2023/10/19 by F. Gerken, Gerken, Felix, Ingo Runkel +5 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Cold Atom Physics and Bose-Einstein Condensates #Degeneracy (biology) #Eigenvalues and eigenvectors #FOS: Physical sciences #Ferromagnetism #Heisenberg model #Magnetism #Mathematical physics #Mathematics #Opinion Dynamics and Social Influence #Physics #Pure mathematics #Quantum #Quantum Physics (quant-ph) #Quantum mechanics #Spin (aerodynamics) #Strongly Correlated Electrons (cond-mat.str-el) #Tensor product #Theoretical physics
paper · pdf · doi:10.48550/arxiv.2310.13158
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, large degeneracy based on product eigenstates has been found in spin ladders, kagome-like lattices, and motif magnetism, connected to spin liquids, anyonic phases, and quantum scars. We unify these systems by a complete classification of product eigenstates of Heisenberg XXZ Hamiltonians with Dzyaloshinskii-Moriya interaction on general graphs in the form of Kirchhoff rules for spin supercurrent. By this, we construct spin systems with extensive degree of degeneracy linked to exotic condensates which could be studied in atomic gases and quantum spin lattices.