Strong-coupling Approach Research Articles

Quantum phase transitions in three-leg spin tubes

We investigate the properties of a three-leg quantum spin tube using several techniques such as the density-matrix renormalization-group (DMRG) method, strong-coupling approaches and the nonlinear sigma model. For integer $S$, the model proves to exhibit a particularly rich phase diagram consisting of an ensemble of $2S$ phase transitions. They can be accurately identified by the behavior of a nonlocal string order parameter associated to the breaking of a hidden symmetry in the Hamiltonian. The nature of these transitions is further elucidated within the different approaches. We carry a detailed DMRG analysis in the specific cases $S=1$. The numerical data confirm the existence of two Haldane phases with broken hidden symmetry separated by a trivial singlet state. The study of the gap and of the von Neumann entropy suggest a first-order phase transition but at the close proximity of a tricritical point separating a gapless and a first-order transition line in the phase diagram of the quantum spin tube.

Comparing Weak and Strong PEEC-MoM Coupling

The aim of this paper is to compare strong and weak coupling of the PEEC and MoM method applied to the modeling of magnetoharmonic problem, and to generalize the weak coupling approach. MoM and PEEC are dedicated to the modeling of specific parts of the overall device. As an example of validation, we have chosen the modeling of a simple transformer. Resolutions of several weak couplings are compared to the strong coupling approach. A new strategy of weak coupling is proposed to improve the time of resolution.

Magnetic transitions induced by tunneling electrons in individual adsorbedM-phthalocyanine molecules (M=Feand Co)

We report on a theoretical study of magnetic transitions induced by tunneling electrons in individual adsorbed $M$-Phthalocyanine $(M\text{-Pc})$ molecules where $M$ is a metal atom: Fe-Pc on a $\text{Cu}(110)(2\ifmmode\times\else\texttimes\fi{}1)\text{-O}$ surface and Co-Pc layers on Pb(111) islands. The magnetic transitions correspond to the change in orientation of the spin angular momentum of the metal ion with respect to the surroundings and possibly an applied magnetic field. The adsorbed Fe-Pc system is studied with a density-functional-theory-transport approach showing that (i) the magnetic structure of the Fe atom in the adsorbed Fe-Pc is quite different from that of the free Fe atom or of other adsorbed Fe systems and (ii) that injection of electrons (holes) into the Fe atom in the adsorbed Fe-Pc molecule dominantly involves the $\text{Fe}\text{ }3{d}_{{z}^{2}}$ orbital. These results fully specify the magnetic structure of the system and the process responsible for magnetic transitions. The dynamics of the magnetic transitions induced by tunneling electrons is treated in a strong-coupling approach. The Fe-Pc treatment is extended to the Co-Pc case. The present calculations accurately reproduce the strength of the magnetic transitions as observed by magnetic inelastic electron tunneling spectroscopy experiments; in particular, the dominance of the inelastic current in the conduction of the adsorbed $M\text{-Pc}$ molecule is accounted for.

Dressed counterions: Strong electrostatic coupling in the presence of salt

We reformulate the theory of strong electrostatic coupling in order to describe an asymmetric electrolyte solution of monovalent salt ions and polyvalent counterions using field-theoretical techniques and Monte Carlo simulations. The theory is based on an asymmetric treatment of the different components of the electrolyte solution. The weak coupling Debye-Hückel approach is used in order to describe the monovalent salt ions while a strong coupling approach is used to tackle the polyvalent counterions. This combined weak-strong coupling approach effectively leads to dressed interactions between polyvalent counterions and thus directly affects the correlation attraction mediated by polyvalent counterions between like-charged objects. The general theory is specifically applied to a system composed of two uniformly charged plane-parallel surfaces in the presence of salt and polyvalent counterions. In the strong coupling limit for polyvalent counterions, the comparison with Monte Carlo simulations shows good agreement for large enough values of the electrostatic coupling parameter. We delineate two limiting laws that in fact encompass all the Monte Carlo data.

Superconductivity from purely repulsive interactions in the strong-coupling approach: Application of SU(2) slave-rotor theory to the Hubbard model

We propose a mechanism of superconductivity from purely repulsive interactions in the strong coupling regime, where the BCS (Bardeen-Cooper-Schrieffer) mechanism such as the spin-fluctuation approach is difficult to apply. Based on the SU(2) slave-rotor representation of the Hubbard model, we find that the single energy scale for the amplitude formation of Cooper pairs and their phase coherence is separated into two energy scales, allowing the so called pseudogap state where such Cooper pairs are coherent locally but not globally, interpreted as realization of the density-phase uncertainty principle. This superconducting state shows the temperature-linear decreasing ratio of superfluid weight, resulting from strong phase fluctuations.

