Pseudospin Models Research Articles

Residual entropy of the dilute Ising chain in a magnetic field.

The properties of the ground state of the simplest frustrated system, the dilute Ising chain in a magnetic field, are rigorously investigated over the entire range of concentrations of charged nonmagnetic impurities. Analytical methods are proposed for calculating the residual entropy of frustrated states, including states at phase boundaries, which are based on the Markov property of the system and involve solving a linear optimization problem for energy and a nonlinear optimization problem for entropy. These methods allow obvious generalizations for one-dimensional pseudospin models with anisotropic interactions. We calculate the composition, entropy, and magnetization for the ground state phases. We prove the absence of pseudotransitions in the dilute Ising chain, since the residual entropy of states at phase boundaries is always higher than the entropy of adjacent phases. The concentration dependencies of magnetization at the phase boundaries are obtained, and unlike linear dependencies for adjacent phases, they have nonlinear behavior. Field-induced transitions between ground states and entropy jumps associated with them are also considered, and in particular, it is shown that the field-induced transition from an antiferromagnetic state to a frustrated one is accompanied by charge ordering.

Optical conductivity of semi-Dirac and pseudospin-1 models: Zitterbewegung approach

We present a method to calculate the optical conductivity of semi-Dirac and pseudospin models based on the evaluation of quasiparticle velocity correlators which also describe the phenomenon of zitterbewegung. Applying this method to the semi-Dirac model with merging Dirac cones and gapped dice and Lieb lattice models we find exact analytical expressions for optical longitudinal and Hall conductivities. For the semi-Dirac model the obtained expressions allow us to analyze the role of spectrum anisotropy, van Hove singularities and Dirac cones in longitudinal conductivity. In addition, we predict signatures of topological phase transition with changing gap parameter in such a system that are manifested in dc transport at low temperatures. For the dice and Lieb lattices we emphasize the role of spectral gap, which defines frequency thresholds related to transitions to and from flat band.

Exchange interactions, Jahn-Teller coupling, and multipole orders in pseudospin one-half 5d2 Mott insulators

We develop a microscopic theory of multipole interactions and orderings in $5{d}^{2}$ transition metal ion compounds. In a cubic environment, the ground state of $5{d}^{2}$ ions is a non-Kramers ${E}_{g}$ doublet, which is nonmagnetic but hosts quadrupole and octupole moments. We derive low-energy pseudospin one-half Hamiltonians describing various spin-orbital exchange processes between these ions. Direct overlap of the ${t}_{2g}$ orbitals results in bond-dependent pseudospin interactions similar to those for ${e}_{g}$ orbitals in manganites, except for different orientations of the pseudospin easy axes. On the other hand, the superexchange process, where two different ${t}_{2g}$ orbitals communicate via oxygen ions, generates new types of pairwise interactions. In perovskites with ${180}^{\ensuremath{\circ}}$ bonding, we find nearly equal mixture of Heisenberg and ${e}_{g}$ orbital compass-type couplings. The ${90}^{\ensuremath{\circ}}$ superexchange in compounds with edge-shared octahedra is most unusual: Despite highly anisotropic shapes of the ${E}_{g}$ wave functions, the pseudospin interactions have no bond dependence. We consider the ${E}_{g}$ pseudospin models on various lattices and obtain their ground state properties using analytical and numerical methods. On the honeycomb lattice, we observe a duality with the extended Kitaev model, and use it to uncover a critical point where the quadrupole and octupole states are exactly degenerate. On the triangular lattice, an exotic pseudospin state, corresponding to the coherent superposition of vortex-type quadrupole and ferri-type octupole orders, is realized due to geometrical frustration. This state breaks both spatial and time-reversal symmetries, but possesses no dipolar magnetism. We also consider Jahn-Teller coupling effects and lattice mediated interactions between ${E}_{g}$ pseudospins, and find that they support quadrupole order. Possible implications of the results for recent experiments on double perovskite osmates are discussed, including effects of local distortions on the pseudospin wave functions and interactions.

Divergence of the Grüneisen ratio at symmetry-enhanced first-order quantum phase transitions

Studies of the Gr\"uneisen ratio, i.e., the ratio between thermal expansion and specific heat, have become a powerful tool in the context of quantum criticality since it was shown theoretically that the Gr\"uneisen ratio displays characteristic power-law divergencies upon approaching the transition point of a continuous quantum phase transition. Here we show that the Gr\"uneisen ratio also diverges at a symmetry-enhanced first-order quantum phase transition, albeit with mean-field exponents, as the enhanced symmetry implies the vanishing of a mode gap which is finite away from the transition. We provide explicit results for simple pseudospin models, both with and without Goldstone modes in the stable phases, and discuss implications.

