Temperley-Lieb-Jones Algebraic Structures in Higher Spin Chain Models

We investigate the Temperley-Lieb-Jones algebraic structures in isomorphic higher spin chain modgls with nearest neighbour interactions and SU(2) symmetry. The Ternperley-Lieb-Jones algebraic constructions for such chains of spins from 1 to 7/2 are presented. For the case of spin-1 we also give the Temperley-Lieb-Jones algebraic representations related to the anisomorphic spin chain with q-deformed SU_q(2) symmetry. Their related spin chain Harniltonians with SU(2) and SU_q(2) symmetries as well as the corresponding solutions of Yang-Baxter equation are also discussed.     

2D multipartite valence bond states in quantum anti-ferromagnets

A quantum anti-ferromagnetic spin-1 model is characterised on a 2D lattice with the following requirements: (i) The Hamiltonian is made out of nearest neighbour interactions. (ii) It is homogeneous, translational and rotational invariant. (iii) The ground state is a real singlet state of SU(2) (non-chiral). (iv) It has a local spin-1 representation. Along the way to characterise the system, connections with classical statistical mechanics and integrable models are explored. Finally, the relevance of the model in the physics of low dimensional anti-ferromagnetic Mott-Hubbard insulators is discussed.     

The Faddeev equations for the Heisenberg ferromagnet

The Faddeev equations for the three-magnon T-matrix of the Heisenberg ferromagnet with nearest neighbour interactions are derived for the cubic lattice in arbitrary dimensions. The extreme case of spin $\text{1}\text{2}$ is considered and the kinematical restriction, that only one spin deviation per site is possible, has been taken into account rigorously. Hence the T-matrix is unitary and suited for the study of bound state as well as scattering state properties. The analytic solution of the homogeneous Faddeev equations in one dimension is given.     

Spin configurations in hexagonal antiferromagnets with competing interactions

The ordered phase of the most part of ABX₃ antiferromagnets appears as a stacking of 120°-three sublattice spin layers with alternate spin direction along thec-axis. This configuration is easy to be explained because it is the minimum energy configuration of the Heisenberg hexagonal model with nearest neighbour antiferromagnetic interaction. However we show that moderate competitive interactions between in plane next nearest and third nearest neighbours stabilize incommensurate spin configurations. This gives some insight into the unexplained spin configuration observed in RbMnBr₃ by elastic neutron scattering experiment.     

Quantum spin liquid in the FCC lattice

The properties of the spin system in the FCC lattice described by the Heisenberg model (s=1/2) with antiferromagnetic interactions between the nearest neighbors were studied. It was shown within the framework of spin-wave theory that long-range antiferromagnetic order was absent because of frustration of exchange coupling and transverse quantum spin fluctuations. The system was in the quantum spin liquid state. A method for describing it within linear second-order theory with self-consistently calculated parameters was suggested. It was proved that the ground spin liquid state was singlet. The thermodynamic properties of the spin liquid in the whole temperature range and the character of spatial spin correlations, which had alternating signs and a finite correlation length, were determined. The theory was constructed based on the method of two-time Green temperature functions.     

Star-triangle relations in the exactly solvable statistical models

A regular method for analysis of lattice spin models with a nearest neighbour interaction is proposed. Star-triangle relations in the form of functional equations are used. Parametric families of transfer matrices commuting due to star-triangle relations are constructed. The eigenvalues of transfer matrices as functions of the spectral parameter are shown to obey two functional equations. The solution of these equations for the maximal eigenvalue yields the partition function of the model. The method is applied for evaluation of the partition function of the critical Potts models, the Ising model, the Ashkin-Teller model equivalent to the eight-vertex model.     

Spin wave relaxation and magnetic properties in [M/Cu] super-lattices; M=Fe, Co and Ni

In this work, we study the elementary excitations and magnetic properties of the [M/Cu] super-lattices with: M=Fe, Co and Ni, represented by a Heisenberg ferromagnetic system with N atomic planes. The nearest neighbour (NN), next nearest neighbour (NNN) exchange, dipolar interactions and surface anisotropy effects are taken into account and the Hamiltonian is studied in the framework of the linear spin wave theory. In the presence of the exchange alone, the excitation spectrum E(k) and the magnetization 〈S^z〉/S analytical expressions are obtained using the Green's function formalism. The obtained relaxation time of the magnon populations is nearly the same in the Fe and Co-based super-lattices, while these magnetic excitations would last much longer in the Ni-based super lattice. A numerical study of the surface anisotropy and long-ranged dipolar interaction combined effects are also reported. The exchange integral values deduced from a comparison with experience for the three super-lattices are coherent.     

