Large Coupling Limit Research Articles

Møller-Plesset Adiabatic Connection at Large Coupling Strengths for Open-Shell Systems.

We study the adiabatic connection that has as weak-coupling expansion the Møller-Plesset perturbation series, generalizing to the open-shell case previous closed-shell results for the large-coupling limit. We first focus on the hydrogen atom with fractional spins, providing results along the adiabatic connection from small to large coupling strengths. We reveal an intriguing phase diagram and an equation for the large-coupling leading order that has closed-form solutions for specific choices of its relevant quantum numbers. We then show that the hydrogen atom results provide variational estimates for the large-coupling leading terms for the general many-electron open-shell case in terms of functionals of the Hartree-Fock α-spin and β-spin densities.

Moduli spaces of instantons in flag manifold sigma models. Vortices in quiver gauge theories

In this paper, we discuss lumps (sigma model instantons) in flag manifold sigma models. In particular, we focus on the moduli space of BPS lumps in general Kähler flag manifold sigma models. Such a Kähler flag manifold, which takes the form Un1+⋯+nL+1Un1×⋯×UnL+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{\ extrm{U}\\left({n}_1+\\cdots +{n}_{L+1}\\right)}{\ extrm{U}\\left({n}_1\\right)\ imes \\cdots \ imes \ extrm{U}\\left({n}_{L+1}\\right)} $$\\end{document}, can be realized as a vacuum moduli space of a U(N1) × ··· × U(NL) quiver gauged linear sigma model. When the gauge coupling constants are finite, the gauged linear sigma model admits BPS vortex configurations, which reduce to BPS lumps in the low energy effective sigma model in the large gauge coupling limit. We derive an ADHM-like quotient construction of the moduli space of BPS vortices and lumps by generalizing the quotient construction in U(N) gauge theories by Hanany and Tong. As an application, we check the dualities of the 2d models by computing the vortex partition functions using the quotient construction.

Skyrmion crystal phases in Kondo lattice model on triangular lattices

Very often the magnetic skyrmions (topologically protected spin textures) form a triangular crystal in chiral magnets. Here we study the effect of itinerant electrons on the structure of skyrmion crystal (SkX) on triangular lattice using Kondo lattice model in the large coupling limit and treating the localized spins as classical vectors. To simulate the system, we employ hybrid Markov Chain Monte Carlo method (hMCMC) which includes electron diagonalization in each MCMC update for classical spins. We present the low-temperature results for system at electron density which show a sudden jump in skyrmion number reducing the size of the skyrmions when we increase the hopping strength of the itinerant electrons. We find that this high skyrmion number SkX phase is stabilized by a combined effect: lowering of density of states at electron filling and also pushing the bottom energy states further down. We show that these results hold for larger system using traveling cluster variation of hMCMC. We expect that itinerant triangular magnets might exhibit the possible transition between low-density to high-density SkX phases by applying external pressure.

An efficient decoherence scheme for fewest switches surface hopping method.

The fewest switches surface hopping method, in its original form, is known to be over-coherent. An accurate and efficient decoherence scheme is still a question of concern in the community. We propose a modification of the augmented fewest switches surface hopping (A-FSSH) scheme to make it efficient without compromising on its accuracy. We compare our proposed decoherence scheme with a recently proposed parameter-free decoherence scheme by Wang and co-workers. We show that for all model systems investigated here, our scheme is as accurate as the original A-FSSH method while at least 30 times more efficient. The decoherence scheme of Wang is more than ten times more efficient than our scheme although it does not give accurate results in the limit of large diabatic coupling.

