange parameters. However, there are rare cases where all ground states obtained in this way have unphysical dimensions M>3 and the theory would have to be extended. Further results concern the degree of additional degeneracy, additional to the trivial degeneracy of ground states due to rotations or reflections. The theory is illustrated by a couple of elementary examples.