Degeneracy Structure Research Articles

Structural evolution, electronic and optical properties of praseodymium doped silicon cluster PrSin0/- (n = 10–20): A theoretical investigation

The rare earth dope d nano-cluster can be a building block for the next-generation photo-electrical industry, so the imminent discovery of novel, suitable nano-functional material is urgent. Praseodymium element as a wonderful dopant, bestow a novel photoelectrochemical properties for nanomaterials especially for semiconductor, derived from its unfulfilled 4f electrons configuration and active electronic transitions between 4f to 4f and 4f to 5d. In view of this, the neutral and anionic clusters of PrSin0/- with a medium size of n = 10–20 are comprehensively investigated by the quantum chemistry method of mPW2PLYP associated with the global searching potential energy surface techniques. The geometry evolution in medium size for PrSin can be attributed to three stages of replaced (n = 10–12), linked (n = 13–19), and cage (n = 20) structure. For PrSin-, two evolution phases are obviously observed by linked (n = 10–19) and cage (n = 20) structure. The PES spectra of the anionic most stable cluster and several degeneracy structures are simulated to identify the ground state structure. Each cluster of AEA, charge transfer, and VDE values are all calculated. Combined with binding energy, HOMO-LUMO gap, molecular orbital analysis, and a series of optical properties estimated, including simulated UV–vis, IR, and Raman spectra, excitation behavior shows PrSi20- has not only prominent stability but also has a proper range of lighting absorption, higher electron-hole recombination, possible as a functional material for optoelectronic devices.

Engineering Symmetry Breaking in Twisted MoS2-MoSe2 Heterostructures for Optimal Thermoelectric Performance.

Engineering symmetry breaking in thermoelectric materials holds promise for achieving an optimal thermoelectric efficiency. van der Waals (vdW) layered transition metal dichalcogenides (TMDCs) provide critical opportunities for manipulating the intrinsic symmetry through in-plane symmetry breaking interlayer twists and out-of-plane symmetry breaking heterostructures. Herein, the symmetry-dependent thermoelectric properties of MoS2 and MoSe2 obtained via first-principles calculations are reported, yielding an advanced ZT of 2.96 at 700 K. The underlying mechanisms reveal that the in-plane symmetry breaking results in a lowest thermal conductivity of 1.96 W·m-1·K-1. Additionally, the electric properties can be significantly modulated through band flattening and bandgap alteration, stemming directly from the modified interlayer electronic coupling strength owing to spatial repulsion effects. In addition, out-of-plane symmetry breaking induces band splitting, leading to a decrease in the degeneracy and complex band structures. Consequently, the power factor experiences a notable enhancement from ∼1.32 to 1.71 × 10-2 W·m-1·K-2, which is attributed to the intricate spatial configuration of charge densities and the resulting intensified intralayer electronic coupling. Upon simultaneous implementation of in-plane and out-of-plane symmetry breaking, the TMDCs exhibit an indirect bandgap to direct bandgap transition compared to the pristine structure. This work demonstrates an avenue for optimizing thermoelectric performance of TMDCs through the implementation of symmetry breaking.

Consistency of matter coupling in modified gravity

Matter coupling in modified gravity theories is a nontrivial issue when the gravitational Lagrangian possesses a degeneracy structure to avoid the problem of the Ostrogradsky ghost. Recently, this issue was addressed for bosonic matter fields in the generalized disformal Horndeski class, which is so far the most general class of ghost-free scalar-tensor theories obtained by performing a higher-derivative generalization of invertible disformal transformations on Horndeski theories. In this paper, we clarify the consistency of fermionic matter coupling in the generalized disformal Horndeski theories. We develop the transformation law for the tetrad associated with the generalized disformal transformation to see how it affects the fermionic matter coupling. We find that the consistency of the fermionic matter coupling requires an additional condition on top of the one required for the bosonic case. As a result, we identify a subclass of the generalized disformal Horndeski class which allows for consistent coupling of ordinary matter fields, including the standard model particles.

