The role of q-spin singlet pairs of physical spins in the dynamical properties of the spin-1/2 Heisenberg-Ising XXZ chain
arXiv:2111.13118 · doi:10.1016/j.nuclphysb.2021.115610
Abstract
Dynamical correlation functions contain important physical information on correlated spin models. Here a dynamical theory suitable suitable to the isotropic spin-1/2 Heisenberg chain in a longitudinal magnetic field is extended to anisotropy larger than one . The aim of this paper is the study of the line shape of the spin dynamical structure factor components +-, -+ and zz of the spin-1/2 Heisenberg-Ising chain in a longitudinal magnetic field near their sharp peaks. To reach that goal, the nature of the specific type of elementary magnetic configurations both unbound and associated with real Bethe-ansatz rapidities and bound and described by complex Bethe strings is clarified: They are singlet q-spin pairs of physical spins 1/2. We derive analytical expressions for the line shapes of dynamical structure factor components +-, -+ and zz valid in the vicinity of lines of sharp peaks. Those are mostly located at and just above lower thresholds of continua associated with both real-rapidity states with only unbound q-spin singlet pairs and states with real and complex rapidities populated by such unbound pairs and a single 2-string or a single 3-string. The latter contain 2 and 3 bound q-spin singlet pairs, respectively. Our results provide physically interesting and important information on the microscopic processes that determine the dynamical properties of the non-perturbative spin-1/2 Heisenberg-Ising chain in a longitudinal magnetic field.
arXiv comment42 pages, 9 figures
References in corpus (29)
- One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
- Spin transport in a one-dimensional anisotropic Heisenberg model
- Finite temperature Drude weight of the one dimensional spin 1/2 Heisenberg model}
- Spin transport in a tunable Heisenberg model realized with ultracold atoms
- Universal theory of nonlinear Luttinger liquids
- Families of quasi-local conservation laws and quantum spin transport
- Computation of dynamical correlation functions of Heisenberg chains in a field
- Experimental Observation of Bethe Strings
- Exact edge singularities and dynamical correlations in spin-1/2 chains
- Shadow band in the one-dimensional large Hubbard model
- Spectral functions of the 1D Hubbard model in the U -> \infty limit: How to use the factorized wave-function
- Spin transport in a magnetic insulator with zero effective damping
- Spin transport in the XXZ chain at finite temperature and momentum
- Finite-temperature Drude weight within the anisotropic Heisenberg chain
- Geometry and the Hidden Order of Luttinger Liquids: the Universality of Squeezed Space
- Dispersions of Many-Body Bethe strings
- Lineshape predictions via Bethe ansatz for the one-dimensional spin-1/2 Heisenberg antiferromagnet in a magnetic field
- Finite-Energy Spectral-Weight Distributions of a 1D Correlated Metal
- Spectral properties of one dimensional insulators and superconductors
- Theory of hole propagation in one dimensional insulators and superconductors
- Quasiparticles governing the zero-temperature dynamics of the 1D spin-1/2 Heisenberg antiferromagnet in a magnetic field
- New perturbation theory of low-dimensional quantum liquids II: operator description of Virasoro algebras in integrable systems
- One-dimensional Quantum Spin Dynamics of Bethe String States
- Large N behavior of string solutions in the Heisenberg model
- Tracking the effects of interactions on spinons in gapless Heisenberg chains
- Pseudoparticle approach to 1D integrable quantum models
- Absence of high-temperature ballistic transport in the spin- chain within the grand-canonical ensemble
- Dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field
- Bethe strings in the dynamical structure factor of the spin-1/2 Heisenberg XXX chain