Phase diagrams of the Bose-Fermi-Hubbard model: Hubbard operator approach

The phase transitions in the Bose-Fermi-Hubbard model are investigated. The boson Green's function is cal- culated in the random phase approximation (RPA) and the formalism of the Hubbard operators is used. The regions of existence of the superuid and Mott insulator phases are established and the (; t) (the boson chemical potential vs. hopping parameter) phase diagrams are built at different values of boson-fermion in- teraction constant (in the regimes of x ed chemical potential or x ed concentration of fermions). The effect of temperature change on this transition is analyzed and the phase diagrams in the (T; ) plane are constructed. The role of thermal activation of the ion hopping is investigated by taking into account the temperature depen- dence of the transfer parameter. The reconstruction of the Mott-insulator lobes due to this effect is analyzed. parameters of the BFHM which describes these objects can be tuned in experiments and results of theoretical calculations can be tested in practice. Dieren t theoretical approaches were used to investigate the BFHM: mean eld theory (2), strong coupling approach (3), density matrix renormalization group (4), quantum Monte Carlo (5) and others. Another example of systems which can be described by the Bose-Fermi-Hubbard-type Hamil- tonian are intercalated crystals (for example, TiO2 intercalated by Li ions). In such systems the impurity ions and electrons play the role of the bosons and fermions, respectively. A lattice gas type models are also used for the description of ionic conductors (7{9). In (10) the pseudospin-electron model of intercalation was formulated and thermodynamics of the model was investigated in the mean eld approximation. It was shown that due to the presence of electrons the eectiv e inter- action between ions is generated and the character of this interaction depends on the lling of the electron band (when the chemical potential of the electrons is near the band edges, the rst order phase transition between uniform phases or phase separation in the regime of the xed electron concentration takes place; such an eect is important when constructing batteries (11)). In this work we consider the BFHM and propose a method for calculation of correlation func- tions and average values of boson and fermion concentrations. The method is based on the intro- duction of Hubbard operators acting in the on-site basis of states and is similar to the composite fermion approach used in (2) (the composite fermions are formed by a fermion and bosons or bosonic holes) but is more general and universal. Introducing the on-site Hubbard operators we can employ a known technique developed for the calculation of a correlation (Green's) function built on these operators, for example, equation of motion method (12) or diagrammatic approach based on the corresponding Wick's theorem (13). In this paper we use the rst of them. As a rst

Strong Coupling Theory for the Jaynes-Cummings-Hubbard Model

We present an analytic strong-coupling approach to the phase diagram and elementary excitations of the Jaynes-Cummings-Hubbard model describing a superfluid-insulator transition of polaritons in an array of coupled QED cavities. In the Mott phase, we find four modes corresponding to particle or hole excitations with lower and upper polaritons, respectively. Simple formulas are derived for the dispersion and spectral weights within a strong-coupling random-phase approximation (RPA). The phase boundary is calculated beyond RPA by including the leading correction due to quantum fluctuations.

Roughness prediction during cold rolling of stainless steel strip: fluid structure approach

The present paper deals with a sequential fluid structure strong coupling approach in order to solution the roughness prediction. The cold rolling model involves the strip with its asperities, the lubricant and the working roll. The strip asperities are modelled in 2D (trapezoidal shape) forming valleys and plateaus. Fluid flow rate between each valley full of lubricant is solved using Reynolds equations. Thus, the volume of lubricant trapped and its pressure are updated on the cold rolling model. During computations, the asperity is deformed from the entry to the exit to obtain its final shape. Global parameters such as front, back tensions, speeds are taken into account but also rheological (fluid, solid) and tribological behaviours.

Lattice symmetry breaking in cuprate superconductors: stripes, nematics, and superconductivity

This article gives an overview of both theoretical and experimental developments concerning states with lattice symmetry breaking in the cuprate high-temperature superconductors. Recent experiments have provided evidence for states with broken rotation as well as translation symmetry, and will be discussed in terms of nematic and stripe physics. Of particular importance here are results obtained using the techniques of neutron and X-ray scattering and scanning tunnelling spectroscopy. Ideas on the origin of lattice-symmetry-broken states will be reviewed, and effective models accounting for various experimentally observed phenomena will be summarized. These include both weak-coupling and strong-coupling approaches, with a discussion of their distinctions and connections. The collected experimental data indicate that the tendency toward uni-directional stripe-like ordering is common to underdoped cuprates, but becomes weaker with increasing number of adjacent CuO2 layers.