Lightwave terahertz quantum manipulation of nonequilibrium superconductor phases and their collective modes

We present a gauge-invariant density matrix description of non-equilibrium superconductor (SC) states with spatial and temporal correlations driven by intense terahertz (THz) lightwaves. We derive superconductor Bloch--Maxwell equations of motion that extend Anderson pseudo-spin models to include the Cooper pair center-of-mass motion and electromagnetic propagation effects. We thus describe quantum control of dynamical phases, collective modes, quasi-particle coherence, and high nonlinearities during cycles of carrier wave oscillations, which relate to our recent experiments. Coherent photogeneration of a nonlinear supercurrent with dc component via condensate acceleration by an effective lightwave field dynamically breaks the equilibrium inversion symmetry. Experimental signatures include high harmonic light emission at equilibrium-symmetry-forbidden frequencies, Rabi--Higgs collective modes and quasi-particle coherence, and non-equilibrium moving condensate states tuned by few-cycle THz fields. We use such lightwaves as an oscillating accelerating force that drives strong nonlinearities and anisotropic quasi-particle populations to control and amplify different classes of collective modes, e.g., damped oscillations, persistent oscillations, and overdamped dynamics via Rabi flopping. Recent phase-coherent nonlinear spectroscopy experiments can be modeled by solving the full nonlinear quantum dynamics including self-consistent light--matter coupling.

Theory of optically controlled anisotropic polariton transport in semiconductor double microcavities

Exciton polaritons in semiconductor microcavities exhibit many fundamental physical effects, with some of them amenable to being controlled by external fields. The polariton transport is affected by the polaritonic spin-orbit interaction, which is caused by the splitting of transverse-electric and transverse-magnetic (TE-TM) modes. This is the basis for a polaritonic Hall effect, called optical spin Hall effect (OSHE), which is related to the formation of spin/polarization textures in momentum space, determining anisotropic ballistic transport, as well as related textures in real space. Owing to Coulombic interactions between the excitonic components of the polaritons, optical excitation of polaritons can affect the OSHE. We present a theoretical analysis of the OSHE and its optical control in semiconductor double microcavities, i.e. two optically coupled cavities, which are particularly well suited for the creation of polaritonic reservoirs that affect the spin-texture-forming polaritons. The theory is formulated in terms of a set of double-cavity spinor-polariton Gross-Pitaevskii equations. Numerical solutions feature, among other things, a controlled rotation of the spin texture in momentum space. The theory also allows for an identification of the effective magnetic field component that determines the optical control in phenomenological pseudo-spin models in terms of exciton interactions and the polariton density in the second lower polariton branch.

Spin Models for Ferroelastics: towards a Spin Glass Description of Strain Glass

We review the description of ferroelastic transitions in terms of spin models. We show how one can systematically obtain a pseudo-spin Hamiltonian from the Landau energy describing the first order transition between Austenite/Martensite phases. It is shown that a Local Mean-field approximation predicts the same microstructure as the continuous Landau model in terms of strain variables. This method can be applied to a wide range of two and three dimensional transitions. We then demonstrate how quenched disorder in such pseudo-spin models yields the existence of a glass phase, characterized by the Edwards-Anderson order parameter. Our approach uses Mean-field approximation and Monte-Carlo simulations (using Zero Field Cooling/Field Cooling experiments) to study the influence of the long-range interactions. Although our model captures the salient features of a ferroelastic material in the presence of disorder, the influence of the disorder on the high symmetry austenite phase is not quite consistent with expected behavior. We examine different means of introducing disorder that can improve upon the results.

Bilayer quantum Hall system atνt=1: Pseudospin models and in-plane magnetic field

We investigate two theoretical pseudomagnon-based models for a bilayer quantum Hall system (BQHS) at total filling factor $\nu_t = 1$. We find a unifying framework which elucidates the different approximations that are made. We also consider the effect of an in-plane magnetic field in BQHSs at $\nu_t = 1$, by deriving an equation for the ground state energy from the underlying microscopic physics. Although this equation is derived for small in-plane fields, its predictions agree with recent experimental findings at stronger in-plane fields, for low electron densities. We also take into account finite-temperature effects by means of a renormalisation group analysis, and find that they are small at the temperatures that were investigated experimentally.

