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.

arXiv comment23 pages, 17 figures

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Cited by in corpus (8)

• Magnetization oscillations in a periodically driven transverse field Ising chain
• Spinon continuum in the Heisenberg quantum chain compound Sr${}_2$V${}_3$O${}_9$
• Exact Spin Correlators of Integrable Quantum Circuits from Algebraic Geometry
• Truncated string state space approach and its application to nonintegrable spin-$\frac{1}{2}$ Heisenberg chain
• Berry connection and quantum geometry in time-dependent systems with instantaneous quantum integrable field theory
• Spin dynamics and dark particle in a weak-coupled quantum Ising ladder with ${\mathcal{D}}_8^{(1)}$ spectrum
• Applied-field magnetic structure and spectroscopy shifts of the effective spin-$\frac{1}{2}$, $XY$-like magnet Li${}_2$CoCl${}_4$
• Thermally activated detection of dark particles in a weakly coupled quantum Ising ladder