Variations on vacuum decay: The scaling Ising and tricritical Ising field theories

We study the decay of the false vacuum in the scaling Ising and tricritical Ising field theories using the Truncated Conformal Space Approach and compare the numerical results to theoretical predictions in the thin wall limit. In the Ising case, the results are consistent with previous studies on the quantum spin chain and the $\varphi^4$ quantum field theory; in particular we confirm that while the theoretical predictions get the dependence of the bubble nucleation rate on the latent heat right, they are off by a model dependent overall coefficient. The tricritical Ising model allows us on the other hand to examine more exotic vacuum degeneracy structures, such as three vacua or two asymmetric vacua, which leads us to study several novel scenarios of false vacuum decay by lifting the vacuum degeneracy using different perturbations.

Extreme structure and spontaneous lift of spin degeneracy in doped perforated bilayer graphenes

Extreme structure and spin states of doped and undoped perforated bigraphenes was studied using DFT simulations. It was found that folded nanopores possess extremely high curvature of 0.34 Å−1. Dramatic structural deformation causes severe changes of the chemical properties of carbon atoms localized at the nanopores converting the folded edges to local oxidative fragments. It was found that asymmetrical coordination of either Li, Ca, or Al to the nanopores is coupled with electron transfer from metal to edge carbon atoms and breakdown of local inversion symmetry. Li-, Ca-, and Al-doped perforated AA bigraphene revealed ferromagnetic spin ordering with magnetic moments of 0.38, 0.14, and 0.32μB/unit cell, respectively, and spin polarization energy gain of 0.037eV for Ca-doped superlattice. It was shown that ferromagnetic spin ordering of bigraphene nanopores contradicts to the Nagaoka's theorem, which excludes strong electron correlations as a reason of spin polarization. Spontaneous lift of spin degeneracy was interpreted in terms of perturbing intense local electrostatic fields from extra electron charges localized at the nanopore edges, coupled with breakdown of space inversion and local translation invariances. It was shown that spin energy splitting is proportional to the matrix elements calculated on Bloch states with opposite wavevectors and perturbing electrostatic fields.

Modular operators and entanglement in supersymmetric quantum mechanics

The modular operator approach of Tomita–Takesaki to von Neumann algebras is elucidated in the algebraic structure of certain supersymmetric (SUSY) quantum mechanical systems. A von Neumann algebra is constructed from the operators of the system. An explicit operator characterizing the dual infinite degeneracy structure of a SUSY two dimensional system is given by the modular conjugation operator. Furthermore, the entanglement of formation for these SUSY systems using concurrence is shown to be related to the expectation value of the modular conjugation operator in an entangled bi-partite supermultiplet state thus providing a direct physical meaning to this anti-unitary, anti-linear operator as a quantitative measure of entanglement. Finally, the theory is applied to the case of two-dimensional Dirac fermions, as is found in graphene, and a SUSY Jaynes Cummings model.

Forced waves of reaction-diffusion model with density-dependent dispersal in shifting environments

This paper is concerned with the existence and global stability of forced waves for reaction diffusion equations with density-dependent diffusion in a shifting environment, which arises from population dynamics. Our argument is based on the introduction of suitable families of upper and lower solutions and on a comparison result through Holmgren's method. Our analysis yields, for any wave speed c>0, the density-dependent dispersal population models with shifting habitats admit forced traveling waves. To overcome the difficulties caused by peculiar structure of forced waves and degeneracy, we develop a novel weighted estimate technique to prove the global and exponential stability of these waves. Different from the spatial homogenous case Huang et al. 2018 [24], the weight function is introduced near the positive equilibrium r(+∞) instead of the zero equilibrium.

Energetic degeneracy and electronic structures of germanium trimers doped with titanium.

Geometries and electronic structures of germanium trimer clusters doped with titanium TiGe3 -/0 were studied making use of the complete active space self-consistent field followed by second-order perturbation theory explicitly correlated coupled cluster singles and doubles method with perturbative triples corrections CCSD(T)-F12 and Tao-Perdew-Staroverov-Scuseria methods. Two electronic states (2A' and 2A″) of the anion (pyramid shape) were determined to be nearly degenerate and energetically competing for the anionic ground state of TiGe3 -. These two anionic states are believed to be concurrently populated in the experiment and induce six observed anion photoelectron bands. Total 14 electronic transitions starting from the 2A' and 2A″ states were assigned to five out of six visible bands in the experimental anion photoelectron spectrum of TiGe3 -. Each band was proven to be caused by multiple one-electron detachments from two populated anionic states. The last experimental band with the highest detachment energy is believed to be the result of various inner one-electron removals.