Macroscopic quantum tunneling effect ofZ2topological order

In this paper, macroscopic quantum tunneling (MQT) effect of Z2 topological order in the Wen-Plaquette model is studied. This kind of MQT is characterized by quantum tunneling processes of different virtual quasi-particles moving around a torus. By a high-order degenerate perturbation approach, the effective pseudo-spin models of the degenerate ground states are obtained. From these models, we get the energy splitting of the ground states, of which the results are consistent with those from exact diagonalization method

Spin density matrix of a two-electron system. II. Application to a system of two quantum dots

This work is a sequel to our preceding work [Phys. Rev. B 77, 045319 (2008)]. Here we compare pure-spin and pseudospin dynamics using as an example a system of two quantum dots, a pair of localized conduction-band electrons in an $n$-doped GaAs semiconductor. Pure-spin dynamics is obtained by tracing out the orbital degrees of freedom, whereas pseudospin dynamics retains (as is conventional) an implicit coordinate dependence. We show that magnetic field inhomogeneity and spin-orbit interaction result in a nonunitary evolution in pure-spin dynamics, whereas these interactions contribute to the effective pseudospin Hamiltonian via terms that are asymmetric in spin permutations, in particular, the Dzyaloshinskii-Moriya (DM) spin-orbit interaction. We numerically investigate the nonunitary effects in the dynamics of the triplet-state population, purity, and Lamb energy shift as a function of interdot distance and magnetic field difference $\ensuremath{\Delta}\stackrel{P\vec}{B}$. The spin-orbit interaction is found to produce effects of roughly 4 orders of magnitude smaller than those due to $\ensuremath{\Delta}\stackrel{P\vec}{B}$ in the pure-spin model. We estimate the spin-orbit interaction magnitude in the DM-interaction term. Our estimate gives a smaller value than that recently obtained by Kavokin [Phys. Rev. B 64, 075305 (2001)], who did not include double-occupancy effects. We show that a necessary and sufficient condition for obtaining a universal set of quantum logic gates, involving only two spins, in both pure-spin and pseudospin models is that the magnetic field inhomogeneity $\ensuremath{\Delta}\stackrel{P\vec}{B}$ and the Heisenberg interaction are both nonvanishing. We also briefly analyze pure-spin dynamics in the electron on liquid helium system recently proposed by Lyon [Phys. Rev. A 74, 052338 (2006)].

Phase transitions and molecular dynamics in the cyclohexane/thiourea inclusion compound

In thiourea inclusion compounds the host structure comprises a hydrogen bonded arrangement of thiourea molecules and contains unidirectional, nonintersecting channels within which guest molecules are located. Structural and dynamic properties of the cyclohexane/thiourea inclusion compound have been studied previously by a wide range of experimental techniques, providing contradictory interpretations. This organic composite crystal displays three thermotropic structural phases on cooling from room temperature, denoted phase I (rhombohedral), phase II (monoclinic), and phase III (monoclinic). However, until now, there has been no attempt to understand the relationship between the dynamics of the guest molecules and the structural and symmetry properties of the composite inclusion compound in the three phases. In the first part of this paper, we determine the space group of each phase from powder x-ray diffraction data. From this knowledge of the symmetry properties of each phase, the phase transitions are described in terms of order parameters defined on the basis of the symmetry principles of Landau theory. Theoretical analysis of the crystal strain occurring at the phase transitions allows a direct comparison between the experimental temperature dependence of the lattice parameters and predictions derived from Landau theory. In the second part of this paper, we report results from powder and single-crystal ${}^{2}\mathrm{H}$ NMR spectroscopy on samples of cyclohexane/thiourea containing perdeuterated cyclohexane guest molecules $({\mathrm{C}}_{6}{\mathrm{D}}_{12}).$ These ${}^{2}\mathrm{H}$ NMR experiments have shown that in phase I, the motionally averaged quadrupole coupling tensor is axially symmetric. On passing from phase I to phase II, the threefold symmetry axis of the $R=3\ifmmode\bar\else\textasciimacron\fi{}c$ space group of phase I is lost, such that the motionally averaged quadrupole interaction tensor is not axially symmetric in phase II. The single crystal ${}^{2}\mathrm{H}$ NMR spectra probe very precisely the relative orientations of the guest molecules, which are consistent with the site symmetry properties of the structure and proposed modes of crystal twinning, and demonstrate that there is only one type of dynamic species of guest molecule in phase II. In phase III, a greater degree of orientational ordering of the cyclohexane molecules is evident. From a detailed consideration of the symmetry properties of the inclusion compound, the dynamics of the guest molecules may be described using simple jump models (i.e., multidimensional pseudospin models) in all three phases. Using these models, the temperature dependence of the order parameter components has been established. These results, in conjunction with x-ray diffraction, provide important information needed to propose a microscopic model for the mechanisms of the phase transitions in the cyclohexane/thiourea inclusion compound.

