A model for real-space singlet pairs, hopping on the quasi 2D antiferromagnetic background of localized spins is further analysed. It is shown that lattice vibrations (if any), which break the symmetry of the in-plane oxygen position with respect to the nearest neighboring copper sites, may strongly influence both the magnitude and the temperature dependence of the ^{17}O NMR relaxation rate. For the Y site a situation is analogous, although the different modes may contribute to the effect. A relation of the results obtained to the Millis-Monien-Pines analysis is discussed. The validity of the mean-field random phase approximation for the description of the 2D antiferromagnet used previously is analysed. It is shown that the 2D fluctuations of the phase of the (bond) mean field parameter lead to the power-law decay with the distance of the corresponding correlation function (which remains finite in the mean field approximation). The spectrum of the phase fluctuations is found to be propagative in the one-loop approximation. An interaction of the real-space singlet pairs with the long-wavelength phase fluctuations is discussed.
The ground-state properties of decorated Heisenberg spin tubes with nearest- and next-nearest-neighbor antiferromagnetic exchange interactions has been studied using perturbation theory and exact diagonalization technique. The possibility of quantum phase transitions mediated by next-nearest neighbor interactions for these tubes is shown.
Spin chains and spin ladders can have a variety of gapless (critical) or gapped (massive) phases depending on the length of the spin and the type of coupling. A brief review of the results on some simple models is given with emphasis on the generation of the Haldane gap in anisotropic spin ladders.
We investigate a frustrated Lieb-Mattis-like spin-1/2 model that is a reference model for the corresponding square-lattice Heisenberg model describing the unusual magnetic properties of Ba_{2}Cu_{3}O_{4}Cl_{2}. Due to frustration we obtain a rich magnetic phase diagram. We find two critical temperatures in accordance with recent experiments on Ba_{2}Cu_{3}O_{4}Cl_{2}.
Low-energy excitations are studied in the 1D S = 1 antiferromagnetic valence-bond-solid model. The lowest states are found to form a discrete triplet branch, separated from a higher-lying scattering continuum. The elementary excitations are argued to be "hidden" domain walls.
Stimulated by the two-dimensional frustrated Heisenberg antiferromagnet with first-, second-, and third-neighbor couplings (J_{1}-J_{2}-J_{3} model) we consider a corresponding three-parameter model with a long-range antiferromagnetic Lieb-Mattis interaction. This model can be solved exactly and leads to a better understanding of the role of frustration in the J_{1}-J_{2}-J_{3} model. We calculate the correlations in the groundstate and consider their finite size behavior. Furthermore we present the full thermodynamic phase diagram. We find the possibility of a disordered phase at T=0.
We show that the most characteristic properties of mesoscopic antiferromagnets can be explained in terms of the response on a spatially inhomogeneous perturbation. This concept allows to explain the dynamic properties (quantum resonance, coherence and tunnelling rates) as well as static perturbations which, for increasing size of an antiferromagnet, leads to a transition from the quantum mechanical oscillating system to a classical antiferromagnet with well defined Néel vectors.
Algebraic Bethe Ansatz, also known as quantum inverse scattering method, is a consistent tool based on the Yang-Baxter equation which allows to construct Bethe Ansatz exact solutions. One of the most important objects in algebraic Bethe Ansatz is a monodromy matrix M̂, which is defined as an appropriate product of so-called Lax operators L̂ (local transition operators). Monodromy matrix as well as each of Lax operators acts in the tensor product of the quantum space 𝓗 with an auxiliary space ℂ². Thus M̂, when written in the standard basis of auxiliary space, consists of four elements Â, B̂, Ĉ, D̂, which are the operators acting in quantum space 𝓗, where B̂ and Ĉ are step operators and the remaining generate all constants of motion. In this work a consistent method of construction of the Bethe Ansatz eigenstates in terms of objects â, b̂, ĉ, d̂ i.e. matrix elements of the Lax operators in the auxiliary space is proposed.
The energy spectrum and peculiarities of field and temperature dependences of the basic thermodynamic characteristics of the finite spin-1/2 XX chain closed by one zz (Ising) bond and open ends XX-chain with two zz-impurities at the both ends have been investigated.
We consider a spin-1/2 XX chain with three-spin interactions which is equivalent to a system of noninteracting spinless fermions.We examine some dynamic quantities of the spin model.In particular, we calculate analytically the dynamic transverse (zz) structure factor which is governed by a two-fermion excitation continuum. Moreover, we compute numerically the dynamic xx structure factor which is a many-fermion dynamic quantity.We illustrate how the three-spin interactions manifest themselves in the dynamic probes.
We examine dynamic quantities of a random spin-1/2 isotropic XY chain in a transverse field. The randomness is related to the sign of the nearest-neighbor exchange interaction and can be eliminated by a suitable transformation. As a result, the dynamic quantities for the random spin chain are related to the same dynamic quantities for the homogeneous spin chain. We use the available results for the latter model to discuss the effect of randomness on the dynamic structure factors of the quantum spin chain.
