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Showing papers in "International Journal of Modern Physics B in 1991"


Journal ArticleDOI
TL;DR: In this paper, the long distance decay of correlation functions in the one-dimensional Hubbard model is determined exactly for arbitrary bandfilling and correlation strength, using the exact solution of Lieb and Wu.
Abstract: A brief introduction to the bosonization method for interacting one-dimensional fermion systems is given. Using these results, the long-distance decay of correlation functions in the one-dimensional Hubbard model is determined exactly for arbitrary bandfilling and correlation strength, using the exact solution of Lieb and Wu. For infinite U the results are generalized to the case of nonzero nearest-neighbour interaction. The behaviour of thermodynamic quantities, of the frequency-dependent conductivity, and of the thermopower is also discussed, in particular in the proximity of the metal-insulator transitions occurring for half- and quarter-filling. The one-dimensional Luttinger liquid is shown to be unstable in the presence of interchain hopping. The results for the metal-insulator transition are compared with other scenarios developed in higher dimensions.

146 citations


Journal ArticleDOI
Subir Sachdev1, N. Read1
TL;DR: In this paper, a large N expansion technique based on symplectic (Sp(N)) symmetry was studied for frustrated magnetic systems, and the phase diagram of a square lattice, spin S, quantum antiferromagnet with first, s
Abstract: A large N expansion technique, based on symplectic (Sp(N)) symmetry, for frustrated magnetic systems is studied. The phase diagram of a square lattice, spin S, quantum antiferromagnet with first, s...

146 citations


Journal ArticleDOI
TL;DR: The Lyapunov exponents are invariants of the dynamical system and are connected with the dimension of the system attractor and to the idea of information generation by the system dynamics as discussed by the authors.
Abstract: We review the idea of Lyapunov exponents for chaotic systems and discuss their evaluation from observed data alone. These exponents govern the growth or decrease of small perturbations to orbits of a dynamical system. They are critical to the predictability of models made from observations as well as known analytic models. The Lyapunov exponents are invariants of the dynamical system and are connected with the dimension of the system attractor and to the idea of information generation by the system dynamics. Lyapunov exponents are among the many ways we can classify observed nonlinear systems, and their appeal to physicists remains their clear interpretation in terms of system stability and predictability. We discuss the familiar global Lyapunov exponents which govern the evolution of perturbations for long times and local Lyapunov exponents which determine the predictability over a finite number of time steps.

142 citations


Journal ArticleDOI
TL;DR: In this paper, it was argued that the three-dimensional (3D) vortex lattice is thermally entangled and may "melt" in high-Tc superconductors.
Abstract: In high-Tc superconductors (HTSC) the thermal fluctuation of the vortex lattice (VL) may become large since the vortex lattice is soft due to the strong overlap of the vortex fields and since the temperature T can be high. It was thus argued that the three-dimensional (3D) vortex lattice is thermally entangled and may “melt”. This type of transition and the consequences of melting are not clear as yet since the always present pinning of the vortex cores by material inhomogeneities may cause similar disorder. In HTSC the pinning energy may become comparable with kBT because the coherence length ξ (vortex radius) is small and T may be high. Therefore, thermally activated depinning competes with possible effects of “flux melting”, and the “irreversibility line” in the B-T-plane (B=magnetic field) should better be called “depinning line”. Due to the diffusive character of flux motion the depinning line of a given experiment, a line of constant flux diffusivity D(T, B), depends on the frequency or sweep rate, ...

129 citations


Journal ArticleDOI
TL;DR: In this paper, the topological orders in strongly correlated quantum liquids are reviewed. And the characterization of the topology through ground state degeneracy, non-Abelian Berry's phases and edge excitations are discussed.
Abstract: We review the topological orders in strongly correlated quantum liquids. The characterization of the topological orders through ground state degeneracy, non-Abelian Berry's phases and edge excitations are discussed.

102 citations


Journal ArticleDOI
TL;DR: In this paper, a review of recent theoretical developments of microscopic lattice and continuum models of the kinetics of irreversible monolayer and multilayer surface adsorption is presented.
Abstract: We review recent theoretical developments of microscopic lattice and continuum models of the kinetics of irreversible monolayer and multilayer surface adsorption. Such models have been used to describe adhesion and reaction processes of colloidal particles and proteins at solid surfaces. Theoretical results surveyed here include the void-filling rate equation approach, exact results for low dimensionalities, the mean-field theory, and large-time kinetics arguments. Numerical simulations serving to test and supplement the analytical theories, are reviewed as well. We also elucidate the crossover from the discrete to continuum behavior, analyzed via scaling arguments in the large-time limit of the deposition kinetics.

