Effective Lattice Model Research Articles

Application of theS=1underscreened Anderson lattice model to Kondo uranium and neptunium compounds

Magnetic properties of uranium and neptunium compounds showing the coexistence of the Kondo screening effect and ferromagnetic order are investigated within the Anderson lattice Hamiltonian with a two-fold degenerate $f$ level in each site, corresponding to $5{f}^{2}$ electronic configuration with $S=1$ spins. A derivation of the Schrieffer-Wolff transformation is presented and the resulting Hamiltonian has an effective $f$-band term, in addition to the regular exchange Kondo interaction between the $S=1$ $f$ spins and the $s=1/2$ spins of the conduction electrons. The resulting effective Kondo lattice model can describe both the Kondo regime and a weak delocalization of the $5f$ electrons. Within this model we compute the Kondo and Curie temperatures as a function of model parameters, namely the Kondo exchange interaction constant ${J}_{K}$, the magnetic intersite exchange interaction ${J}_{H}$, and the effective $f$ bandwidth. We deduce, therefore, a phase diagram of the model which yields the coexistence of the Kondo effect and ferromagnetic ordering and also accounts for the pressure dependence of the Curie temperature of uranium compounds such as UTe.

Order-disorder transitions: structural and magnetic ordering in double perovskites

Using an effective lattice gas-like model for B-B′ site ordering we study order-disorder transitions in double perovskite materials A2BB′O6. We motivate this effective model from a microscopic hamiltonian. Using this model, we are able to address several experimentally observed issues including nonmonotonic dependence of the degree of order on annealing temperature, and the rapid decrease of order upon overdoping with either B or B′ species. We also study ordering in the ‘ternary’ compounds A2BB′1−yB″yO6, using a variant of the Blume-Emery-Griffiths model. Several issues related to structural and magnetic ordering are discussed.

Effective single-band models for strongly interacting fermions in an optical lattice

To test effective Hamiltonians for strongly interacting fermions in an optical lattice, we numerically find the energy spectrum for two fermions interacting across a Feshbach resonance in a double well potential. From the spectrum, we determine the range of detunings for which the system can be described by an effective lattice model, and how the model parameters are related to the experimental parameters. We find that for a range of strong interactions the system is well described by an effective $t-J$ model, and the effective superexchange term, $J$, can be smoothly tuned through zero on either side of unitarity. Right at and around unitarity, an effective one-band general Hubbard model is appropriate, with a finite and small on-site energy, due to a lattice-induced anharmonic coupling between atoms at the scattering threshold and a weakly bound Feshbach molecule in an excited center of mass state.

Artificial staggered magnetic field for ultracold atoms in optical lattices

A time-dependent optical lattice with staggered particle current in the tight-binding regime was considered that can be described by a time-independent effective lattice model with an artificial staggered magnetic field. The low-energy description of a single-component fermion in this lattice at half-filling is provided by two copies of ideal two-dimensional massless Dirac fermions. The Dirac cones are generally anisotropic and can be tuned by the external staggered flux $\ensuremath{\phi}$. For bosons, the staggered flux modifies the single-particle spectrum such that in the weak coupling limit, depending on the flux $\ensuremath{\phi}$, distinct superfluid phases are realized. Their properties are discussed, the nature of the phase transitions between them is established, and Bogoliubov theory is used to determine their excitation spectra. Then the generalized superfluid--Mott-insulator transition is studied in the presence of the staggered flux and the complete phase diagram is established. Finally, the momentum distribution of the distinct superfluid phases is obtained, which provides a clear experimental signature of each phase in ballistic expansion experiments.

Correlation-Induced Metal Insulator Transition in a Two-Channel Fermion-Boson Model

We investigate charge transport within some background medium by means of an effective lattice model with a novel form of fermion-boson coupling. The bosons describe fluctuations of a correlated background. By analyzing ground state and spectral properties of this transport model, we show how a metal-insulator quantum phase transition can occur for the half-filled band case. We discuss the evolution of a mass-asymmetric band structure in the insulating phase and establish connections to the Mott and Peierls transition scenarios.

