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 present an up-to-date survey of theoretical concepts and results in the field of one-dimensional magnetism and of their relevance to experiments and real materials. Main emphasis of the chapter is on quantum phenomena in models of localized spins with isotropic exchange and additional interactions from anisotropy and external magnetic fields.

One-dimensional magnetism

We show that the well-known translation invariant ground states and the recently
 discovered kink and antikink ground states are the complete set of pure infinite-volume
 ground states (in the sense of local stability) of the spin-S ferromagnetic XXZ chains with
 Hamiltonian H=-sum_x [ S^1_x S^1_{x+1} + S^2_x S^2_{x+1} + Delta S^3_x S^3_{x+1} ], for all
 Delta >1, and all S=1/2,1,3/2,.... For the isotropic model (Delta =1) we show that all
 ground states are translation invariant. For the proof of these statements we propose a
 strategy for demonstrating completeness of the list of the pure infinite-volume ground
 states of a quantum many-body system, of which the present results for the XXX and XXZ
 chains can be seen as an example. The result for Delta>1 can also be proved by an easy
 extension to general $S$ of the method used in [T. Matsui, Lett. Math. Phys. 37 (1996) 397]
 for the spin-1/2 ferromagnetic XXZ chain with $\Delta>1$. However, our proof is
 different and does not rely on the existence of a spectral gap. In particular, it also
 works to prove absence of non-translationally invariant ground states for the isotropic
 chains (Delta=1), which have a gapless excitation spectrum. Our results show that, while
 any small amount of the anisotropy is enough to stabilize the domain walls against the
 quantum fluctuations, no boundary condition exists that would stabilize a domain wall in
 the isotropic model (Delta=1).

https://www.intlpress.com/site/pub/files/_fulltext/journals/atmp/1998/0002/0003/ATMP-1998-0002-0003-a004.pdf

The complete set of ground states of the ferromagnetic XXZ chains

We show that the well-known translation invariant ground states and the recently discovered kink and antikink ground states are the complete set of pure infinite-volume ground states (in the sense of local stability) of the spin-S ferromagnetic XXZ chains with Hamiltonian H=-sum_x [ S^1_x S^1_{x+1} + S^2_x S^2_{x+1} + Delta S^3_x S^3_{x+1} ], for all Delta >1, and all S=1/2,1,3/2,.... For the isotropic model (Delta =1) we show that all ground states are translation invariant. 
For the proof of these statements we propose a strategy for demonstrating completeness of the list of the pure infinite-volume ground states of a quantum many-body system, of which the present results for the XXX and XXZ chains can be seen as an example. The result for Delta>1 can also be proved by an easy extension to general $S$ of the method used in [T. Matsui, Lett. Math. Phys. 37 (1996) 397] for the spin-1/2 ferromagnetic XXZ chain with $\Delta>1$. However, our proof is different and does not rely on the existence of a spectral gap. In particular, it also works to prove absence of non-translationally invariant ground states for the isotropic chains (Delta=1), which have a gapless excitation spectrum. 
Our results show that, while any small amount of the anisotropy is enough to stabilize the domain walls against the quantum fluctuations, no boundary condition exists that would stabilize a domain wall in the isotropic model (Delta=1).

Thermal and magnetic effects in a system consisting of thin layers of coupled Ising spins with $S=1/2$ and $S=1$ are considered. The specific heat and the correlation length display maxima at two different temperatures. It is discussed in what sense these maxima can be interpreted as a finite-size rounding of a thermodynamic singularity associated with a phase transition. The connection with ordinary, extraordinary and special surface phase transitions is made. In $2D$, the surface critical exponents are calculated from conformal invariance. The bulk and surface finite-size scaling of the order parameter profiles at the transition points is discussed. In $2D$, an exact scaling function for the profiles is suggested through conformal invariance arguments for the (extra)ordinary transition.

Finite-size effects in layered magnetic systems

The authors describe S=1/2 Ising-like magnetic chains completely in terms of domain walls. They formulate domain wall creation and annihilation operators as fermion operators and calculate the domain wall content of the ground state and of excited states. From exact results for finite chains and from the solution in the one-domain wall subspace they find that a single domain wall behaves like a free particle in a well. The transition between the two equivalent ground states of Ising-like S=1/2 chains is found to be dominated by quantum diffusion: the approach of the magnetization to the asymptotic behaviour is algebraic and not exponential. The analogy of this observation to interface fluctuations in the two-dimensional classical system is pointed out. For domain walls in the presence of impurities they study the phase shift and the transmission coefficient as well as the exact energy spectrum of finite impure lattices. To visualize the domain wall scattering they also demonstrate their real-time dynamics.

https://iopscience.iop.org/article/10.1088/0953-8984/3/17/015/pdf

S Miyashita

Papers

S=1/2 magnetic chains as domain wall systems