90 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of single-electron interchain hopping on the mechanisms of propagation of correlations leading to long range ordering is analyzed in full details for the non-half-filled band case.
Abstract: We review the recent progress made in the application of the renormalization group method to the interacting quasi-one-dimensional electron gas. From the functional integral formulation of the partition function as expressed in terms of anticommuting Grassmann variables, the effects of single-electron interchain hopping on the mechanisms of propagation of correlations leading to long range ordering is analyzed in full details for the non-half-filled band case. Within a unified formalism, the scaling features of the purely one-dimensional correlations, the dimensionality crossover of both single and composite particles, the critical temperatures, and the responses functions are described.

85 citations


Journal ArticleDOI
TL;DR: The possibility of existence of the same variety of phase transitions on grain boundaries as that on the crystal external surface has been demonstrated as discussed by the authors, and recent experimental data and theoretical models concerning grain boundary phase transitions are critically analysed.
Abstract: Recent theories of grain boundary structure have been reviewed briefly. The possibility of existence of the same variety of phase transitions on grain boundaries as that on the crystal external surface has been demonstrated. Recent experimental data and theoretical models concerning grain boundary phase transitions are critically analysed. Grain boundary phase transitions connected with the formation of thin disordered layers on the boundary (prewetting, premelting) are particularly distinguished. Results of recent indirect experiments, which may be treated in terms of prewetting and premelting, have been reviewed. Experimentally observed critical phenomena in the vicinity of the prewetting transition on the tin-germanium interphase boundary have been discussed in terms of the critical exponents theory. Some ideas regarding directions of further research are presented.

59 citations


Journal ArticleDOI
TL;DR: In this paper, the authors present a theory of Raman scattering in the Hubbard model, which involves four terms with distinct symmetry properties, one of them being the chiral spin operator ∑ Si · (Sj×Sk).
Abstract: We present a theory of Raman Scattering in the Hubbard model. The scattering of light has resonant and non-resonant contributions. The resonant term gives rise to scattering by spin degrees of freedom in the insulating case, for which we derive a general form of the effective scattering Hamiltonian. The later involves four terms with distinct symmetry properties, one of them being the “chiral” spin operator ∑ Si · (Sj×Sk). The corresponding four distinct correlation function can be measured directly in the experiments with different scattering geometries. The nonresonant term contributes to the scattering in the doped case and is shown to probe the fluctuations of the “stress tensor”. This quantity is not conserved and hence its fluctuations at small q inherent in optical experiments, need not be small, in striking contrast with the density fluctuation in usual metals.

55 citations


Journal ArticleDOI
Ken Sekimoto1
TL;DR: In this article, the spatial and space-time correlation functions of the domain structures based on the model proposed by Kolmogorov, Johnson, Mehl and Avrami are derived from their model.
Abstract: We review the recent theoretical developments in the study of domain structure dynamics through nucleation-and-growth processes of first-order phase transitions with non-conserved order parameters We introduce the spatial and space-time correlation functions of the domain structures based on the model proposed by Kolmogorov, Johnson, Mehl and Avrami Our main purpose is to show why and how the rigorous correlation functions can be derived from their model

48 citations


Journal ArticleDOI
TL;DR: In this article, the authors describe a Fermi liquid picture of high Tc superconductivity, showing that a density-of-states (dos) peak associated with the CuO2-plane van Hove singularity causes a peak in Tc as a function of hole doping.
Abstract: This review describes a Fermi liquid picture of high-Tc superconductivity. A density-of-states (dos) peak associated with the CuO2-plane van Hove singularity causes a peak in Tc as a function of hole doping. Strong correlation effects drive a Mott transition at half filling. For intermediate doping, the electronic system is unstable against phase separation, with one phase near the insulating state, the other near the Tc peak. The large dos leads to competition between superconductivity and structural instability, in analogy with the A15 compounds. The superconductivity appears to be driven by strong electron-phonon coupling, enhanced by fluctuation effects.