We consider the quantum Heisenberg antiferromagnet in a magnetic field on two one-dimensional lattices containing equilateral triangles (a chain of corner-sharing double tetrahedra and a frustrated three-leg ladder) which support localized-magnon states. By mapping of the localized-magnon degrees of freedom on a classical lattice gas we obtain high-field thermodynamic quantities of the models at low temperatures.
We study the antiferromagnetic phase of three-dimensional Hubbard model with nearest neighbors hopping on a bipartite cubic lattice. We use the quantum SU(2)×U(1) rotor approach that yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of the model and satisfies the Mermin-Wagner theorem. As our theory describes the evolution from a Slater (U ≪ t) to a Mott-Heisenberg (U ≫ t) antiferromagnet, we present the phase diagram of the antiferromagnetic Hubbard model as a function of the crossover parameter U/t.
We consider the spin-1/2 isotropic XY chain in a transverse field with three-site interactions of (XZY - YZX)-type, which can be transformed into a system of noninteracting spinless fermions. We study dynamic properties of the spin model. In particular, we calculate the dynamic structure factors which are governed by a two-fermion excitation continuum. We demonstrate how the three-site interactions manifest themselves in the dynamic properties of the quantum spin chain.
We apply perturbation theory and cyclic spin permutation formalism to study the lowest energy states of the infinite-repulsion Hubbard model on n-leg ladders with alternating values of one-site energies α_{i} for neighboring rungs. We establish the "ferromagnetic" character of ladder ground-state at electron densities in the interval 1 - (2n)¯¹ ≤ ρ ≤ 1 and sufficiently large alternation of one-site energies of neighbor rungs of the ladder. We also show the stability of this state against the small deviations of the values of α_{i} in contrast to the case of two-leg ladder formed by weakly interacting neighbor rungs with equal one-site energies.
The effect of frustration in various localized and itinerant vanadium oxide compounds is discussed within next nearest neighbors Heisenberg and spin fluctuation models, respectively. In the localized moment case the S=1/2 J_1-J_2-model on a square lattice exhibits a rich phase diagram with magnetic as well as exotic hidden order phases due to the interplay of frustration and quantum fluctuations. Their signatures in the high field magnetization and in magnetocaloric quantities are surveyed. The possible quantum phase transitions are discussed and applied to layered vanadium oxides of the type AA'VO(PO_4)_2 where A, A' = Pb, Zn, Sr, Ba, Cd. In itinerant electron systems magnetic frustration may emerge as a result of electron correlations on a geometrically frustrated lattice. This mechanism causes enhanced spin fluctuations in a large region of momentum space and therefore can lead to a heavy fermion state at low temperatures as in the 3d spinel compound LiV_2O_4. The evidence from neutron scattering and NMR experiments is discussed within self-consistent renormalization theory based on local density approximation band structure calculations.
In nano-size antiferromagnetic systems a spatially inhomogeneous field leads to the formation of a staggered magnetization. Thereby the total magnetic moment does not change but the formation of a net magnetic moment at the border of the cluster leads to an energy gain. This type of magnetism is characterised by an ultra-fast dynamics. We suggest it is also responsible for the formation of the exciton magnetic polaron.
We demonstrate an exact diagonalization of the one-dimensional Heisenberg magnet in terms of algebraic Bethe Ansatz. We point out, by a polynomial expansion of the transfer matrix with respect to spectral parameter, a complete set of observables for classification of all eigenstates. We introduce an application of our approach on the example of the Heisenberg magnet consisting of four qubits, including its constants of motion, density matrices and complete classification of eigenstates.
A quantum simulation approach facilitated by the self-consistent algorithm was applied in the present work to ferromagnetic and antiferromagnetic three-dimensional Heisenberg lattices consisting of S = 1 spins. Consequently, the calculated spontaneous magnetizations for the two sorts of lattices are precisely consistent with mean-field theory in the whole temperature range. Especially, the numerical results, such as magnetizations, total energies and total free energies per mole of spins, show no size effects. Thus, the physical properties of a huge bulk magnet can be estimated by performing simulation for a very tiny sample, so that the computational time can be greatly saved.
Zero-temperature limits of the local and global thermodynamic quantities in the nine-membered antiferromagnetic s=3/2 spin ring are investigated by means of numerical exact diagonalization. An anisotropic Heisenberg model with tunable bond defect reflecting continuously varying topology (from closed to open ring) is exploited. The frustrated and non-frustrated phases are identified in the ground-state phase diagram determined by a bond-defect strength and magnetic field. Near the phase boundaries significance of the thermal fluctuations affecting the estimates of the local magnetic quantities found earlier at T=1 K is revealed. For the global quantities the effects of thermal fluctuations are found much weaker. A sequence of the local magnetic moments is analysed and their experimental verification at the edges of the non-frustrated and within the entire frustrated phase is suggested at sufficiently low temperature.
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