We analyze the low-energy dynamics of quasi one dimensional, large-$S$ quantum antiferromagnets with easy-axis anisotropy, using a semi-classical non-linear sigma model. The saddle point approximation leads to a sine Gordon equation which supports soliton solutions. These correspond to the movement of spatially extended domain walls. Long-range magnetic order is a consequence of a weak inter-chain coupling. Below the ordering temperature, the coupling to nearby chains leads to an energy cost associated with the separation of two domain walls. From the kink-antikink two-soliton solution, we compute the effective confinement potential. At distances large compared to the size of the solitons the potential is linear, as expected for point-like domain walls. At small distances the gradual annihilation of the solitons weakens the effective attraction and renders the potential quadratic. From numerically solving the effective one dimensional Schröedinger equation with this non-linear confinement potential we compute the soliton bound state spectrum. We apply the theory to CaFe$_{2}$O$_{4}$, an anisotropic $S=5/2$ magnet based upon antiferromagnetic zig-zag chains. Using inelastic neutron scattering, we are able to resolve seven discrete energy levels for spectra recorded slightly below the Néel temperature $T_\textrm{N}\approx 200$~K. These modes are well described by our non-linear confinement model in the regime of large spatially extended solitons.
Soliton phase near antiferromagnetic quantum critical point in Q1D conductors
在Q1D有机导体反铁磁（SDW）量子临界点的嵌套模型框架中，一级跃迁将金属态与具有周期畴结构的孤子相分离。低温相图还显示了孤子相和均匀带隙SDW相之间的二阶相变线。结果与（TMTSF）$_2$ PF $_6$在临界压力附近的相图一致[T. Vuletic等人，EUR. J. B 25，319（2002）]。讨论了二阶跃迁线的检测问题。本文评述了低温超导性。
The infinite Heisenberg XXZ spin-(1/2) chain in the gapped antiferromagnetic regime has two degenerate vacua and kink topological excitations (which are also called spinons) interpolating between these vacua as elementary excitations. Application of an arbitrary weak staggered longitudinal magnetic field h induces a long-range attractive potential between two adjacent spinons leading to their confinement into 'meson' bound states. Exploiting the integrability of the XXZ model in the deconfined phase h = 0, we perform perturbative calculations of the energy spectra of the two-spinon bound state…
Defects in frustrated antiferromagnetic spin chains are universally present in geometrically frustrated systems. We consider the defects of the one-dimensional, spin-$s$ XXZ chain with single-ion anisotropy on a periodic chain with $N$ sites that was famously studied by Haldane. For $N$ odd the antiferromagnetic model is frustrated, and the ground state must include a soliton defect. We consider the Heisenberg interaction perturbatively and determine the corresponding perturbative solitonic ground state. Then we compute the entanglement spectrum, entanglement entropy (EE), capacity of entangle…
The Heisenberg XXZ spin-1/2 chain is considered in the massive antiferromagnetic regime in the presence of a staggered longitudinal magnetic field. The Hamiltonian of the model is characterised by the anisotropy parameter $Δ<-1$, and by the magnetic field strength h. At zero magnetic field, the model is exactly solvable. In the thermodynamic limit, it has two degenerate vacua and the kinks (which are also called spinons) interpolating between these vacua, as elementary excitations. Application of the staggered magnetic field breaks integrability of the model and induces the long-range attracti…
Understanding of the interaction of antiferromagnetic solitons including domain walls and skyrmions with boundaries of chiral antiferromagnetic slabs is important for the design of prospective antiferromagnetic spintronic devices. Here, we derive the transition from spin lattice to micromagnetic nonlinear $σ$-model with the corresponding boundary conditions for a chiral cubic G-type antiferromagnet and analyze the impact of the slab boundaries and antisymmetric exchange (Dzyaloshinskii--Moriya interaction) on the vector order parameter. We apply this model to evaluate modifications of antiferr…
Based on the mapping between $s=1/2$ spin operators and hard-core bosons, we extend the cluster perturbation theory to spin systems and study the whole excitation spectrum of the antiferromagnetic $J_{1}$-$J_{2}$ Heisenberg model on the square lattice. In the Néel phase for $J_{2}\lesssim0.4J_{1}$, in addition to the dominant magnon excitation, there is an obvious continuum close to $(π,0)$ in the Brillouin zone indicating the deconfined spin-1/2 spinon excitations. In the stripe phase for $J_{2}\gtrsim0.6J_{1}$, we find similar high-energy two-spinon continuums at $(π/2,π/2)$ and $(π/2,π)$, r…
We study the ground state and thermodynamic properties of the spin-half XXZ model, with an Ising interaction $J_z$ and a transverse exchange interaction $J_{x}$, on a pyrochlore tube obtained by joining together elementary cubes in a one-dimensional array. Periodic boundary conditions in the transverse directions ensure that the bulk of the system consists of corner-sharing tetrahedra, with the same local geometry as the pyrochlore lattice. We use exact diagonalization, the density matrix renormalization group (DMRG), and minimally entangled typical thermal states (METTS) methods to study the …
Confinement and deconfinement of spinons in a frustrated spin-1/2 Heisenberg model
在这篇文章中，我讨论了A. A. Nersesyan和A. M. Tsvelik，Phys. Rev. B{ \bf 67}，024422（2003）。相图包含由价键晶体（VBC）状态分离的$(π,0)$和$(π,π)$反铁磁相。我认为，在上述工作中预测的解除限制自旋的相图的点，位于VBC状态的中间，在二聚序参量改变符号的点。
Magnetic skyrmions are topological solitons with a nanoscale winding spin texture that hold promise for spintronics applications. Until now, skyrmions have been observed in a variety of magnets that exhibit nearly parallel alignment for the neighbouring spins, but theoretically, skyrmions with anti-parallel neighbouring spins are also possible. The latter, antiferromagnetic skyrmions, may allow more flexible control compared to the conventional ferromagnetic skyrmions. Here, by combining neutron scattering and Monte Carlo simulations, we show that a fractional antiferromagnetic skyrmion lattic…