Orbital ordering and magnetic interactions in BiMnO3

This work is devoted to the analysis of the orbital ordering patterns and associated interatomic magnetic interactions in the centrosymmetric monoclinic structures of BiMnO3, which have been recently determined experimentally. First, we set up an effective lattice fermion model for the manganese 3d bands and derive parameters of this model from first-principles electronic structure calculations. Then, we solve this model in terms of the mean-field Hartree–Fock method and obtain parameters of interatomic magnetic interactions between Mn ions. We argue that although the nearest-neighbor interactions favor the ferromagnetism, they compete with the longer range antiferromagnetic (AFM) interactions, the existence of which is directly related to the peculiar geometry of the orbital ordering pattern realized in BiMnO3 below 474 K. These AFM interactions favor an AFM alignment, which breaks the inversion symmetry. The formation of the AFM phase is additionally assisted by the orbital degrees of freedom, which tend to adjust the nearest-neighbor magnetic interactions in the direction which further stabilizes this phase. We propose that the multiferroelectric behavior, which was observed in BiMnO3, may be related to the emergence of the AFM phase under certain conditions.

Lateral Diffusion of Proteins in the Plasma Membrane: Spatial Tessellation and Percolation Theory

The obstructed diffusion of proteins in the plasma membrane is studied using computer simulation and an analysis using spatial tessellation and percolation theory. The membrane is modeled as a two-dimensional space with fixed hard disc obstacles, and the proteins are modeled as hard discs. The simulations show a transition from normal to anomalous diffusion as the area fraction, phim, of obstacles is increased and to confined diffusion for area fractions above the pecolation threshold, which occurs for phim=0.22. A Voronoi tessellation procedure is used to map the continuous space system onto an effective lattice model, with the connectivity of bonds determined from a geometric criterion. The estimate of the percolation threshold obtained from this lattice model is in excellent agreement with the simulation results, although the nature of the dynamics in the continuous space model is different from lattice models. At high obstacle area fractions (but below the percolation threshold), the primary mode of transport is a hopping motion between voids, consistent with experiment. The simulations and analysis emphasize the importance of structural correlations between obstacles.

Coherence and localization in AC-driven quantum dots

We investigate the effects of an AC field on the dynamics of interacting electrons in quantum dots (QDs). We first consider a double QD containing two electrons. By mapping the system to an effective lattice model and employing Floquet theory we analyze the dynamics of the two-electron wavefunctions in the singlet space. This system presents a richer phenomenology than the case of a single electron in a double QD, displaying two distinct regimes of behaviour depending on whether the applied field strength or the inter-electron Coulomb repulsion is dominant. We then study the dynamics of two electrons in a 2D square QD in the limit of very low density, where the Coulomb interaction causes the electrons to become highly localized, forming a ‘Wigner molecule’. Using the same techniques we investigate how the AC field drives the dynamics of the Wigner states, and show how the parameters of the effective model may be measured in experiment.

Bond and Néel order and fractionalization in ground states of easy-plane antiferromagnets in two dimensions

We describe the zero-temperature phases and phase boundaries of an effective lattice model for frustrated, easy plane, spin $S=1/2$ quantum antiferromagnets. The model contains states with N\'eel and bond-centered charge order and fractionalization in different limiting regimes, and we describe how these orders compete at intermediate coupling. The complex Berry phase terms render this model unsuitable for direct simulation, however, a duality mapping leads to a model of interacting current loops with positive weights, which is then studied by Monte Carlo simulations.

Lattice regularization of the chiral Schwinger model

We analyze the chiral Schwinger model on an infinite lattice using the continuum definition of the fermion determinant and a linear interpolation of the lattice gauge fields. Using the non-compact formulation of the gauge field action it is proven that the effective lattice model is Osterwalder-Schrader positive, which is a sufficient condition for the reconstruction of a physical Hilbert space from the model defined on a Euclidean lattice. We furthermore establish the existence of critical points where the corresponding continuum theory can be reconstructed. We show that the continuum limit for the two-point functions of field strength and chiral densities can be controlled analytically. The article ends with some remarks on fermionic observables.

