Analysis of the Migdal transformation for models with planar spins on a d-dimensional lattice

We show analytically that in the Migdal approximation and at low temperatures planar spins on a d-dimensional lattice (d ⩾ 2) exhibit the same phase transitions as d-dimensional Z(n)-models. For a three-dimensional lattice part of the flow diagram of the Migdal mapping is found numerically, including large families of relevant fixed points which separate the low-temperature fixed points from the trivial high-temperature one. The critical exponents are obtained and for some two-parameter potentials the phase diagram is constructed and explained. After rescaling, quantitative agreement was obtained for one of the Migdal phase diagrams with the Monte Carlo phase diagram.     

On Heisenberg exchange of high spins

The well-known Kaplan-Alexander equations for chemical exchange are generalized to include Heisenberg exchange of high spins (S > 1/2). General expressions are obtained for the effect of the exchange on the shape and width of lines and on the population of spin eigenstates. The broadening action of an arbitrary spin on a spin of 1/2 is taken as an example.     

Nematic and chiral order for planar spins on a triangular lattice

We propose a variant of the antiferromagnetic XY model which includes a biquadratic (J2) as well as the quadratic (J1) interaction on the triangular lattice. The phase diagram for large J2/J1 exhibits a phase with coexisting quasi-long-range nematic, and long-ranged vector spin chirality orders in the absence of magnetic order, which qualifies our model as the first instance of a classical spin model that exhibits a vector chiral spin liquid phase. The interplay of nematic and spin chirality orders is discussed. A variety of critical properties are derived by means of Monte Carlo simulation.     

Controllable entanglement sudden birth of Heisenberg spins

We investigate the Entanglement Sudden Birth (ESB) of two Heisenberg spins A and B. The third controller, qutrit C is introduced, which only has the Dzyaloshinskii-Moriya (DM) spin-orbit interaction with qubit B. We find that the DM interaction is necessary to induce the Entanglement Sudden Birth of the system qubits A and B, and the initial states of the system qubits and the qurit C are also important to control its Entanglement Sudden Birth.     

Spin-wave modes in a compressible Heisenberg chain of classical spins

The spin dynamics of a compressible chain of classical spins is studied by means of a four pole approximation for the spin relaxation function. The frequency moments are calculated with the help of a computer. The general qualitative influence of the coupling to the phonons on the dynamic structure factor is discussed. Quantitative results for frequency shift, line width and the condition for the observability of spin waves are obtained. Especially the latter is quite different from the result for the rigid Heisenberg chain. The coupling to the phonon degrees of freedom does not lead to additional resonances in the spin spectrum.Aspirant van het Belgisch Nationaal Fonds voor Wetenschappelijk Onderzoek     

Spin-glass transition in bond-disordered Heisenberg antiferromagnets coupled with local lattice distortions on a pyrochlore lattice

Motivated by puzzling characteristics of spin-glass transitions widely observed in pyrochlore-based frustrated materials, we investigate the effects of coupling to local lattice distortions in a bond-disordered antiferromagnet on the pyrochlore lattice by extensive Monte Carlo simulations. We show that the spin-glass transition temperature T(f) is largely enhanced by the spin-lattice coupling and, furthermore, becomes almost independent of Δ in a wide range of the disorder strength Δ. The critical property of the spin-glass transition is indistinguishable from that of the canonical Heisenberg spin glass in the entire range of Δ. These peculiar behaviors are ascribed to a modification of the degenerate manifold from a continuous to semidiscrete one by spin-lattice coupling.     

Competition between Ising spins and classical n-vector spins on the honeycomb and the diced lattice

The competition between ordering and disordering is investigated for mixed spin models of Ising spins and classical n-vector spins on the honeycomb and the diced lattice. The critical indices of the specific heat and the spontaneous magnetization for the mixed spin models turn out to be the same as those for the two-dimensional Ising model.     

Bond operator theory for the frustrated anisotropic Heisenberg antiferromagnet on a square lattice

The quantum anisotropic antiferromagnetic Heisenberg model with single ion anisotropy, spin S=1 and up to the next-next-nearest neighbor coupling (the J₁–J₂–J₃ model) on a square lattice, is studied using the bond-operator formalism in a mean field approximation. The quantum phase transitions at zero temperature are obtained. The model features a complex T=0 phase diagram, whose ordering vector is subject to quantum corrections with respect to the classical limit. The phase diagram shows a quantum paramagnetic phase situated among Neél, spiral and collinear states.     

Non-Fermi-liquid behavior of impurity spins in the anisotropic Heisenberg chain

We consider a U(1)-invariant model consisting of the integrable anisotropic Heisenberg chain of arbitrary spin S embedding an impurity of spin S′. The impurity is assumed located on the mth link of the chain and interacting only with both neighboring sites. The coupling of the impurity to the lattice can be tuned by the impurity rapidity. The model is then integrable as a function of two continuous parameters (the anisotropy and the impurity rapidity) and two discrete variables (the spins S and S′). The thermodynamic Bethe ansatz equations are derived and used to analyze the small field and low temperature properties. Three situations have to be distinguished: (i) If S′ = S the impurity just corresponds to one more site in the chain. (ii) If S′ > S the impurity spin is only partially compensated at T = 0 and the entropy has an essential singularity at T = H = 0. (iii) If S′ < S the impurity is overcompensated, and again the entropy has an essential singularity at T = H = 0. The essential singularity gives rise to a quantum critical point and hence non-Fermi-liquid-like behavior as H and T tend to zero. While cases (i) and (iii) are analogous to the n-channel Kondo problem, case (ii) differs considerably as a consequence of critical behavior induced by the anisotropy.