2009/03/31 by Giovanni Feverati, Paul A. Pearce, Nicholas S. Witte +1 · 5 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Bethe ansatz #Bijection #Bose gas #Combinatorics #Conformal map #Eigenvalues and eigenvectors #Geometry #Hamiltonian (control theory) #Hyperplane #Ising model #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Quantum mechanics #Scaling #Scaling limit #Supersymmetry #Transfer matrix #hep-th
paper · pdf · open access · doi:10.1088/1742-5468/2009/10/p10013
published in Journal of Statistical Mechanics Theory and Experiment 2009(10), P10013 (Institute of Physics) · 57 pages, in version 2: typos corrected, some sentences clarified, one appendix removed
arxiv created 2009/10/16 · openalex publication_date 2009/10/19 · arxiv updated 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We consider the physical combinatorics of critical lattice models and their associated conformal field theories arising in the continuum scaling limit. As examples, we consider A-type unitary minimal models and the level-1 Wess–Zumino–Witten (WZW) model. The Hamiltonian of the WZW model is the invariant XXX quantum spin chain. For simplicity, we consider these theories only in their vacuum sectors on the strip. Combinatorially, fermionic particles are introduced as certain features of RSOS paths. They are composites of dual-particles and exhibit the properties of quasiparticles. The particles and dual-particles are identified, through a conjectured energy-preserving bijection, with patterns of zeros of the eigenvalues of the fused transfer matrices in their analyticity strips. The associated ( m , n ) systems arise as geometric packing constraints on the particles. The analyticity encoded in the patterns of zeros is the key to the analytic calculation of the excitation energies through the thermodynamic Bethe ansatz (TBA). As a by-product of our study, in the case of the WZW or XXX model, we find a relation between the location of the Bethe root strings and the location of the transfer matrix 2-strings.