Curvature induced scalarization of Kerr-Newman black hole spacetimes

With certain nonminimal coupling between a massless scalar field and the Gauss-Bonnet curvature invariant in the extended scalar-tensor-Gauss-Bonnet (ESTGB) field theory, tachyonic instability of the Kerr-Newman (KN) black hole is promoted. Critical spin and charge for the onset of the spontaneous scalarization phenomenon for the KN black hole are calculated in the infinitely large coupling limit. Then the analytical formula for the coupling-strength-dependent critical existence line is obtained for the black-hole-scalar-field configuration in a finite large coupling regime. Moreover, numerical methods are used to perform threshold curves that are boundaries between bald KN black holes and their hairy counterparts. Intriguingly, we get to know the KN black hole can be scalarized in the vanishing spin limit in ESTGB theory.

A theoretical study of magnetization reversal in exchange biased synthetic antiferromagnet

Magnetization reversal of exchange biased synthetic antiferromagnet (SAF) was analyzed at the initial stage back to the exchange biasing direction, based on the single domain assumption of each layer. Both static and dynamical methods were employed wherever appropriate. Results show that the reversal process can either start from an asymmetric continuous rotation of magnetizations or an abrupt switching of direction by any one or both magnetizations, and either layer can have the reversal priority over the other depending on materials parameters. In the limit of large interlayer coupling or large exchange bias, simple criteria were obtained for triggering a switching event in the system at the critical field of instability, as well as reversal priority flipping of the two layers. Interlayer antiferromagnetic coupling tends to prevent magnetic switching, and helps the reversal of the pinned layer. The results reveal the interplay of interlayer coupling, exchange bias, and magnetic anisotropy in governing the complicated magnetization behaviors of exchange biased SAF.

Multipolar structure of rotating boson stars

The relativistic multipole moments provide a key ingredient to characterize the gravitational field around compact astrophysical objects. They play a crucial role in the description of the orbital evolution of coalescing binary systems and encode valuable information on the nature of the binary's components, which leaves a measurable imprint in their gravitational-wave emission. We present a new study on the multipolar structure of a class of arbitrarily spinning boson stars with quartic self-interactions in the large coupling limit, where these solutions are expected to be stable. Our results strengthen and extend previous numerical analyses, showing that even for the most compact configurations the multipolar structure deviates significantly from that of a Kerr black hole. We provide accurate data for the multipole moments as functions of the object's mass and spin, which can be directly used to construct inspiral waveform approximants, and to perform parameter estimations and searches for boson star binaries.

The LeClair-Mussardo series and nested Bethe Ansatz

We consider correlation functions in one dimensional quantum integrable models related to the algebra symmetries gl(2|1) and gl(3). Using the algebraic Bethe Ansatz approach we develop an expansion theorem, which leads to an infinite integral series in the thermodynamic limit. The series is the generalization of the LeClair-Mussardo series to nested Bethe Ansatz systems, and it is applicable both to one-point and two-point functions. As an example we consider the ground state density-density correlator in the Gaudin-Yang model of spin-1/2 Fermi particles. Explicit formulas are presented in a special large coupling and large imbalance limit.

Quantum critical phase transition between two topologically ordered phases in the Ising toric code bilayer

We demonstrate that two toric code layers on the square lattice coupled by an Ising interaction display two distinct phases with intrinsic topological order. The second-order quantum phase transition between the weakly-coupled $\mathbb{Z}_2\times\mathbb{Z}_2$ and the strongly-coupled $\mathbb{Z}_2$ topological order can be described by the condensation of bosonic quasiparticles from both sides and belongs to the 3d Ising$^*$ universality class. This can be shown by an exact duality transformation to the transverse-field Ising model on the square lattice, which builds on the existence of an extensive number of local $\mathbb{Z}_2$ conserved parities. These conserved quantities correspond to the product of two adjacent star operators on different layers. Notably, we show that the low-energy effective model derived about the limit of large Ising coupling is given by an effective single-layer toric code in terms of the conserved quantities of the Ising toric code bilayer. The two topological phases are further characterized by the topological entanglement entropy which serves as a non-local order parameter.