Journal ArticleDOI
TL;DR: In this paper, the authors show that classical fluid dynamics in a plane is a gauge theory useful for studying aspects of the quantum Hall system, and apply the fluid picture to a gas of anyons.
Abstract: In this paper we show that classical fluid dynamics in a plane is a gauge theory useful for studying aspects of the quantum Hall system. When the fluid is charged and placed in a magnetic field, Chern-Simons fields appear naturally and the fractional statistics of vortex excitations can be understood qualitatively. Applying the fluid picture to a gas of anyons shows that it superconducts.

Journal ArticleDOI
Dung-Hai Lee1, Matthew P. A. Fisher1
TL;DR: In this article, a formal duality transformation which takes one from a particle to a vortex representation of a 2D boson model is described in detail, employed to obtain detailed properties of both the FQHE hierarchy and a hierarchy of anyon superconducting phases.
Abstract: We review recent work on a bosonic formulation of both anyon superconductivity and the fractional quantum Hall effect (FQHE). Central to this approach is the concept of charge-vortex duality in two-dimensional (2d) boson systems. A formal duality transformation which takes one from a particle to a vortex representation of a 2d boson model is described in detail. The duality transformation is employed to obtain detailed properties of both the FQHE hierarchy and a hierarchy of anyon superconducting phases.

Journal ArticleDOI
TL;DR: In this paper, an overview of the theoretical work on the problem of the influence of the antiferromagnetic ordering of localized spins on the superconducting state is provided, and separate treatment is given to the electron-magnon part of this interaction.
Abstract: An overview of the theoretical work on the problem of the influence of the antiferromagnetic ordering of localized spins on the superconducting state is provided. Effects of the exchange interaction of electrons with localized spins, are investigated. Separate treatment is given to the electron-magnon part of this interaction. The electron-magnon contribution is shown to affect both the singlet and triplet pairings. For different antiferromagnets — a collinear antiferromagnetic structure and a simple spiral structure — we investigate in detail the effect of the electron spectrum exchange readjustment due to the magnetic structure and analyse the relation of this effect to superconductivity. The influence of nonmagnetic impurities on the superconducting transition temperature in antiferromagnets is also noted. The entire treatment is carried out in terms of a unified approach of strong-coupling theory, by invoking the use of Eliashberg equations.


Journal ArticleDOI
Masuo Suzuki1
TL;DR: In this paper, the relationship among the density matrix formalism, the double-space formulation and the thermo field dynamics is discussed in non-equilibrium dissipative quantum systems.
Abstract: General relationship among the density matrix formalism, the double-space formulation and thermo field dynamics is discussed in non-equilibrium dissipative quantum systems. The concept of weakly equivalent operators in the double space formulation is introduced to review many well-known results and it is shown to be useful in mapping between the density matrix formalism and the double space formulation. A new non-equilibrium thermo field dynamics is formulated to discuss dissipative quantum systems. A simple example of damped harmonic oscillators is discussed in the present representation.

Journal ArticleDOI
TL;DR: For a simple Hubbard model, using a particleparticle pairing operator and a particlehole pairing operator, it was shown in this paper that one can write down two commuting sets of angular momenta operators J and J′, both of which commute with the Hamiltonian.
Abstract: For a simple Hubbard model, using a particle-particle pairing operator η and a particle-hole pairing operator ζ, it is shown that one can write down two commuting sets of angular momenta operators J and J′, both of which commute with the Hamiltonian. These considerations allow the introduction of quantum numbers j and j′, and lead to the fact that the system has SO4 = (SU2 × SU2)/Z2 symmetry. j is related to the existence of superconductivity for a state and j′ to its magnetic properties.

Journal ArticleDOI
TL;DR: In this article, the so-called parquet equations for electron systems are derived pedagogically, and the principal advantages of the parquet approach are outlined, and its relationship to simpler self-consistent field methods, including the Baym-Kadanoff technique, is discussed in detail.
Abstract: In recent years increases in computational power have provided new motivation for the study of self-consistent-field theories for interacting electrons. In this set of notes, the so-called parquet equations for electron systems are derived pedagogically. The principal advantages of the parquet approach are outlined, and its relationship to simpler self-consistent-field methods, including the Baym-Kadanoff technique, is discussed in detail.