Cooper-pair formation by anharmonic rattling modes in the β-pyrochlore superconductor KOs2O6

We study the influence of anharmonic rattling phonons in the β-pyrochlore superconductor KOs2O6 using the strong-coupling Eliashberg approach. In particular, by analyzing the specific heat data, we find that the rattling phonon frequency changes discontinuously at the critical temperature of the first-order phase transition. Solving the strong-coupling Eliashberg equations with effective temperature-dependent α2F(ω), we investigate the consequence of this first-order phase transition for the anomalous temperature dependence of the superconducting gap. We discuss our results in the context of the recent experimental data.

Electronic structure of the iron-based superconductor LaOFeP

The recent discovery of superconductivity in the iron oxypnictide family of compounds has generated intense interest. The layered crystal structure with transition-metal ions in planar square-lattice form and the discovery of spin-density-wave order near 130 K (refs 10, 11) seem to hint at a strong similarity with the copper oxide superconductors. An important current issue is the nature of the ground state of the parent compounds. Two distinct classes of theories, distinguished by the underlying band structure, have been put forward: a local-moment antiferromagnetic ground state in the strong-coupling approach, and an itinerant ground state in the weak-coupling approach. The first approach stresses on-site correlations, proximity to a Mott-insulating state and, thus, the resemblance to the high-transition-temperature copper oxides, whereas the second approach emphasizes the itinerant-electron physics and the interplay between the competing ferromagnetic and antiferromagnetic fluctuations. The debate over the two approaches is partly due to the lack of conclusive experimental information on the electronic structures. Here we report angle-resolved photoemission spectroscopy (ARPES) of LaOFeP (superconducting transition temperature, T(c) = 5.9 K), the first-reported iron-based superconductor. Our results favour the itinerant ground state, albeit with band renormalization. In addition, our data reveal important differences between these and copper-based superconductors.

Spin-gapped incoherent metal with preformed pairing in the doped antiferromagnetic Mott insulator

We investigate how the antiferromagnetic Mott insulator evolves into the $d$-wave BCS superconductor through hole doping. Allowing spin fluctuations in the strong-coupling approach, we find a spin-gapped incoherent metal with preformed pairing as an intermediate phase between the antiferromagnetic Mott insulator and $d$-wave superconductor. This non-Fermi-liquid metal is identified with an infrared stable fixed point in the spin-decomposition gauge theory, analogous to the spin liquid insulator in the slave-boson gauge theory. We consider the single particle spectrum and dynamical spin susceptibility in the anomalous metallic phase, and discuss physical implications.

Microscopic quantum superpotential in 𝒩 = 1 gauge theories

We consider the N=1 super Yang-Mills theory with gauge group U(N), adjoint chiral multiplet X and tree-level superpotential Tr W(X). We compute the quantum effective superpotential W_mic as a function of arbitrary off-shell boundary conditions at infinity for the scalar field X. This effective superpotential has a remarkable property: its critical points are in one-to-one correspondence with the full set of quantum vacua of the theory, providing in particular a unified picture of solutions with different ranks for the low energy gauge group. In this sense, W_mic is a good microscopic effective quantum superpotential for the theory. This property is not shared by other quantum effective superpotentials commonly used in the literature, like in the strong coupling approach or the glueball superpotentials. The result of this paper is a first step in extending Nekrasov's microscopic derivation of the Seiberg-Witten solution of N=2 super Yang-Mills theories to the realm of N=1 gauge theories.

The chiral ring and the periods of the resolvent

The strongly coupled vacua of an N = 1 supersymmetric gauge theory can be described by imposing quantization conditions on the periods of the gauge theory resolvent, or equivalently by imposing factorization conditions on the associated N = 2 Seiberg–Witten curve (the so-called strong-coupling approach). We show that these conditions are equivalent to the existence of certain relations in the chiral ring, which themselves follow from the fact that the gauge group has a finite rank. This provides a conceptually very simple explanation of why and how the strongly coupled physics of N = 1 theories, including fractional instanton effects, chiral symmetry breaking and confinement, can be derived from purely semi-classical calculations involving instantons only.