Construction of variational matrix product states for the Heisenberg spin-1 chain

We propose a simple variational wave function that captures the correct ground state energy of the spin-1 Heisenberg chain model to within 0.04\%. The wave function is written in the matrix product state (MPS) form with the bond dimension $D=8$, and characterized by three fugacity parameters. The proposed MPS generalizes the Affleck-Kennedy-Lieb-Tasaki (AKLT) state by dressing it with dimers, trimers, and general $q$-dimers. The fugacity parameters control the number and the average size of the $q$-mers. Furthermore, the $D=8$ variational MPS state captures the ground states of the entire family of bilinear-biquadratic Hamiltonian belonging to the Haldane phase to high accuracy. The 2-4-2 degeneracy structure in the entanglement spectrum of our MPS state is found to match well with the results of density matrix renormalization group (DMRG) calculation, which is computationally much heavier. Spin-spin correlation functions also find excellent fit with those obtained by DMRG.

Mechanics of infinitesimal gyroscopes on Mylar balloons and their action‐angle analysis

Here, we apply the general scheme for description of mechanics of infinitesimal bodies in Riemannian spaces to the example of geodetic and non‐geodetic (for two different model potentials) motions of infinitesimal rotators on the Mylar balloon. The structure of partial degeneracy is investigated with the help of the corresponding Hamilton‐Jacobi equation and action‐angle analysis. In all situations, it was found that for any of the sixth disjoint regions in the phase space among the three action variables only two are essential for the description of our models at the level of the old quantum theory (according to the Bohr‐Sommerfeld postulates).Moreover, in both non‐geodetic models, the action variables were intertwined with the quantum number N corresponding to the quantized value of the radius r of the inflated Mylar balloon.

Geometric characterization of non-Hermitian topological systems through the singularity ring in pseudospin vector space

This work unveils how geometric features of two-band non-Hermitian Hamiltonians can completely classify the topology of their eigenstates and energy manifolds. Our approach generalizes the Bloch sphere visualization of Hermitian systems to a ``Bloch torus'' picture for non-Hermitian systems, where a singularity ring (SR) captures the degeneracy structure of generic exceptional points. The SR picture affords convenient visualization of various symmetry constraints and reduces their topological characterization to the classification of simple intersection or winding behavior, as detailed by our explicit study of chiral, sublattice, particle-hole and conjugated particle-hole symmetries. In 1D, the winding number about the SR corresponds to the band vorticity measurable through the Berry phase. In 2D, more complicated winding behavior leads to a variety of phases that illustrate the richness of the interplay between SR topology and geometry beyond mere Chern number classification. Through a normalization procedure that puts generic 2-band non-Hermitian Hamiltonians on equal footing, our SR approach also allows for vivid visualization of the non-Hermitian skin effect.

Non-Abelian nature of systems with multiple exceptional points

The defining characteristic of an exceptional point (EP) in the parameter space of a family of operators is that upon encircling the EP eigenstates are permuted. In case one encircles multiple EPs, the question arises how to properly compose the effects of the individual EPs. This was thought to be ambiguous. We show that one can solve this problem by considering based loops and their deformations. The theory of fundamental groups allows to generalize this technique to arbitrary degeneracy structures like exceptional lines in a three-dimensional parameter space. As permutations of three or more objects form a non-abelian group, the next question that arises is whether one can experimentally demonstrate this non-commutative behavior. This requires at least two EPs of a family of operators that have at least 3 eigenstates. A concrete implementation in a recently proposed $\mathcal{PT}$ symmetric waveguide system is suggested as an example of how to experimentally check the composition law and show the non-abelian nature of non-hermitian systems with multiple EPs.

