Degenerate States Research Articles

Excitations of bubbling geometries for line defects

The half-Bogomolny-Prasad-Sommerfield (BPS) Wilson line operators in the irreducible representations labeled by the Young diagrams for N=4 U(N) super Yang-Mills theory have gravity dual descriptions. When the number k of boxes of the diagram grows as k∼N2, the bubbling geometries emerge. We evaluate the spectra of quantum fluctuations on the particular bubbling geometry involving the largest degeneracy from the large N and large k limit of the supersymmetric indices decorated by the Wilson lines. The spectra of excitations over multiparticle 1/8- and 1/2-BPS states agree with the numbers of conjugacy classes of general linear group over finite fields while degeneracies of single particle BPS states are given by the general necklace polynomial. The bubbling geometry exhibits a new class of asymptotic degeneracy of states. Published by the American Physical Society 2024

Translational eigenstates of He@C60 from four-dimensional abinitio potential energy surfaces interpolated using Gaussian process regression.

We investigate the endofullerene system 3He@C60 with a four-dimensional potential energy surface (PES) to include the three He translational degrees of freedom and C60 cage radius. We compare second order Møller-Plesset perturbation theory (MP2), spin component scaled-MP2, scaled opposite spin-MP2, random phase approximation (RPA)@Perdew, Burke, and Ernzerhof (PBE), and corrected Hartree-Fock-RPA to calibrate and gain confidence in the choice of electronic structure method. Due to the high cost of these calculations, the PES is interpolated using Gaussian Process Regression (GPR), owing to its effectiveness with sparse training data. The PES is split into a two-dimensional radial surface, to which corrections are applied to achieve an overall four-dimensional surface. The nuclear Hamiltonian is diagonalized to generate the in-cage translational/vibrational eigenstates. The degeneracy of the three-dimensional harmonic oscillator energies with principal quantum number n is lifted due to the anharmonicity in the radial potential. The (2l + 1)-fold degeneracy of the angular momentum states is also weakly lifted, due to the angular dependence in the potential. We calculate the fundamental frequency to range between 96 and 110 cm-1 depending on the electronic structure method used. Error bars of the eigenstate energies were calculated from the GPR and are on the order of ∼±1.5 cm-1. Wavefunctions are also compared by considering their overlap and Hellinger distance to the one-dimensional empirical potential. As with the energies, the two abinitio methods MP2 and RPA@PBE show the best agreement. While MP2 has better agreement than RPA@PBE, due to its higher computational efficiency and comparable performance, we recommend RPA as an alternative electronic structure method of choice to MP2 for these systems.

Stable π-Extended Thio[7]helicene-Based Diradical with Predominant Through-Space Spin-Spin Coupling.

In this work, a novel π-extended thio[7]helicene scaffold was synthesized, where the α-position of the thiophene unit could be functionalized with bulky phenoxy radicals after considerable synthetic attempts. This open-shell helical diradical, ET7H-R, possesses high stability in the air, nontrivial π conjugation, persistent chirality, and a high diradical character (y0 of 0.998). The key feature is a predominant through-space spin-spin coupling (TSC) between two radicals at the helical terminals. Variable-temperature continuous-wave electron spin resonance (cw-ESR) and superconducting quantum interference device (SQUID) magnetometry in the solid state reveal a singlet ground state with a nearly degenerate triplet state of ET7H-R. These results highlight the significance of a stable helical diradicaloid as a promising platform for investigating intramolecular TSCs.

Direct Observation of Semimetal Contact Induced Charge Doping and Strain Effect in CVD‐Grown Monolayer MoS2 Transistors

AbstractTwo‐dimensional Materials (2DMs) offer significant promise for advancing device miniaturization and extending Moore's law. Despite the challenges posed by high contact resistance in transistors, recent discoveries highlight semimetals as an effective approach for achieving ohmic contact with near‐quantum‐limit contact resistance. The energy band hybridization between semimetal and MoS2 is found to create degenerate states and heavily doped contact, which is proposed as the underlying mechanism responsible for reducing contact resistance. However, a quantitative and comprehensive characterization of the semimetal‐MoS2 interface is lacking, leaving the physical interactions elusive. This study reveals that semimetals induce n‐type doping and tensile strain in monolayer MoS2 grown using CVD, which serve as the contact resistance and mobility boosters. Among the semimetals investigated, including Bismuth (Bi), Antimony (Sb), and their alloy, Bi results in the highest electron doping of 2 × 1013 cm−2 and a 0.5% tensile strain, leading to reduced contact resistance and enhanced mobility. First‐principles calculations and spectroscopy measurements unveil the impact of electron doping and strain in MoS2, and the thermal effects are subsequently explored. This research underscores the potential of semimetals in boosting device performance and lays the foundation for reducing contact resistance in transistors made from 2D materials.

Complete Selective Switching of Ferroelastic Domain Stripes in Multiferroic Thin Films by Tip Scanning

AbstractBiFeO3 is a rare single‐phase multiferroic which shows coupled ferroelectricity, ferroelasticity and antiferromagnetism at room temperature. Many fantastic properties of BiFeO3 are regulated by its domain structure. While (001) rhombohedral BiFeO3 thin films can possibly develop up‐to eight degenerate states of two‐variant 71° ferroelastic domain stripes, complete selective control of all possible switching paths between these states has not yet been achieved. Here, combining phase field simulations and scanning probe microscopy experiments, we demonstrated such a complete selective control. The tip bias and the built‐in field were shown to affect the volume fraction of the 71°, 109° and 180° switched domains in rhombohedral BiFeO3 thin films under single‐point loading. Meanwhile, tip scanning further broke the symmetry of the nucleated domains, leading to different switched domain patterns. We then grew BiFeO3 thin films with a specific two‐variant 71° ferroelastic domain state and showed that such a state could be deterministically switched into the other seven two‐variant domain states by collaborative controlling tip scanning and tip bias in scanning probe microscopy experiments. These results should deepen our current understanding on the domain switching kinetics in BiFeO3 thin films and indicate they are promising platforms for developing configurable electronic and spintronic devices.

