Mass Spectrum of the Two-Dimensional O(3) Sigma Model with aθTerm

2003/07/22 by Davide Controzzi, D. Controzzi, Giuseppe Mussardo +1 · 2 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced NMR Techniques and Applications #Combinatorics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Sigma #Spectrum (functional analysis) #Term (time) #Theoretical and Computational Physics #cond-mat #hep-lat #hep-th

paper · pdf · doi:10.1103/physrevlett.92.021601

published as Phys.Rev.Lett. 92 (2004) 021601 · 4 pages REVTEX4, 2 figures reference added,corrected typos

arxiv created 2003/07/22 · openalex publication_date 2004/01/15 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Form factor perturbation theory is applied to study the spectrum of the O(3) nonlinear sigma model with the topological term in the vicinity of \ensuremathθ=\ensuremathπ. Its effective action near this value is given by the nonintegrable double sine-Gordon model. Using previous results by Affleck and the explicit expressions of the form factors of the exponential operators e^\ifmmode±\else\textpm\fii√8\ensuremathπ\ensuremathφ(x), we show that the spectrum consists of a stable triplet of massive particles for all values of \ensuremathθ and a singlet state of higher mass. The singlet is a stable particle only in an interval of values of \ensuremathθ close to \ensuremathπ, whereas it becomes a resonance below a critical value \ensuremathθ_c.

Citations

• Critical theory of quantum spin chains
• Integrable sigma models and perturbed coset models
• Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State
• Non-integrable quantum field theories as perturbations of certain integrable models
• Exclusion Statistics in Conformal Field Theory Spectra
• Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models
• Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model

Cited by

• Dynamical response functions in the quantum Ising chain with a boundary
• Mass generation in perturbed massless integrable models