Ferroquadrupolar Order in the Spin-1 Bilinear-Biquadratic Model up to the Second Nearest Neighbor

We have studied some ferroquadrupolar phases of the S = 1 Heisenberg model with bilinear and biquadratic exchange interactions on the square lattice up to the second nearest neighbor, using the SU(3) Schwinger bosons formalism in a mean field approximation. This technique is very convenient to treat nematic order. This technique has the advantage of using the fundamental representation of the SU(N) group instead of SU(2), designed to capture spin-quadrupolar order in addition to the dipolar magnetic order. We also present quadrupole structure factors that can be measured in future experiments. Our calculations can have implications in the study of iron-based superconductors.     

Critical temperature for a system with Heisenberg-like nearest neighbour and Ising-like next nearest neighbour interactions

A ferromagnetic system with $\text{S =}\text{1}\text{2}$, where the interactions between nearest neighbours are isotropic (having Heisenberg character) and those between the next nearest neighbours anisotropic (Ising-like), is investigated. Using the effective hamiltonian approach we find the change in the critical temperature due to the inclusion of next nearest neighbour interactions of different character. The change is greatest in two dimensions where the critical temperature is shifted up from its zero value for a system with the Ising-like interactions switched off. We also calculate the T_c for a system with both nearest and next nearest neighbours interactions of the Ising-type. The results for the two models are compared.     

Physical realization and possible identification of topological excitations in quantum Heisenberg anti-ferromagnet on a two dimensional lattice

Physical spin configurations corresponding to topological excitations, expected to be present in the XY limit of a quantum spin 1/2 Heisenberg anti-ferromagnet, are probed on a two dimensional square lattice. Quantum vortices (anti-vortices) are constructed in terms of coherent staggered spin field components, as limiting case of meronic (anti-meronic) configurations. The crucial role of the associated Wess-Zumino-like (WZ-like) term is highlighted in our procedure. The time evolution equation of coherent spin fields used in this analysis is obtained by applying variational principle on the quantum Euclidean action corresponding to the Heisenberg anti-ferromagnet on lattice. It is shown that the WZ-like term can distinguish between vortices and anti-vortices only in a charge sector with odd topological charges. Our formalism is distinctly different from the conventional approach for the construction of quantum vortices (anti-vortices).     

Phase transitions in quantum spin systems with isotropic and nonisotropic interactions

We prove the existence of spontaneous magnetization at sufficiently low temperature, and hence of a phase transition, in a variety of quantum spin systems in three or more dimensions. The isotropic spin 1/2x-y model and the Heisenberg antiferromagnet with spin 1, 3/2,...and with nearest neighbor interactions on a simple cubic lattice are included.Research supported by U.S. National Science Foundation under grants GP-40768X (F.J.D.), MCS 75-21684 (E.H.L.), and GP-39048 (B.S.).Alfred Sloan Fellow.     

A generalized spin ladder in a magnetic field

We study the phase diagram of coupled spin-1/2 chains with bilinear and (chiral) three-spin exchange interactions in a magnetic field. The model is soluble on a one-parametric line in the space of coupling constants connecting the limiting cases of a single and two decoupled Heisenberg chains with nearest neighbour exchange only. We give a complete classification of the low-energy properties of the integrable system and introduce a numerical method which allows to study the possible phases of spin ladder systems away from the soluble line in a magnetic field. Received 17 November 1998 and Received in final form 22 January 1999     

Microscopic spin-wave theory for yttrium-iron garnet films

Motivated by recent experiments on thin films of the ferromagnetic insulator yttrium-iron garnet (YIG), we have developed an efficient microscopic approach to calculate the spin-wave spectra of these systems. We model the experimentally relevant magnon band of YIG using an effective quantum Heisenberg model on a cubic lattice with ferromagnetic nearest neighbour exchange and long-range dipole-dipole interactions. After a bosonization of the spin degrees of freedom via a Holstein-Primakoff transformation and a truncation at quadratic order in the bosons, we obtain the spin-wave spectra for experimentally relevant parameters without further approximation by numerical diagonalization, using efficient Ewald summation techniques to carry out the dipolar sums. We compare our numerical results with two different analytic approximations and with predictions based on the phenomenological Landau-Lifshitz equation.     

Three-sublattice ordering of the SU(3) Heisenberg model of three-flavor fermions on the square and cubic lattices

Combining a semiclassical analysis with exact diagonalizations, we show that the ground state of the SU(3) Heisenberg model on the square lattice develops three-sublattice long-range order. This surprising pattern for a bipartite lattice with only nearest-neighbor interactions is shown to be the consequence of a subtle quantum order-by-disorder mechanism. By contrast, thermal fluctuations favor two-sublattice configurations via entropic selection. These results are shown to extend to the cubic lattice, and experimental implications for the Mott-insulating states of three-flavor fermionic atoms in optical lattices are discussed.     

