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 (13)

• Exact edge singularities and dynamical correlations in spin-1/2 chains
• Spectral function of spinless fermions on a one-dimensional lattice
• Antiferromagnetic Kitaev interaction in $J_\rm{eff}=1/2$ cobalt honeycomb materials Na${}_3$Co${}_2$SbO${}_6$ and Na${}_2$Co${}_2$TeO${}_6$
• Dynamically dominant excitations of string solutions in the spin-1/2 antiferromagnetic Heisenberg chain in magnetic fields
• Magnetic correlations of the quasi-one-dimensional half-integer spin-chain antiferromagnets Sr$M_2$V${}_2$O${}_8$ ($M$ = Co, Mn)
• Magnons and Excitation Continuum in XXZ triangular antiferromagnetic model: Application to $B{a}_{3}CoS{b}_2{O}_9$
• The two-spinon transverse structure factor of the gapped Heisenberg antiferromagnetic chain
• 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
• Cascade of singularities in the spin dynamics of a perturbed quantum critical Ising chain
• Local dynamics and thermal activation in the transverse-field Ising chain
• The exact two-spinon longitudinal dynamical structure factor of the anisotropic XXZ model

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