Models for the description of uniaxially modulated materials

Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables assigned to discrete crystallographic units (unit cells or parts of them). Especially considered are symmetry-based pseudo spin models. Methods are discussed which permit the handling of the statistical mechanics of such models, the translation of model calculation results to a form allowing the prediction of experimental data, and the theoretical determination of point defect influences.

From crystal structure to phase diagrams: Use of annni- and related models

Abstract The suitability of different pseudo spin models for a description of materials exhibiting modulated structures is discussed. We propose certain local generalized coordinates as a basis for an expansion of the displacements in BCCD. The theoretical treatment is simplified by a mapping to corresponding pseudo spin models with one or more spin components depending on the number of local normal modes relevant for the phase transitions. Furthermore, critical exponents at the boundary of the para phase as expected from the ANNNI model are compared with experimental results.

THE UNDERLYING PHYSICS OF q-DEFORMED PSEUDOSPIN MODELS

In this paper, we have used the q-deformed version of the Lipkin-Meshkov-Glick (LMG) model to summarize the utilization of quantum algebras already applied to soluble pseudospin models. Within the suq(2) context, we have checked the validity of the co herent states variational method, then used the Time Dependent Hartree-Fock (TDHF) approximation to compare with the exact evolution in time of the system, and finally observed the temperature effects undergone by the system, through the study of the Helmholtz free energy. We have also investigated the LMG model within the contexts of the supq(2) and suq(3) algebras and some of the features mentioned above have been rediscussed.

Pseudospin Models of Superconductors with Very Short Coherence Length

We discuss a few models developed for description of superconductivity with very short coherence length and point out their formal equivalence to specific spin models, such as an anisotropic Heisenberg model (s = 1/2) with twoand four-spin exchange coupling and with fixed magnetization in the z-direction, an XY-Z model with single ion anisotropy and a Kondo-lattice model with anisotropic on-site exchange. New results concerning the phase diagram of the Hubbard model with strong attraction, the electromagnetic properties of systems with the first order superconducting transition and a possibility of local charge moment compensation in systems of coexisting bound pairs and itinerant electrons are presented. PACS numbers: 74.20.—z, 05.30.Jp,

In situ observation of the polytypic phase transition 2H-12R in PbI2: investigations of the thermodynamic structural and dielectric properties

A reversible phase transition between the two polytypic phases 2H and 12R was found in PbI2 near 367K which proves that these polytypes are thermodynamic equilibrium phases and not the result of growth processes. Disordered stackings were observed in samples which were annealed at temperatures above 420K. The phase transition is kinetically hindered with an activation energy of 3.8 eV. The character of the phase transition is first order with a latent heat of around 276 J mol-1. The absence of dielectric anomalies with electric fields along the hexagonal c axis indicates that dipole-dipole interactions are not involved in the transition mechanism. The nature of the inter-layer forces are exclusively based on short-range interactions leading to a description of the phase transition in terms of pseudo-spin models. The elastic energy released during the phase transition is 1.2 J mol-1 as determined from the observed jump of the c lattice parameter. A thermodynamic description of the phase transition leads to the conclusion that its driving forces are related to the gain of phonon energy and elastic energy during the transformation. The entropy gain is due to the differences of the phonon frequencies between the two phases. Higher polytypes, if thermodynamically stable phases, can be described as mixtures of structural elements of the basic polytypes with additional stabilisation energies. The temperature evolution of the free energies of the different phases is anticipated. The experimental results are expressed in terms of the Landau theory which shows that the phase transition 2H-12H must be first order as observed. The Landau theory also explains the disordered polytype as a common para-phase for all ordered polytypes. Further insight into the origin of polytypism can be derived from the current understanding of ANNNI models.

Optical Study on the Phase Transitions in KH2PO4 and KD2PO4

The infrared spectra of the PO4 stretching vibrations have been studied on KH2PO4 and KD2PO4 over a wide range of temperature. A trend of the intensity variation with temperature for these bands is similar in each compound, but is very different between both compounds. An inspection of the intensity behaviors indicates that each PO4 group is attached equivalently by four hydrogen atoms in KH2PO4, and by two deuterium atoms in KD2PO4, above the respective transition points. Namely, each of the hydrogen and phosphorus atoms in KH2PO4 moves in a single-minimum potential well with a flattened bottom, while each of the corresponding atoms in KD2PO4 moves in a double-minimum potential well. Further, non-existence is evidenced for a Slater configuration connected with an energy parameter ε0 in his model. As a result, it is concluded that the displacive and pseudospin models are the most relevant in describing the phase transition mechanisms in KH2PO4 and KD2PO4, respectively.