Antiferromagnetic metal to heavy-fermion metal quantum phase transition in the Kondo lattice model: A strong-coupling approach

We study the quantum phase transition from an antiferromagnetic metal to a heavy fermion metal in the Kondo lattice model. Based on the strong coupling approach we {\it first} diagonalize the Kondo coupling term. Since this strong coupling approach makes the resulting Kondo term {\it relevant}, the Kondo hybridization persists even in the antiferromagnetic metal, indicating that fluctuations of Kondo singlets are not critical in the phase transition. We find that the quantum transition in our strong coupling approach results from {\it softening of antiferromagnetic spin fluctuations of localized spins}, driven by the Kondo interaction. Thus, the volume change of Fermi surface becomes continuous across the transition. ......

Effect of Fermi Surface Curvature on Low-Energy Properties of Fermions with Singular Interactions

We discuss the effect of Fermi surface curvature on long-distance or time asymptotic behaviors of two-dimensional fermions interacting via a gapless mode described by an effective gauge-field-like propagator. By comparing the predictions based on the idea of multidimensional bosonization with those of the strong-coupling Eliashberg approach, we demonstrate that an agreement between the two requires a further extension of the former technique.

Self-localized impurities embedded in a one-dimensional Bose-Einstein condensate and their quantum fluctuations

We consider the self-localization of neutral impurity atoms in a Bose-Einstein condensate in a 1D model. Within the strong coupling approach, we show that the self-localized state exhibits parametric soliton behavior. The corresponding stationary states are analogous to the solitons of non-linear optics and to the solitonic solutions of the Schroedinger-Newton equation (which appears in models that consider the connection between quantum mechanics and gravitation). In addition, we present a Bogoliubov-de-Gennes formalism to describe the quantum fluctuations around the product state of the strong coupling description. Our fluctuation calculations yield the excitation spectrum and reveal considerable corrections to the strong coupling description. The knowledge of the spectrum allows a spectroscopic detection of the impurity self-localization phenomenon.

Strong-Coupling Polarons in Dilute Gas Bose-Einstein Condensates

A neutral impurity atom immersed in a dilute Bose-Einstein condensate (BEC) can have a bound ground state in which the impurity is self-localized. In this polaronlike state, the impurity distorts the density of the surrounding BEC, thereby creating the self-trapping potential minimum. We describe the self-localization in a strong-coupling approach.

A Solution for the Incompressibility Dilemma in Partitioned Fluid–Structure Interaction with Pure Dirichlet Fluid Domains

In a subset of fluid–structure interaction (FSI) problems of incompressible flow and highly deformable structures all popular partitioned approaches fail to work. This also holds for recently quite popular strong coupling approaches based on Dirichlet–Neumann substructuring. This subset can be described as the special case where the fluid domain is entirely enclosed by Dirichlet boundary conditions, i.e. prescribed velocities. A vivid simple example would be a balloon with prescribed inflow rate. In such cases the incompressibility of the fluid cannot be satisfied during standard alternating FSI iterations as the deformation of the coupling surface is determined by the structural displacement that usually does not know about the current constraint on the fluid field. By analyzing this deficiency of the partitioned algorithm a small augmentation is proposed which allows to overcome the dilemma of incompressibility and fixed boundary velocities by introducing the volume constraint on the structural system of equations. In contrast to the original accelerated strong coupling partitioned method, the relaxation which ensures convergence of the iteration over the different fields has now to be performed on the coupling forces rather than on the displacements. In addition, two alternative approaches are discussed for the solution of the dilemma. The capability of the proposed method to deal with largely changing volumes of enclosed fluid is demonstrated by means of numerical examples.

Magnetic-exciton-mediated superconductivity in UPd2Al3

Abstract There is compelling evidence from inelastic neutron scattering and tunnelling experiments that the heavy fermion superconductor UPd2Al3 can be understood as a dual system consisting of magnetic excitons, arising from crystal-field-split U4+ levels, coupled to delocalised f electrons [N. Sato, et al., Nature 410 (2001) 340 [1] ]. We have computed the superconducting transition temperature and the mass renormalisation arising from a dual model with maximal spin anisotropy using a strong-coupling approach [P. McHale, et al., Phys. Rev. B 70 (2004) 014513 [2] ]. We find that superconducting states with a line node in the ab-plane are favoured in agreement with NMR relaxation-rate, specific-heat and thermal-conductivity measurements. The signature of line nodes on the low temperature field-angle resolved magnetothermal conductivity in the vortex phase of UPd2Al3, as investigated in T. Watanabe, et al., cond-mat/0405211 [3] , is studied within the Doppler shift approximation for the quasiparticle energies.