Renormalization of generalized vector field models in curved spacetime

We calculate the one-loop divergences for different vector field models in curved spacetime. We introduce a classification scheme based on their degeneracy structure, which encompasses the well-known models of the non-degenerate vector field, the Abelian gauge field and the Proca field. The renormalization of the generalized Proca model, which has important applications in cosmology, is more complicated. By extending standard heat-kernel techniques, we derive a closed form expression for the one-loop divergences of the generalized Proca model.

Polarized Redundant-Baseline Calibration for 21 cm Cosmology Without Adding Spectral Structure

21 cm cosmology is a promising new probe of the evolution of visible matter in our universe, especially during the poorly-constrained Cosmic Dawn and Epoch of Reionization. However, in order to separate the 21 cm signal from bright astrophysical foregrounds, we need an exquisite understanding of our telescopes so as to avoid adding spectral structure to spectrally-smooth foregrounds. One powerful calibration method relies on repeated simultaneous measurements of the same interferometric baseline to solve for the sky signal and for instrumental parameters simultaneously. However, certain degrees of freedom are not constrained by asserting internal consistency between redundant measurements. In this paper, we review the origin of these "degeneracies" of redundant-baseline calibration and demonstrate how they can source unwanted spectral structure in our measurement and show how to eliminate that additional, artificial structure. We also generalize redundant calibration to dual-polarization instruments, derive the degeneracy structure, and explore the unique challenges to calibration and preserving spectral smoothness presented by a polarized measurement.

Ultrafast Carrier dynamics of InxGa1-xN nanostructures grown directly on Si(111)

We show a flux dependence changes in structural, optical and electronic properties of InxGa1-xN nanostructures (NSs) namely nanocolumns (NCs), nanoflakes (NFs) and nanowall network (NWN) grown directly on Si(111) surface. Field emission scanning electron microscopy (FESEM) images were recorded to see morphological changes from NFs to NCs and NWNc etc, while high-resolution X-ray diffraction (HRXRD) ω−2θ scans were used to determine In incorporation. The maximum In incorporation was observed to be 20, 33 and 38% for the sharp transition from NFs to NCs and NWNs, respectively. The charge carrier dynamics of these grown NSs were probed using Ultrafast Femtosecond Transient Absorption Spectroscopy (UFTAS) with excitation at 350 nm pump wavelength. The UFTAS studies show the comparative charge carriers dynamics of the NWS, NCs and NFs. The charge carrier studies show a higher lifetime in NWNs as compare to NCs and NFs. Further, to examine electronic structure and level of degeneracy of these NSs, core-level and valence band spectra were analyzed by X-ray photoelectron spectroscopy (XPS), which manifest the upward band bending ranging from 0.2 eV to 0.4 eV.

Influence of laser linewidth on light-induced drift velocity of atom

Light-induced drift has many applications in astrophysics, semiconductor physics, and isotope separation. Light-induced drift velocity is a key parameter to characterize the effect of light-induced drift. Laser linewidth exerts a great influence on light-induced drift velocity through influencing the velocity selectivity of atomic excitation, so it is an important factor that cannot be ignored in the study of light-induced drift. However, in existing theoretical studies, the influence of laser linewidth is seldom considered and the exciting light is always treated as monochromatic light. Furthermore, in a few theoretical studies about laser linewidth, the numerical model adopted does not include all the factors of light-induced drift, such as energy level degeneracy, hyperfine structure, and collision model, which will cause the error of calculation. In order to study the influence of laser linewidth on light-induced drift velocity, a four-level rate equation model is established to describe the atomic energy level transition in the process of light-induced drift. In the theoretical model, we introduce strong collision model to describe collisions between atoms and buffer gas. The influences of energy level degeneracy and hyperfine structure are also taken into account. Numerical method is used to calculate the four-level rate equation. According to the calculation results, the influence of laser linewidth on drift velocity of alkali metal atoms is analyzed. The results show that as the linewidth increases, the value of drift velocity first increases and then decreases. There is an optimal linewidth that maximizes the drift velocity. For the best light-induced drift effect, the laser should work under the optimal linewidth condition. When the laser linewidth fluctuates near the optimum linewidth, the laser linewidth should be set to be slightly wider than the optimal linewidth. This can reduce the influence of fluctuation and obtain a better drift effect. In addition, as the laser linewidth increases, the optimum power density corresponding to the maximum drift velocity decreases. When the laser linewidth is narrow, small fluctuations near the optimal laser power density will not have great influence on drift velocity. When the laser linewidth is wide, the power density should be set strictly. The optimum linewidth is related to laser power density, temperature and buffer gas pressure. As the laser power density increases, the value of optimum linewidth first increases rapidly and then decreases slowly. The value of optimal linewidth also increases linearly with the increase of temperature, and it decreases with the increase of buffer gas pressure. In conclusion, the laser linewidth does play a key role in the process of light-induced drift. The results of this study can provide a theoretical basis for future experiments, and be a good reference to the selection of exciting light.