Journal ArticleDOI
TL;DR: In this article, the edge states of the quantum Hall effect carry representations of chiral current algebras and their associated groups, and they are used to construct vertex operators which create localised edge excitations, and indicate how they are related to the bulk quasi-particles.
Abstract: The edge states of the quantum Hall effect carry representations of chiral current algebras and their associated groups. In the simplest case of a single filled Landau level, I demonstrate explicitly how the group action affects the many-body states, and why the Kac-Peterson cocycle appears in the group multiplication law. I show how these representations may be used to construct vertex operators which create localised edge excitations, and indicate how they are related to the bulk quasi-particles.

Journal ArticleDOI
TL;DR: In this article, a review of numerical work on the t-J model and the frustrated spin-heisenberg antiferromagnet is presented, and the current active search for nontrivial ground states of the frustrated Heisenberg model is summarized.
Abstract: Recent numerical work on the t-J model and the frustrated spin- Heisenberg antiferromagnet is reviewed. Lanczos results are mainly discussed but other methods are also mentioned. Static and dynamical properties of one and more holes in the t-J model are presented. The current active search for nontrivial ground states of the frustrated Heisenberg model is summarized. It is concluded that numerical methods are providing useful information in the study of these models.

Journal ArticleDOI
TL;DR: In this paper, the authors consider the A+B→0 irreversible reaction under stoichiometric conditions and focus on the influence of the initial distribution of striation thicknesses, the time evolution of this distribution, on the structure of the reaction layers and on the role of mixing.
Abstract: Mixing of two viscous liquids often produces arrays of alternating striations. The geometrical structure of these arrays controls the course of the reactions between the liquids, both when the reaction occurs after mixing and also when mixing and reaction take place simultaneously. In the present review we consider some aspects of the problem for the A+B→0 irreversible reaction under stoichiometric conditions. We focus on the influence of the initial distribution of striation thicknesses, on the time evolution of this distribution, on the structure of the reaction layers and on the role of mixing.

Journal ArticleDOI
TL;DR: In this article, Renormalization Group (RG) techniques are applied to dynamic scaling in one-dimensional hierarchical Glauber chains, loopless fractals and fully ultrametric spaces.
Abstract: Diffusion processes in the presence of hierarchical distributions of transition rates or waiting times are investigated by Renormalization Group (RG) techniques. Diffusion on one-dimensional chains, loop-less fractals and fully ultrametric spaces are considered. RG techniques are shown to be most natural and powerful to apply when infinitely many time scales are simultaneously involved in a problem. Generalizations and extensions of existing models and results are easily accomplished in the RG context. Wherever possible, heuristic scaling arguments are also presented in order to give an easier physical interpretation of the analytical results. Two relevant applications of ultradiffusion models are reviewed in detail. One of them concerns breakdown of dynamic scaling in a one-dimensional hierarchical Glauber chain. The other one is in the context of tethered random surface models.

Journal ArticleDOI
TL;DR: In this paper, the Lanczos approach has been applied to the analysis of strongly correlated electronic models, such as the spin-half Heisenberg antiferromagnet and the Hubbard, t-J and t-1-J models.
Abstract: Recent numerical work on strongly correlated electronic models using the Lanczos approach is reviewed. In particular static and dynamical properties of the Hubbard, t—J (with one, two and more holes) and the spin-½ Heisenberg antiferromagnet are presented. An attempt to summarize the current active search for nontrivial ground states of the frustrated Heisenberg model is made. Numerical methods like the Lanczos technique are providing useful information in the study of these models.

Journal ArticleDOI
TL;DR: In this article, the authors discuss the formulation and distinguishing characteristics of discrete gauge theories, and describe several important applications of the concept, and show that, as a consequence of unbroken discrete gauge symmetries, Grand Unified cosmic strings generically exhibit Callan-Rubakov effect.
Abstract: In this review we discuss the formulation and distinguishing characteristics of discrete gauge theories, and describe several important applications of the concept. For the abelian (ℤN) discrete gauge theories, we consider the construction of the discrete charge operator F(Σ*) and the associated gauge-invariant order parameter that distinguishes different Higgs phases of a spontaneously broken U(1) gauge theory. We sketch some of the important thermodynamic consequences of the resultant discrete quantum hair on black holes. We further show that, as a consequence of unbroken discrete gauge symmetries, Grand Unified cosmic strings generically exhibit a Callan-Rubakov effect. For non-abelian discrete gauge theories we discuss in some detail the charge measurement process, and in the context of a lattice formulation we construct the non-abelian generalization of F(Σ*). This enables us to build the order parameter that distinguishes the different Higgs phases of a non-abelian discrete lattice gauge theory with matter. We also describe some of the fascinating phenomena associated with non-abelian gauge vortices. For example, we argue that a loop of Alice string, or any non-abelian string, is super-conducting by virtue of charged zero modes whose charge cannot be localized anywhere on or around the string (“Cheshire charge”). Finally, we discuss the relationship between discrete gauge theories and the existence of excitations possessing exotic spin and statistics (and more generally excitations whose interactions are purely “topological”).

