2007/06/30 by R G Pereira, R. G. Pereira, J. Sirker +11 · 1 citation
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum many-body systems #Topological Materials and Phenomena #cond-mat.str-el
paper · pdf · doi:10.1088/1742-5468/2007/08/p08022
published as J. Stat. Mech. (2007) P08022 · 67 pages, 25 figures
arxiv created 2007/08/10 · openalex publication_date 2007/08/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We combine Bethe ansatz and field theory methods to study the longitudinal dynamical structure factor S zz ( q ,ω) for the anisotropic spin-1/2 chain in the gapless regime. Using bosonization, we derive a low-energy effective model, including the leading irrelevant operators (band curvature terms) which account for boson decay processes. The coupling constants of the effective model for finite anisotropy and finite magnetic field are determined exactly by comparison with corrections to thermodynamic quantities calculated by Bethe ansatz. We show that a good approximation for the shape of the on-shell peak of S zz ( q ,ω) in the interacting case is obtained by rescaling the result for free fermions by certain coefficients extracted from the effective Hamiltonian. In particular, the width of the on-shell peak is argued to scale like δω q ∼ q 2 and this prediction is shown to agree with the width of the two-particle continuum at finite fields calculated from the Bethe ansatz equations. An exception to the q 2 scaling is found at finite field and large anisotropy parameter (near the isotropic point). We also present the calculation of the high-frequency tail of S zz ( q ,ω) in the region using finite-order perturbation theory in the band curvature terms. Both the width of the on-shell peak and the high-frequency tail are compared with S zz ( q ,ω) calculated by Bethe ansatz for finite chains using determinant expressions for the form factors and excellent agreement is obtained. Finally, the accuracy of the form factors is checked against the exact first moment sum rule and the static structure factor calculated by density matrix renormalization group (DMRG).