The present situation in theoretical and experimental studies on one-dimensional magnetic systems is fully discussed. Equal-time as well as the dynamic properties are included with an emphasis on the latter. Four model systems are examined in detail: TMMC (Heisenberg antiferromagnet), CsNiF3 (planar ferromagnet), CoCl2. 2NC5H5 (Ising ferromagnet), CuCl2. 2NC5H5 (Heisenberg antiferromagnet with S = ½). The equal-time properties are quite well understood in theory and in experiment but the dynamical properties much less so. The open questions and possible investigations for the future are discussed.

Theoretical and experimental studies on one-dimensional magnetic systems

The existence of bound states of elementary spin waves (magnons) in one-dimensional quantum magnets was predicted almost 80 years ago. Identifying signatures of magnon bound states has so far remained the subject of intense theoretical research and their detection has proved challenging for experiments. Ultracold atoms offer an ideal setting in which to find such bound states by tracking the spin dynamics with single-spin and single-site resolution, following a local excitation. Here we use in situ correlation measurements to observe two-magnon bound states directly in a one-dimensional Heisenberg spin chain comprising ultracold bosonic atoms in an optical lattice. We observe the quantum dynamics of free and bound magnon states through time-resolved measurements of two spin impurities. The increased effective mass of the compound magnon state results in slower spin dynamics as compared to single-magnon excitations. We also determine the decay time of bound magnons, which is probably limited by scattering on thermal fluctuations in the system. Our results provide a new way of studying fundamental properties of quantum magnets and, more generally, properties of interacting impurities in quantum many-body systems.

/pdf/microscopic-observation-of-magnon-bound-states-and-their-5d897igrm9.pdf

Microscopic observation of magnon bound states and their dynamics

The present status of theoretical and experimental investigations of solitary excitations in one-dimensional magnetic systems is reviewed. A survey of exact solutions to the nonlinear equations of motion for pertinent classical chain systems (sine-Gordon chain and ferromagnetic Heisenberg chains with various anisotropies) is given. Particular emphasis is devoted to the role of solitons in the thermodynamics of such systems. Models corresponding to real quasi-one-dimensional magnets are broadly discussed to demonstrate the properties of their solitary excitations. The experimental significance of such nonlinear excitations in the static and dynamic quantities of such systems is discussed in detail. The models and model substances are the easy-plane ferromagnet (model substances CsNiF3 and (C6H11NH3)CuBr3), the easy-plane antiferromagnet (CH3)4NMnCl3) and the S = ½ Ising chain with transverse interactions (CsCoCl3). The quantum aspects of solitary excitations are treated in some theoretical detail....

Solitary excitations in one-dimensional magnets

We suggest a protocol for perfect quantum communication through spin-chain channels. By combining a dual-rail encoding with measurements only at the receiving end, we can get conclusively perfect state transfer, whose probability of success can be made arbitrarily close to unity. As an example of such an amplitude-delaying channel, we show how two parallel Heisenberg spin chains can be used as quantum wires. Perfect state transfer with a probability of failure lower than P in a Heisenberg chain of N spin-(1/2) particles can be achieved in a timescale of the order of (0.33({Dirac_h}/2{pi})/J)N{sup 1.7} vertical bar ln P vertical bar. We demonstrate that our scheme is more robust to decoherence and nonoptimal timing than any scheme using single spin chains.

https://arxiv.org/pdf/quant-ph/0406112.pdf

Conclusive and arbitrarily perfect quantum-state transfer using parallel spin-chain channels

The permanent profile solutions of the continuous classical Heisenberg chain is reviewed and the author expounds on the application of the inverse scattering method. Extending and amplifying the work of Takhtajan (1977) he exhibits the 'diagonal' action angle representation of the model. The spectrum of the Hamiltonian is exhausted by a magnon band and a soliton band. The magnons have no internal degrees of freedom and can be characterised by the dispersion law E=p2. Like the sine Gordon doublet, the solitons have internal structure, they carry a continuous angular momentum m, and are characterised by the dispersion law E=16 sin2(p/4)/ mod m mod , in accordance with Tjon and Wright (1977). The continuous Heisenberg chain is a completely integrable Hamiltonian system possessing an infinite number of constants of motion. The recursive procedure for the determination of the conserved integrated densities is established.

http://iopscience.iop.org/article/10.1088/0305-4470/13/4/035/pdf

Solitons and magnons in the classical Heisenberg chain

The recent observation of two-, three-, four-, and five-magnon bound states in the linear chains of Co${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{H}}_{2}$O has prompted a theoretical examination of such states in an anisotropic linear ferromagnetic chain with $S=\frac{1}{2}$. A new method called the Ising-basis-function (IBF) method is developed. This method treats the conventional, localized Ising wave functions as Wannier functions, from which a complete, orthonormal set of Bloch functions (IBF's) is formed. Using these IBF's as basis functions, we obtain the expression for the energy of the two-magnon bound state originally found by Orbach for general longitudinal exchange anisotropy. Furthermore, we can calculate the energy of the ($ng2$)-magnon bound states for the case of strong longitudinal anisotropy. The method is also applied to describe the effect of transverse exchange anisotropy. It is shown that this anisotropy causes an interaction between bound states, particularly important near zero field, and gives rise to a finite probability of exciting the bound states by photon absorption. The generalization of this method to treat bound states in two and three dimensions and for $Sg\frac{1}{2}$ is also discussed. The method is simple and has a direct physical interpretation. As an example, a physical description of the two-magnon bound state in a general system is given. Since the IBF method automatically contains some of the magnon-magnon interactions in zero order, it should be useful in other problems where these interactions are important.

Magnon Bound States in Anisotropic Linear Chains

The results of far-infrared transmission measurements on Co${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{H}}_{2}$O at helium temperatures are reported and compared with theoretical predictions. Antiferromagnetic resonance, ferrimagnetic resonance, and ferromagnetic resonance have been observed in the respective metamagnetic phases of this material. Furthermore, these magnons appear to interact with an unexpected excitation which is believed to be an optical phonon. The most striking feature of the data, however, is the appearance of absorption lines in each phase which shift with magnetic field at a rate corresponding to $g$ values of about 14, 21, 28, and even 35, as compared to the $g$ value of \ensuremath{\sim}7 for the single magnons. Furthermore, the energy of each of these $n$-fold multiple excitations is markedly less than $n$ times the energy of a onefold one. These excitations are identified as clustered spin reversals or magnon bound states, and this is the first direct observation of such states. In the simple Ising-model approximation, such clusters of $n$ adjacent spin reversals are eigen-states, and the Ising-model energies qualitatively describe the observed energy spectra in all three phases. Using the theoretical results of the preceding paper, the small non-Ising terms are included in the theory, and excellent quantitative agreement is obtained. The reasons why bound states can be observed in Co${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{H}}_{2}$O are also discussed.

J. B. Torrance

Papers

Magnon Bound States in Anisotropic Linear Chains

Excitation of Multiple-Magnon Bound States in Co Cl 2 ·2 H 2 O