Journal ArticleDOI
TL;DR: A general introduction to the subject of nonlinear wave propagation in disordered media and the basic models and the ways to study disorder in connection with them are described.
Abstract: We briefly review the state-of-the-art of research on nonlinear wave propagation in disordered media. The paper is intended to provide the non-specialist reader with a flavor of this active field of physics. Firstly, a general introduction to the subject is made. We describe the basic models and the ways to study disorder in connection with them. Secondly, analytical and numerical techniques suitable for this purpose are outlined. We summarize their features and comment on their respective advantages, drawbacks and applicability conditions. Thirdly, the Nonlinear Klein-Gordon and Schrodinger equations are chosen as specific examples. We collect a number of results that are representative of the phenomena arising from the competition between nonlinearity and disorder. The review is concluded with some remarks on open questions, main current trends and possible further developments.

Journal ArticleDOI
TL;DR: In this article, the Laue group of quasiperiodic patterns with eight-and twelvefold symmetry was derived by means of the dualization method and investigated key properties like vertex configurations, local deflation/inflation symmetries and kinematic diffraction.
Abstract: Quasiperiodic patterns with eight- and twelvefold symmetry are presented which share the root lattice D4, i.e., the 4-D face-centered hypercubic lattice, for their minimal embedding in four-space. We derive the patterns by means of the dualization method and investigate key properties like vertex configurations, local deflation/inflation symmetries and kinematic diffraction. The generalized point symmetries (and thus the Laue group) of these patterns are the dihedral groups d8 and d12, respectively, which share a common subgroup, d4. We introduce a contiunous one-parameter rotation between the two phases which leaves this subgroup invariant. This should prove useful for modelling alloys like V15Ni10Si where quasicrystalline phases with eight- and twelvefold symmetry coexist.

Journal ArticleDOI
TL;DR: In this article, the dependence of energy levels on boundary conditions has been evaluated for the Heisenberg spin chain with respect to a change of boundary conditions, and the effective charge-carrying mass has been calculated.
Abstract: In a recent paper, B. Sutherland and B.S. Shastry have constructed an adiabatic process for the Heisenberg spin chain (spin ½) with respect to a change of boundary conditions. In this paper we calculate Berry’s phase for this process. We also evaluate the dependence of energy levels on boundary conditions which permits us to calculate the effective charge-carrying mass.

Journal ArticleDOI
TL;DR: In this article, the authors review the dynamical statistical theory of the interaction of an atom with a cavity radiation field in the framework of exactly solvable Jaynes-Cummings type models.
Abstract: We review the dynamical statistical theory of the interaction of an atom with a cavity radiation field in the framework of exactly solvable Jaynes-Cummings type models.

Journal ArticleDOI
TL;DR: In this paper, an approach to quantum mechanics, based on diffeomorphism groups and local current algebras, is presented. But this approach is restricted to the case of anyons.
Abstract: We explain an approach to quantum mechanics, based on diffeomorphism groups and local current algebras, that predicts many of the fundamental properties of anyons. Our formulation also yields further insight into the meaning of particle statistics, and permits the unified description of a wide variety of quantum systems.

Journal ArticleDOI
TL;DR: In this paper, the three band Hubbard model with nearest neighbour repulsion was studied in the U=∞ limit using the large N expansion technique to order. A charge transfer (CT) instability was found like in weak coupling theory.
Abstract: The three band Hubbard model with nearest neighbour repulsion is studied in the U=∞ limit using the large N expansion technique to order . A charge transfer (CT) instability is found like in weak coupling theory. However at small doping a major role is played by the Brinkman-Rice point. The CT instability is always associated with a diverging compressibility leading to a phase separation. The evaluation to order of the effective scattering amplitude in the Cooper channel shows the presence of superconducting instabilities in the s and d wave channel near the phase separation.