Magnetic excitations in the one-dimensional Heisenberg-Ising model with external fields and their experimental realizations

Abstract

The one dimensional (1D) spin-1/2 Heisenberg-Ising model, a prototype quantum many-body system, has been intensively studied for many years. In this review, after a short introduction on some basic concepts of group theory for the octahedral group, a detailed pedagogical framework is laid down to derive the low-energy effective Hamiltonian for the Co-based materials. The 1D spin-1/2 Heisenberg-Ising model is obtained when applying the analysis to quasi-1D antiferromagnetic materials $\mathrm{BaC}{\mathrm{o}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ and $\mathrm{SrC}{\mathrm{o}}_2{\mathrm{V}}_2{\mathrm{O}}_8$. After the preparation, we review the theoretical progresses of a variety of novel magnetic excitations and emergent physics in the 1D spin-1/2 Heisenberg-Ising model, and further summarize their recent experimental realizations.

23 pages, 17 figures

References in corpus (10)

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• Spectral function of spinless fermions on a one-dimensional lattice
• Dynamically dominant excitations of string solutions in the spin-1/2 antiferromagnetic Heisenberg chain in magnetic fields
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• Observation of E8 Particles in an Ising Chain Antiferromagnet
• Experimental Observation of Quantum Many-Body Excitations of $E_8$ Symmetry in the Ising Chain Ferromagnet CoNb${}_2$O${}_6$
• Finite temperature spin dynamics in a perturbed quantum critical Ising chain with an $E_8$ symmetry
• The exact two-spinon longitudinal dynamical structure factor of the anisotropic XXZ model