Quantum mechanics on thin cylinders.

We discuss the quantum mechanics of particles of arbitrary statistics on an infinite cylinder with and without a magnetic field perpendicular to the surface. In the presence of a magnetic field, the translational symmetry along the cylinder is broken down to a discrete one by the Aharonov-Bohm effect. For interacting fermions in a strong field we get an effective one-dimensional lattice model that in a limit can be mapped on an Ising chain. We also show that a system of anyons on a cylinder are, in a certain limit closely related to the one-dimensional (integrable) Sutherland model. By order of magnitude estimates we demonstrate that none of these effects are likely to be experimentally observed with present techniques.

Dynamics of holes and spins in the Hubbard t-J model and high-temperature superconductivity.

We study the t-J model as a microscopic model of high-temperature superconductors. The local constraints in the slave-fermion representation are solved by the projection operator onto the spin states and the ${\mathrm{CP}}^{1}$ spin variables. This resolution reveals that the antiferromagnetic (AF) J coupling of spins is accompanied with a four-Fermi interaction of charged holes. It describes attraction of fermionic holes on nearest-neighbor (NN) sites and induces formation of pairs of NN holes. Each pair carries two units of charge. Condensation of such hole pairs breaks the global U(1) charge symmetry and generates the superconductivity. The possible phase-separation state may become unstable against the uniform superconducting state due to the kinetic energy of holes. We obtain an effective lattice model in the short-range AF state by integrating out the odd-site spin fluctuations in the short-range AF order. Spin fluctuations induce attractions between next-NN holes. The model includes the effective model of Shraiman and Siggia for mobile holes in AF magnets as its normal-state part.Global magnetic properties, such as the N\'eel state and the spiral state, are described by this model. To study the superconducting phase, we develop a hole-pair theory by introducing auxiliary link variables as a hole-pair field. Their effective action gives the ``gap'' equation. The Ginzburg-Landau theory of it describes the superconducting-normal phase transition. We identify its general structure, which takes a form very similar to U(1) lattice gauge theory coupled with Higgs field. The pure gauge part reflects the magnetic J coupling, while the Higgs part is supplied by the elctron-hopping t term. The hole-pair condensation is expected at sufficiently large hole density because the phases of pair field are to be stabilized there coherently through a Higgs mechanism. A superconducting ``flux'' state of pairs is favored energetically. In this background condensation, low-energy excitations of holes are described by normal hopping of Fermi-liquid-type plus relativistic massive Dirac particles in a parity doublet. They are coupled with the gauge fields of ${\mathrm{CP}}^{1}$ spins in a U(1) gauge-invariant manner. This composes the hole part of our effective field theory in the superconducting phase. The spin part is the familiar nonlinear ${\mathrm{CP}}^{1}$ \ensuremath{\sigma} model. Our microscopic derivation of the effective field theory at low-temperature relates its parameters to those of the original t-J model. Throughout the study, we recognize a global and strong correlation between the magnetism and the superconductivity, or spins and holes, reflecting their common origin, i.e., the J coupling. The study of a simple solvable model presents a plausible critical line of superconductivity in the temperature-concentration plane.

Kinetics of Liquid‐Solid Phase Transition and Absolute Kinetic Coefficient for One‐Component Systems Derived from Molecular Theory

AbstractA master equation is derived to describe the kinetics of the phase transition from the liquid to the perfect f.c.c. crystalline state, and a straightforward calculation of the kinetic coefficient in terms of microscopie parameters is given for one‐component Lennard‐Jones systems just above the triple point. The considerations are based on an effective lattice model description of the interface structure and the calculation of elementary transition probabilities starting from the molecular theory of thermal equilibrium which is given in earlier papers, extending these results to non‐equilibrium by the local equilibrium principle. The calculated crystal growth velocity versus supercooling is about 10−3 m/sK which agrees with experimental data for some organic substances, but it is to small by a factor 101 to 102 for metals, probably for reasons of a rapid growth velocity enhancement due to an increasing defect density under a strong supercooling regime of 10–100 K, as reported.