Spin Seebeck effect induced by a Majorana zero mode in a nanomagnet

Abstract In mesoscopic devices, spin-resolved thermoelectrics induced by Majorana zero modes (MZMs) has attracted much attention. In this work we study an exactly solvable model consisting of a quantum dot coupled to metallic leads and side-coupled to a local large spin and a topological superconductor wire hosting MZMs. Because of MZMs’ helical property, the spin-up component of the dot spin is coupled with the MZM We mainly focus on one of the thermoelectric quantities—the Seebeck coefficient. By using Green’s function method combined with Hubbard operators, we obtain an analytical result for the spectral function. Then it is shown that spin Seebeck effects are determined by the interplay of temperature, exchange coupling, and the strength of coupling to Majorana wire. It is found that the spin-up thermopower is immune to local impurities in the limit of low temperature or large coupling to topological superconductor. Then we show that the spin-resolved thermopowers exhibit angular-quantum-number-dependent zero points. Specifically, the spin-down thermopower exhibits 4 S + 1 zero points due to the presence of local large spin, and the spin-up thermopower exhibits 8 S + 3 zero points near the transition point (where the competition of hole and electron processes reaches equilibrium), due to the interplay of local large spin and MZM. The charge and spin Seebeck coefficients also show S -dependent and MZM-involved behaviors. The results show that the interplay of local large spin and Majorana zero mode generates some interesting results, which may provide additional information as the signature of Majorana zero modes.

Scaling limits of dS vacua and the swampland

We discuss the properties of massive type IIA flux compactifications. In particular, we investigate in which case one can obtain dS vacua at large volume and small coupling. We support a general discussion of scaling symmetries with the analysis of a concrete example. We find that the large volume and weak coupling limit requires a large number of O6-planes. Since these are bound for any given compactification space one cannot get arbitrarily good control over α′ and string loop corrections.

Robin Laplacian in the Large coupling limit: Convergence and spectral asymptotic

We study convergence modes as well as their respective rates for the resolvent difference of Robin and Dirichlet Laplacian on bounded smooth domains in the large coupling limit. Asymptotic expansions for the resolvent, the eigenprojections and the eigenvalues of the Robin Laplacian are performed. Finally we apply our results to the case of the unit disc.

Explicit construction of quasiconserved local operator of translationally invariant nonintegrable quantum spin chain in prethermalization

We numerically construct translationally invariant quasi-conserved operators with maximum range M which best-commute with a non-integrable quantum spin chain Hamiltonian, up to M = 12. In the large coupling limit, we find that the residual norm of the commutator of the quasi-conserved operator decays exponentially with its maximum range M at small M, and turns into a slower decay at larger M. This quasi-conserved operator can be understood as a dressed total "spin-z" operator, by comparing with the perturbative Schrieffer-Wolff construction developed to high order reaching essentially the same maximum range. We also examine the operator inverse participation ratio of the operator, which suggests its localization in the operator Hilbert space. The operator also shows almost exponentially decaying profile at short distance, while the long-distance behavior is not clear due to limitations of our numerical calculation. Further dynamical simulation confirms that the prethermalization-equilibrated values are described by a generalized Gibbs ensemble that includes such quasi-conserved operator.

Theory of the magnetism in La2NiMnO6

The magnetism of ordered and disordered La$_2$NiMnO$_6$ is explained using a model involving double exchange and superexchange. The concept of majority spin hybridization in the large coupling limit is used to explain the ferromagnetism of La$_2$NiMnO$_6$ as compared to the ferrimagnetism of Sr$_{2}$FeMoO$_{6}$. The ferromagnetic insulating ground state in the ordered phase is explained. The essential role played by the Ni-Mn superexchange between the Ni $e_{g}$ electron spins and the Mn $t_{2g}$ core electron spins in realizing this ground state, is outlined. In presence of antisite disorder, the model system is found to exhibit a tendency of becoming a spin-glass at low temperatures, while it continues to retain a ferromagnetic transition at higher temperatures, similar to recent experimental observations [D. Choudhury .et.al., Phys. Rev. Lett. 108, 127201 (2012)]. This reentrant spin-glass or reentrant ferromagnetic behaviour is explained in terms of the competition of the ferromagnetic double exchange between the Ni $e_{g}$ and the Mn $e_{g}$ electrons, and the ferromagnetic Ni-Mn superexchange, with the antiferromagnetic antisite Mn-Mn superexchange.

