2005/09/06 by Davide Controzzi, D. Controzzi, Eli Hawkins +1
Mathematics · Physics and Astronomy · #Computer science #Geometry #Heisenberg model #Homogeneous space #Integer (computer science) #Lattice (music) #Mathematical physics #Mathematics #Nonlinear system #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Regularization (linguistics) #Sigma #Sigma model #Theoretical physics #cond-mat.str-el
paper · pdf · doi:10.1142/s0217979205032826
published as Int.J.Mod.Phys. B19 (2005) 4449-4466 · To appear in Int. J. MOd. Phys. B
arxiv created 2005/09/06 · openalex publication_date 2005/12/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the two-dimensional O (3) non-linear sigma model with topological term using a lattice regularization introduced by Shankar and Read [Nucl. Phys. B336, 457 (1990)], that is suitable for studying the strong coupling regime. When this lattice model is quantized, the coefficient θ of the topological term is quantized as θ=2πs, with s integer or half-integer. We study in detail the relationship between the low energy behaviour of this theory and the one-dimensional spin-s Heisenberg model. We generalize the analysis to sigma models with other symmetries.