Many-Spinon States and the Secret Significance of Young Tableaux

2007/05/10 by Martin Greiter, Dirk Schuricht · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Chain (unit) #Combinatorics #Condensed matter physics #Eigenvalues and eigenvectors #Mathematical physics #Mathematics #Physics #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Spin (aerodynamics) #Spinon #Spins #Theoretical physics #Young tableau #cond-mat.str-el #math-ph #math.MP

paper · pdf · doi:10.1103/physrevlett.98.237202

published as Phys. Rev. Lett. 98, 237202 (2007) · 4 pages, 3 figures

arxiv created 2007/05/10 · openalex publication_date 2007/06/08 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We establish a one-to-one correspondence between the Young tableaux classifying the total spin representations of N spins and the exact eigenstates of the Haldane-Shastry model for a chain with N sites classified by the total spins and the fractionally spaced single-particle momenta of the spinons.

Citations

• DressedSmatrices in models with long-range interactions
• No attraction between spinons in the Haldane-Shastry model
• Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
• Yangian symmetry of integrable quantum chains with long-range interactions and a new description of states in conformal field theory
• Finite-temperature structure factor in the Haldane–Shastry spin chain
• Integrals of motion of the Haldane-Shastry model
• Exclusion Statistics in Conformal Field Theory Spectra
• Conformal Field Theory

Cited by

• Resurrecting the partially isotropic Haldane-Shastry model