A. K. Kolezhuk

One-dimensional magnetism

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.

FINITELY CORRELATED GENERALIZED SPIN LADDERS

We study two-leg S=1/2 ladders with general isotropic exchange interactions between spins on neighboring rungs, whose ground state can be found exactly in a form of finitely correlated (matrix product) wave function. Two families of models admitting an exact solution are found: one yields translationally invariant ground states and the other describes spontaneously dimerized models with twofold degenerate ground state. Several known models with exact ground states (Majumdar–Ghosh and Shastry–Sutherland spin-1/2 chains, Affleck–Kennedy–Lieb–Tasaki spin-1 chain, Δ-chain, Bose–Gayen ladder model) can be obtained as particular cases from the general solution of the first family, which includes also a set of models with only bilinear interactions. Those two families of models have nonzero intersection, which enables us to determine exactly the phase boundary of the second-order transition into the dimerized phase and to study the properties of this transition. The structure of elementary excitations in the dimerized phase is discussed on the basis of a variational ansatz. For a particular class of models, we present exact wave functions of the elementary excitations becoming gapless at second-order transition lines. We also propose a generalization of the Bose–Gayen model which has a rich phase diagram with all phase boundaries being exact.

NON-HALDANE SPIN-LIQUID MODELS WITH EXACT GROUND STATES

We present a family of spin ladder models which admit exact solution for the ground state and exhibit non-Haldane spin liquid properties as predicted recently by Nersesyan and Tsvelik [Phys. Rev. Lett. v.78, 3939 (1997)], and study their excitation spectrum using a simple variational ansatz. The elementary excitation is neither a magnon nor a spinon, but a pair of propagating triplet or singlet solitons connecting two spontaneously dimerized ground states. Second-order phase transitions separate this phase from the Haldane phase and the rung-dimer phase.

Effective field theory for the S = 1 quantum nematic

For the

Excitation hierarchy of the quantum sine-gordon spin chain in a strong magnetic field.

S=1

Dynamics of an anisotropic spin dimer system in a strong magnetic field

system with general isotropic nearest-neighbor exchange, we derive the low-energy description of the spin nematic phase in terms of the

Electron Spin Resonance in Sine-Gordon Spin Chains in the Perturbative Spinon Regime

{\mathrm{RP}}^{2}

Variational and density-matrix renormalization-group studies of the frustrated antiferromagnetic Heisenberg S=1 quantum spin chain

nonlinear

Massive triplet excitations in a magnetized anisotropic Haldane spin chain

\ensuremath{\sigma}

Electron spin resonance in high-field critical phase of gapped spin chains

model. In one dimension, quantum fluctuations destroy long-range nematic (quadrupolar) ordering, leading to the formation of a gapped spin liquid state being an analog of the Haldane phase for a spin nematic. Nematic analog of the Belavin-Polyakov instanton with