Nedko B. Ivanov

Additional three-site exchange interactions, naturally arising, e.g., in the strong-coupling expansion of the two-band Hubbard model and in various effective spin Hamiltonians, may stabilize various exotic spin phases which are not typical for the pure Heisenberg models on frustrated lattices and/or with extra biquadratic exchange terms. The reason is hidden in some specific features of the isotropic three-site exchange interactions, such as the promotion of collinear spin configurations as well as the reinforcing tendency towards clustering of the quantum spins on the shortest exchange bonds. As a result, systems with integer and half­integer composite spins in the unit cell might be expected to support different quantum phase diagrams. In this work, we study this phenomenon by comparing the quantum phase diagrams of two Heisenberg chains with extra three-site exchange terms and two different alternating pairs of site spins S and σ [(S, σ) = and (], resulting in half-integer and integer cell spins S + σ, respectively.

The low-temperature elementary spin excitations in the AFM molecular wheel Fe18 were studied experimentally by inelastic neutron scattering and theoretically by modern numerical methods, such as dynamical density matrix renormalization group or quantum Monte Carlo techniques, and analytical spin-wave theory calculations. Fe18 involves eighteen spin-5/2 FeIII ions with a Hilbert space dimension of $\sim${}1014, constituting a physical system that is situated in a region between microscopic and macroscopic. The combined experimental and theoretical approach allowed us to characterize and discuss the magnetic properties of Fe18 in great detail. It is demonstrated that physical concepts such as the rotational-band or LandE-band concepts developed for smaller rings are still applicable. In particular, the higher-lying low-temperature elementary spin excitations in Fe18 or AFM wheels, in general, are of discrete antiferromagnetic spin-wave character.

We report on theoretical and experimental results concerning the low-temperature specific heat of the frustrated spin-tube material [(CuCl2tachH)3Cl]Cl2 (tach denotes 1,3,5-triaminocyclohexane). This substance turns out to be an unusually perfect spin-tube system which allows to study the physics of quasi-one-dimensional antiferromagnetic structures in rather general terms. An analysis of the specific-heat data demonstrates that at low enough temperatures the system exhibits a Tomonaga-Luttinger liquid behavior corresponding to an effective spin-3/2 antiferromagnetic Heisenberg chain with short-range exchange interactions. On the other hand, around 2~K the composite spin structure of the chain is revealed through a Schottky-type peak in the specific heat. We argue that the dominating contribution to the peak originates from gapped magnon-type excitations related to the internal degrees of freedom of the rung spins.

We study the phase diagram of a symmetric spin-1/2 Heisenberg diamond chain with additional cyclic four-spin exchange interactions. The presented analysis supplemented by numerical exact-diagonalization results for finite periodic clusters implies a rich phase diagram containing, apart from standard magnetic and spin-liquid phases, two different tetramer-dimer phases as well as an exotic fourfold degenerate dimerized phase. The characteristics of the established spin phases as well as the nature of quantum phase transitions are discussed as well.

We present a brief survey of the recent theoretical work related to generic Heisenberg spin models describing\ud quasi-one-dimensional quantum ferrimagnets. The emphasis is on quantum chains and ladders with strong\ud competing interactions, such as the frustrated J₁ - J₂ chain with alternating (1, 1/2) spins, the spin-1/2\ud diamond chain with four-spin cyclic couplings, and some generic types of mixed-spin ladders with geometric\ud frustration. As a rule, the discussed models exhibit rich quantum phase diagrams and provide some interesting\ud examples of one-dimensional magnetic-paramagnetic quantum phase transitions. A number of open problems\ud in the reviewed research area are discussed.Ми представляємо короткий огляд недавньої теоретичної роботи, пов’язаної з загальними спiновими моделями Гайзенберга, що описують квазiодновимiрнi квантовi ферiмагнетики. Наголос зроблено на квантових ланцюжках i драбинках з сильною конкуренцiєю взаємодiй, таких, як фрустрований J₁ - J₂ ланцюжок зi змiнними (1, 1/2) спiнами, спiн-1/2 ромбiчний ланцюжок з чотириспiновими циклiчними взаємодiями i деякi загальнi типи драбинок з геометричними фрустрацiями з рiзними значеннями спiна. Як правило, обговорюванi моделi виявляють багатi квантовi фазовi дiаграми i становлять цiкавi приклади одновимiрних квантових фазових переходiв магнетик – парамагнетик. Оговорюються деякi вiдкриттi проблеми у цiй областi дослiджень