Irrational charge from topological order

Topological or deconfined phases of matter exhibit emergent gauge fields and quasiparticles that carry a corresponding gauge charge. In systems with an intrinsic conserved U(1) charge, such as all electronic systems where the Coulombic charge plays this role, these quasiparticles are also characterized by their intrinsic charge. We show that one can take advantage of the topological order fairly generally to produce periodic Hamiltonians which endow the quasiparticles with continuously variable, generically irrational, intrinsic charges. Examples include various topologically ordered lattice models, the three-dimensional resonating valence bond liquid on bipartite lattices as well as water and spin ice. By contrast, the gauge charges of the quasiparticles retain their quantized values.     

Induced electric charges of photons and neutrinos in an ultra-relativistic degenerate dense plasma

It is shown that photons and neutrinos acquire effective electric charges due to the space charge electric fields that are created by the ponderomotive forces of photons and neutrinos in an ultra-relativistic degenerate dense plasma. Explicit expressions for the induced charges are presented.     

Two dimensional gases of weight charges and SU(N) fermino theories

We analyze two dimensional gases composed of particles interacting via a Coulomb or Yakawa potential through their “non-Abelian” charges. These charges are taken to be elementary weight or root vectors of SU(N). The grand partition function of these gases is shown to be equivalent to the generating functional of sine-Gordon models with weight vectors and hence to that of SU(N) fermion models. The fermion field creates or annihilates topological solitons which have elementary weight vectors as topological quantum numbers. Then, we discuss the confinement of fermions in the SU(N) Higgs models, where instantons (Z_N vortices) constitute a Yukawa gas of weight charges. We prove that fermions are confirmed by the effects of instantons in the SU(N) Higgs models in contrast with the Abelian Higgs model.     

Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas

Many two-dimensional spin models can be transformed into Coulomb-gas systems in which charges interact via logarithmic potentials. For some models, such as the eight-vertex model and the Ashkin-Teller model, the Coulomb-gas representation has added significantly to the insight in the phase transitions. For other models, notably theXY model and the clock models, the equivalence has been instrumental for almost our entire understanding of the critical behavior. Recently it was shown that theq-state Potts model and then-vector model are equivalent to a Coulomb gas with an asymmetry between positive and negative charges. Fieldlike operators in these spin models transform noninteger charges and magnetic monopoles. With the aid of exactly solved models the Coulombgas representation allows analytic calculation of some critical indices.     

Exclusion Processes with Degenerate Rates: Convergence to Equilibrium and Tagged Particle

Stochastic lattice gases with degenerate rates, namely conservative particle systems where the exchange rates vanish for some configurations, have been introduced as simplified models for glassy dynamics. We introduce two particular models and consider them in a finite volume of size in contact with particle reservoirs at the boundary. We prove that, as for non-degenerate rates, the inverse of the spectral gap and the logarithmic Sobolev constant grow as ². It is also shown how one can obtain, via a scaling limit from the logarithmic Sobolev inequality, the exponential decay of a Lyapunov functional for a degenerate parabolic differential equation (porous media equation). We analyze finally the tagged particle displacement for the stationary process in infinite volume. In dimension larger than two we prove that, in the diffusive scaling limit, it converges to a Brownian motion with non-degenerate diffusion coefficient.     

Matter Collineations in Kantowski-Sachs, Bianchi Types I and III Spacetimes

The matter collineation classifications of Kantowski-Sachs, Bianchi types I and III space times are studied according to their degenerate and non-degenerate energy-momentum tensor. When the energy-momentum tensor is degenerate, it is shown that the matter collineations are similar to the Ricci collineations with different constraint equations. Solving the constraint equations we obtain some cosmological models in this case. Interestingly, we have also found the case where the energy-momentum tensor is degenerate but the group of matter collineations is finite dimensional. When the energy-momentum tensor is non-degenerate, the group of matter collineations is finite-dimensional and they admit either four which coincides with isometry group or ten matter collineations in which four ones are isometries and the remaining ones are proper.     

Phase separation of highly dissymmetric binary ionic mixtures

We study the phase separation of binary ionic mixtures involving two species of classical point ions in a rigid uniform neutralizing background of degenerate electrons. The thermodynamic properties of the ionic fluid are calculated on the basis of the HNC integral equation for the three partial pair distribution functions. We develop a systematic technique which allows the properties of mixtures of arbitrary composition to be expressed in terms of infinitely dilute solutions. Phase diagrams and critical parameters are determined for 12 different binary systems involving ionic charge ratios between 2 and 8. The dependence of the critical temperature on the ionic charges, on the pressure and an ionic quantum corrections is examined in detail.     