Pseudo-Hermitian Systems with P T $\mathcal {P}\mathcal {T}$ -Symmetry: Degeneracy and Krein Space

We show in the present paper that pseudo-Hermitian Hamiltonian systems with even PT-symmetry admit a degeneracy structure. This kind of degeneracy is expected traditionally in the odd PT-symmetric systems which is appropriate to the fermions as shown by Jones-Smith and Mathur [1] who extended PT-symmetric quantum mechanics to the case of odd time-reversal symmetry. We establish that the pseudo-Hermitian Hamiltonians with even PT-symmetry admit a degeneracy structure if the operator PT anticommutes with the metric operator {\eta} which is necessarily indefinite. We also show that the Krein space formulation of the Hilbert space is the convenient framework for the implementation of unbroken PT-symmetry. These general results are illustrated with great details for four-level pseudo-Hermitian Hamiltonian with even PT-symmetry.

Entanglement and corner Hamiltonian spectra of integrable open spin chains

Entanglement spectra (ES) for the critical SU(N) (2 <= N <= 4) spin chains and other integrable models of finite length are studied with the density matrix renormalization group method. For all models under investigation, the level spacings and the degeneracy structure of the ES are in excellent agreement with the spectra of the corner Hamiltonian, defined as the generator of the associated corner transfer matrix. The correspondence holds between the ES (n) at the n-th cut position from the edge of the spin model, and the corner Hamiltonian of length n, for all small values of n. The cut position dependence of the ES shows a period-N oscillatory behavior for a given SU(N) chain, reminiscent of the oscillatory part of the entanglement entropy observed in the past for the same models. Oscillations of the ES do not die out in the bulk of the chain, in contrast to the asymptotically vanishing oscillation of the entanglement entropy. Heuristic argument based on Young tableaux consideration can explain the period-N structure of the ES qualitatively.

Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice atm=23magnetization

We perform an exact diagonalization study of the spin-$1/2$ XXZ Heisenberg antiferromagnet on the kagome lattice at finite magnetization $m = \frac{2}{3}$ with an emphasis on the XY point ($J_z = 0$), and in the presence of a small chiral term. Recent analytic work by Kumar, Sun and Fradkin [Phys. Rev. B 90, 174409 (2014)] on the same model, using a newly developed flux attachment transformation, predicts a plateau at this value of the magnetization described by a chiral spin liquid (CSL) with a spin Hall conductance of $\sigma_{xy} = \frac{1}{2}$. Such a state is topological in nature, has a ground state degeneracy and exhibits fractional excitations. We analyze the degeneracy structure in the low energy manifold, identify the candidate topological states and use them to compute the modular matrices and Chern numbers all of which strongly agree with expected theoretical behavior for the $\sigma_{xy} = \frac{1}{2}$ CSL. We argue that the evidence suggests the CSL is robust even in the limit of zero external chirality.

Quantum non-Abelian Potts model and its exact solution

We generalize the classical one dimensional Potts model to the case where the symmetry group is a non-Abelian finite group. It turns out that this new model has a quantum nature in that its spectrum of energy eigenstates consists of entangled states. We determine the complete energy spectrum, i.e. the ground states and all the excited states with their degeneracy structure. We calculate the partition function by two different algebraic and combinatorial methods. We also determine the entanglement properties of its ground states.