Newtonian analysis of multiscalar boson stars with large self-couplings

We study solutions for boson stars in the multi-scalar field theory with global symmetry $[U(1)]^N$. The properties of the boson stars are investigated by the Newtonian approximation with the large coupling limit. Our purpose is to study the models bringing about exotic mass distributions which explain flat rotation curves of galaxies. We propose plausible models in which coupling matrices are associated with various graphs in graph theory.

Coherent and incoherent charge transport in linear triple quantum dots

One of the fundamental questions in quantum transport is how charge transfer through complex nanostructures is influenced by quantum coherence. We address this issue for linear triple quantum dots by comparing a Lindblad density matrix description with a Pauli rate equation approach and analyze the corresponding zero-frequency counting statistics of charge transfer. The impact of decaying coherences of the density matrix due to dephasing is also studied. Our findings reveal that the sensitivity to coherence shown by shot noise and skewness, in particular in the limit of large coupling to the drain reservoir, can be used to unambiguously evidence coherent processes involved in charge transport across triple quantum dots. Our analytical results are obtained by using the characteristic polynomial approach to full counting statistics.

Electronic correlations in the Hubbard model on a bi-partite lattice

In this work we study the Hubbard model on a bi-partite lattice using the coupled-cluster method (CCM). We first investigate how to implement this approach in order to reproduce the lack of magnetic order in the 1D model, as predicted by the exact Bethe-Ansatz solution. This result can only be reproduced if we include an algebraic correlation in some of the coupled-cluster model coefficients. Using the correspondence between the Heisenberg model and the Hubbard model in the large-coupling limit, we use very accurate results for the CCM applied to the Heisenberg and its generalisation, the XXZ model, to determine CCM coefficients with the correct properties. Using the same approach we then study the 2D Hubbard model on a square and a honeycomb lattice, both of which can be thought of as simplified models of real 2D materials. We analyse the charge and spin excitations, and show that with care we can obtain good results.

Analytical approximation for Newtonian boson stars in four and five dimensions

In this paper, we study rotating boson stars in the large coupling limit as well as in the Newtonian limit. We investigate the equilibrium solutions in four and five dimensions by adopting some analytical approximations. We show that the relations among the radius, angular momentum, Newtonian energy and quadrupole moment (for the four-dimensional solution) of the boson star can be qualitatively realized for the minimal number of boson star parameters.

Remarks on meson loop effects on quark models

We investigate the effect of meson loops on the spectrum of quark states. We demonstrate that in general quark states do not tend to get very broad if their coupling to the continuum increases, but instead they decouple from the latter in the large coupling limit. We ascribe this effect to the essentially nonperturbative unitarization procedure involved. In the meantime, some quark resonances behave very differently and demonstrate collectivity in the sense that their pole trajectories span a wide, as compared to the level spacing, region therefore acquiring contributions from multiple bare poles rather than from the closest neighbors. While the actual calculations are done within particular, very simplified models, it is argued that the findings might well be general.

Rate of convergence for large coupling limits in Sobolev spaces

ABSTRACTWe estimate the rate of convergence, in the so-called large coupling limit, for Schrödinger-type operators on bounded domains with “interaction potentials” supported in a compact inclusion. We show that if the boundary of the inclusion is sufficiently smooth, one essentially recovers the “free Hamiltonian” in the exterior domain with Dirichlet boundary conditions. In addition, we obtain a convergence rate, in L2, that is , where λ is the coupling parameter. Our methods include energy estimates, trace estimates, interpolation, and duality.