A multi-orbital iterated perturbation theory for model Hamiltonians and real material-specific calculations of correlated systems

The dynamical mean field theory (DMFT) has emerged as one of the most importantframeworks for theoretical investigations of strongly correlated lattice models and realmaterial systems. Within DMFT, a lattice model can be mapped onto the problem of amagnetic impurity embedded in a self-consistently determined bath. The solution of thisimpurity problem is the most challenging step in this framework. The available numericallyexact methods such as quantum Monte Carlo, numerical renormalization group or exactdiagonalization are naturally unbiased and accurate, but are computationally expensive.Thus, approximate methods, based e.g. on diagrammatic perturbation theory have gainedsubstantial importance. Although such methods are not always reliable in various parameterregimes such as in the proximity of phase transitions or for strong coupling, theadvantages they offer, in terms of being computationally inexpensive, with real frequencyoutput at zero and finite temperatures, compensate for their deficiencies and offer aquick, qualitative analysis of the system behavior. In this work, we have developed such amethod, that can be classified as a multi-orbital iterated perturbation theory (MO-IPT) tostudy N-folddegenerate and non degenerate Anderson impurity models. As applications of the solver, wehave embedded the MO-IPT within DMFT and explored lattice models like the single orbitalHubbard model, covalent band insulator and the multi-orbital Hubbard model fordensity-density type interactions in different parameter regimes. The Hund’s couplingeffects in case of multiple orbitals is also studied. The limitations and quality ofresults are gauged through extensive comparison with data from the numerically exactcontinuous time quantum Monte Carlo method (CTQMC). In the case of the single orbitalHubbard model, covalent band insulators and non degenerate multi-orbital Hubbard models,we obtained an excellent agreement between the Matsubara self-energies of MO-IPT andCTQMC. But for the degenerate multi-orbital Hubbard model, we observe that the agreementwith CTQMC results gets better as we move away from particle-hole symmetry. We have alsointegrated MO-IPT+DMFT with density functional theory based electronic structure methodsto study real material systems. As a test case, we have studied the classic, stronglycorrelated electronic material, SrVO₃. A comparison of density of states and photo emissionspectrum (PES) with results obtained from different impurity solvers and experimentsyields good agreement.     

Classification of conformal field theories based on Coulomb gases. Application to loop models

We present a method for classifying conformal field theories based on Coulomb gases (bosonic free-field construction). Given a particular geometric configuration of the screening charges, we give necessary conditions for the existence of degenerate representations and for the closure of the vertex-operator algebra. The resulting classification contains, but is more general than, the standard one based on classical Lie algebras. We then apply the method to the Coulomb gas theory for the two-flavoured loop model of Jacobsen and Kondev. The purpose of the study is to clarify the relation between Coulomb gas models and conformal field theories with extended symmetries.     

Instabilities due to charge-density-curvature coupling in charged membranes

Instabilities are caused by the reduction in the electrostatic energy when the membrane is curved with the higher charge density on the bilayer which is stretched by the curvature. In a bilayer where the charges can flip from one lipid layer to the other, there is a thermodynamic instability to a spontaneously curved state with different charge densities on the two sides. If the charges are not permitted to flip, there is a dynamical instability due to the correlated modulation of the charge density and curvature fields. Numerical estimates show that these effects are present in parameter regimes relevant to biological systems.     

On topological excitations with isovector topological charges

It is shown that degenerate systems with order parameter ψ taking on values in compact homogeneous subspaces T _G or G/T _G (where G is a simple compact group and T _G is its maximum commutative subgroup) possess a rich collection of topological excitations (vortices or, correspondingly, instantons) with isovector topological charges. The corresponding homotopy groups are found for all G. The possibility of a topological interpretation of the quantum numbers of the groups and particles is discussed. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 10, 758–762 (25 May 1996)     

Tracer Kinetics: Modelling by Partial Differential Equations of Inhomogeneous Compartments with Age-Dependent Elimination Rates; Part 2: Examples of Application

The general theory of inhomogeneous compartments with age-dependent elimination rates given in part I in a deterministic frame by sets of partial differential equations is illustrated by examples. Mathematically, it turns out that models consisting of partial differential equations include ordinary, delayed and integro-differential equations, a general fact which is treated here in the context of linear tracer kinetics. The examples include standard compartments as a degenerate case, systems of standard compartments (compartment blocks), models resulting in special residence time distributions, models with pipes, and systems with heterogeneous particles.     