Quantum decoration transformation for spin models

It is quite relevant the extension of decoration transformation for quantum spin models since most of the real materials could be well described by Heisenberg type models. Here we propose an exact quantum decoration transformation and also showing interesting properties such as the persistence of symmetry and the symmetry breaking during this transformation. Although the proposed transformation, in principle, cannot be used to map exactly a quantum spin lattice model into another quantum spin lattice model, since the operators are non-commutative. However, it is possible the mapping in the “classical” limit, establishing an equivalence between both quantum spin lattice models. To study the validity of this approach for quantum spin lattice model, we use the Zassenhaus formula, and we verify how the correction could influence the decoration transformation. But this correction could be useless to improve the quantum decoration transformation because it involves the second-nearest-neighbor and further nearest neighbor couplings, which leads into a cumbersome task to establish the equivalence between both lattice models. This correction also gives us valuable information about its contribution, for most of the Heisenberg type models, this correction could be irrelevant at least up to the third order term of Zassenhaus formula. This transformation is applied to a finite size Heisenberg chain, comparing with the exact numerical results, our result is consistent for weak xy-anisotropy coupling. We also apply to bond-alternating Ising–Heisenberg chain model, obtaining an accurate result in the limit of the quasi-Ising chain.     

The spin-1/2 Heisenberg Chains in Constant Magnetic Field and Coherent states1

In the ferromagnetic Heisenberg chains of XXX and XXZ types with the hidden symmetries of Lie bi-algebra su(2) and quantum bi-algebra su_q(2), we show that at thermodynamic limit the algebra contractions give the boson algebra h(4) and the q-deformed boion algebra h_q(2) as the hidden symmetries respectively. The chains in constant magnetic field are studied and the ground states and lowest excited states are given explicitly with energy spectra. The phonon (or angular momentum) excitations are shown to be bosonic for the isotropic case and q-bosonic for the anisotropic case, and the ground states and lowest excited states of the systems of the chains in field are given explicitly. We give the phonon coherent states in the isotropic Heisenberg chain and the q-coherent states of the anisotropic chain at the thermodynamic limit. The q-coherent states are shown to be a squeezed states of phonon excitations.     

Fractional charges in pyrochlore lattices

A pyrochlore lattice is considered where the average electron number of electrons per site is half‐integer, concentrating on the case of exactly half an electron per site. Strong on‐site repulsions are assumed, so that all sites are either empty or singly occupied. When there are in addition strong nearest‐neighbour repulsions, a tetrahedron rule comes into effect, as previously suggested for magnetite. We show that in this case, there exist excitations with fractional charge ±e/2. These are intimately connected with the high degeneracy of the ground state in the absence of kinetic energy terms. When an additional electron is inserted into the system, it decays into two point like excitations with charge ‐e/2, connected by a Heisenberg spin‐chain which carries the electron's spin.     

Physical realization of topological excitations in quantum Heisenberg ferromagnet on lattice

The physical spin configurations corresponding to the topological excitations expected to be present in the XY limit of a purely quantum spin \frac 12\frac {1}{2} Heisenberg ferromagnet, are investigated on a two dimensional square lattice. Quantum vortices (anti-vortices) are constructed by making use of the coherent spin field components from meronic (anti-meronic) configurations in the limiting case of very strong XY anisotropy. The equations for pseudo-time evolution of coherent spin fields used in this analysis, are obtained by applying variational principle on the quantum Euclidean action corresponding to the Heisenberg ferromagnet on lattice. The important role of the associated topological-like term extracted from the Wess-Zumino-like contribution, is highlighted in our procedure. It is shown that this term can identify a large class of vortices (anti-vortices). In particular the excitations having odd topological charges form this class. Our present formalism is markedly different from the conventional approach for the construction of quantum vortices (anti-vortices).     

Spin chains with nearest and next nearest neighbour interactions

The 1/n-expansion is applied to a classical one dimensionaln-vector model in an external field with nearest and next nearest neighbour exchange interactions of both signs. Various effects caused by helical spin structures are discussed for the Heisenberg magnet (n=3).—For the spherical model with multi-neighbour interactions Lifshitz points of higher order are found.     

Spin and isospin in a gauge theory with monopoles

The mechanism by which systems of spinless bosons with isospin and spinless magnetic monopoles acquire a spin in their ground states is investigated in the context of SU(2) gauge models. Contrary to recent claims, it is demonstrated that isospin degrees of freedom are not converted into spin degrees of freedom. For a spin $\text{1}\text{2}$ state, solutions are explicitly constructed, exhibiting the isospin degree of freedom.