Convergent expansions for asymptotically degenerate inverse correlation lengths of classical lattice spin systems

We obtain convergent expansions for the inverse correlation length associated with various spin-spin correlation functions for some weakly coupled multicomponent classical lattice spin systems. In terms of the lattice quantum field theory associated with the models the expansions provide a convergent perturbation theory for particle masses which are asymptotically degenerate in the limit of zero coupling.Reseach partially supported by CNPq, Brazil.     

Radiative stability of neutrino-mass textures

Neutrino-mass textures proposed at high scales are known to be unstable against radiative corrections especially for nearly degenerate mass eigenvalues. We find a mechanism in a class of gauge models including 2HDM where the RG constraints can be evaded. Consequently, a high-scale texture can match the low-energy data or be reproduced at low energies.     

Peierls instabilities in one-dimensional systems with Jahn-Teller-active monomers

A one-dimensional system is investigated which consists of monomers with Jahn-Teller-active vibrational coordinates. Peierls distortions in the ground states of the half- and quarter-filled systems are studied as a function of the electron-lattice and Jahn-Teller coupling constants. For both degrees of filling and for all the values of the coupling constants the band structure of the ground state is doubly degenerate. The interrelation is discussed between the present system and systems where the active internal degrees of freedom are not of the Jahn-Teller type.     

Electron fractionalization in two-dimensional graphenelike structures

Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall fluids, where time-reversal symmetry is broken by a large external magnetic field. Recently, there has been a tremendous effort in the search for examples of fractionalization in two-dimensional systems with time-reversal symmetry. In this Letter, we show that fractionally charged topological excitations exist on graphenelike structures, where quasiparticles are described by two flavors of Dirac fermions and time-reversal symmetry is respected. The topological zero modes are mathematically similar to fractional vortices in p-wave superconductors. They correspond to a twist in the phase in the mass of the Dirac fermions, akin to cosmic strings in particle physics.     

Coulomb correlations and electron-hole liquid in double quantum wells

It has been shown that many-body Coulomb correlations in double quantum wells with spatially separated electrons and holes result in the formation of a degenerate electron-hole liquid where an average distance between the particles is smaller than the size of an isolated exciton. This state turns out to be energetically more favorable than the exciton gas. The results have been obtained under the assumption that there are many different sorts of electrons and holes in the system, which is the case, in particular, in multivalley semiconductors. The relation to the experiments on the observation of luminescent regions in such systems is discussed.     

Charge distribution in structurally disordered systems

In this paper we calculate the charge distribution n(Q) for a structurally disordered system of identical atoms. The atoms have non-zero charges associated to them only because the spatial configuration around each atom is different. The systems considered are those for which an atomic basis set is adequate and an iterative tight binding scheme, where the matrix elements depend on the atomic charges, is used. We study the effect of including explicitly the electrostatic interaction among the charges associated to the atoms in the calculation of n(Q). We propose that the atomic positions of a totally random configuration be modified by amounts proportional to the electrostatic forces on the atoms. We call this a relaxation effect. We find that the new atomic configurations give a narrower n(Q) although they have practically the same energy and radial distribution function as the original configuration.     

Branch Processes of Regular Magnetic Monopole

In this paper, by making use of Duan＇s topological current theory, the branch process of regular magnetic monopoles is discussed in detail. Regular magnetic monopoles are found generating or annihilating at the limit point and encountering, splitting, or merging at the bifurcation point and the degenerate point systematically of the vector order parameter field φ（x）. Furthermore, it is also shown that when regular magnetic monopoles split or merge at the degenerate point of field function φ, the total topological charges of the regular magnetic monopoles are stilI unchanged.     

Role of spin in quasiparticle interference

Quasiparticle interference patterns measured by scanning tunneling microscopy can be used to study the local electronic structure of metal surfaces and high-temperature superconductors. Here, we show that even in nonmagnetic systems the spin of the quasiparticles can have a profound effect on the interference patterns. On Bi(110), where the surface state bands are not spin degenerate, the patterns are not related to the dispersion of the electronic states in a simple way. In fact, the features which are expected for the spin-independent situation are absent and the observed interference patterns can be interpreted only by taking spin-conserving scattering events into account.