Multichannel coupling induced topological insulating phases with full multimerization

We propose and experimentally realize a class of quasi-one-dimensional topological lattices whose unit cells are constructed by coupled multiple identical resonators, with uniform hopping and inversion symmetry. In the presence of coupling-path-induced effective zero hopping within the unit cells, the systems are characterized by complete multimerization with degenerate −1 energy edge states for open boundary condition. Su–Schrieffer–Heeger subspaces with fully dimerized limits corresponding to pairs of nontrivial flat bands are derived from the Hilbert spaces. In particular, topological bound states in the continuum (BICs) are inherently present in even multimer chains, manifested by embedding the topological bound states into a continuous band assured by bulk-boundary correspondence. Moreover, we experimentally demonstrate the degenerate topological edge states and topological BICs in radio-frequency circuits.

Mott insulator-density ordered superfluid transition and ‘shamrock transition’ in a frustrated triangle lattice

Density order is usually a consequence of the competition between long-range and short-range interactions. Here we report a density ordered superfluid emergent from a homogeneous Mott insulator due to the competition between frustrations and local interactions. This transition is found in a Bose–Hubbard model on a frustrated triangle lattice with an extra pairing term. Furthermore, we find a quantum phase transition between two different density ordered superfluids, which is beyond the Landau–Ginzburg (LG) paradigm. A U(1) symmetry is emergent at the critical point, while the symmetry in each density ordered superfluid is Z 2 × Z 3. We call the transition a ‘shamrock transition’, due to its degenerate ground state in the parameter space being a shamrock-like curve rather than a circle in an LG-type transition. Effective low energy theories are established for the two transitions mentioned above and we find their resemblance and differences with clock models.

Polarization singularity index determination using wedge plate lateral shear interferometry

Polarization singularity is a point in an inhomogeneous polarization distribution at which the azimuth of the polarization ellipse is indeterminate. The azimuth gradient is solenoidal around the polarization singular point. In metrology, shear interferometry enables the visualization of phase gradients in optical beams. Since the polarization azimuth gradient is related to the Stokes phase gradient, we adopt the shear interferometry technique to visualize these phase gradients for the detection of polarization singularity. We use a wedge plate lateral shear interferometer (LSI) in our experiments for the detection of the ellipse and vector field singularities. Being a self-referencing and intensity-based technique, this method is convenient for practical use. Unlike the traditional Stokes polarimetry method, where the polarization distribution at every spatial point is evaluated, this technique can distinguish degenerate states of polarization singularities simply by visual observation of intensity fringes. Index and helicity measurement of these polarization singularities without using polarization measurement methods are novel aspects of this scheme. Both theoretical and experimental results are presented to support our claim.

Nonreciprocal Frustration: Time Crystalline Order-by-Disorder Phenomenon and a Spin-Glass-like State

Active systems are composed of constituents with interactions that are generically nonreciprocal in nature. Such nonreciprocity often gives rise to situations where conflicting objectives exist, such as in the case of a predator pursuing its prey, while the prey attempts to evade capture. This situation is somewhat reminiscent of those encountered in geometrically frustrated systems where conflicting objectives also exist, which result in the absence of configurations that simultaneously minimize all interaction energies. In the latter, a rich variety of exotic phenomena are known to arise due to the presence of accidental degeneracy of ground states. Here, we establish a direct analogy between these two classes of systems. The analogy is based on the observation that nonreciprocally interacting systems with antisymmetric coupling and geometrically frustrated systems have in common that they both exhibit marginal orbits, which can be regarded as a dynamical system counterpart of accidentally degenerate ground states. The former is shown by proving a Liouville-type theorem. These “accidental degeneracies” of orbits are shown to often get “lifted” by stochastic noise or weak random disorder due to the emergent “entropic force” to give rise to a noise-induced spontaneous symmetry breaking, in a similar manner to the order-by-disorder phenomena known to occur in geometrically frustrated systems. Furthermore, we report numerical evidence of a nonreciprocity-induced spin-glass-like state that exhibits a short-ranged spatial correlation (with stretched exponential decay) and an algebraic temporal correlation associated with the aging effect. Our work establishes an unexpected connection between the physics of complex magnetic materials and nonreciprocal matter, offering a fresh and valuable perspective for comprehending the latter. Published by the American Physical Society 2024

Ensemble Ground State of a Many-Electron System with Fractional Electron Number and Spin: Piecewise-Linearity and Flat-Plane Condition Generalized.

Description of many-electron systems with a fractional electron number (Ntot) and fractional spin (Mtot) is of great importance in physical chemistry, solid-state physics, and materials science. In this Letter, we provide an exact description of the zero-temperature ensemble ground state of a general, finite, many-electron system and characterize the dependence of the energy and the spin-densities on both Ntot and Mtot, when the total spin is at its equilibrium value. We generalize the piecewise-linearity principle and the flat-plane condition and determine which pure states contribute to the ground-state ensemble. We find a new derivative discontinuity, which manifests for spin variation at a constant Ntot, as a jump in the Kohn-Sham potential. We identify a previously unknown degeneracy of the ground state, such that the total energy and density are unique, but the spin-densities are not. Our findings serve as a basis for development of advanced approximations in density functional theory and other many-electron methods.

Physical Properties of an Aperiodic Monotile with Graphene-like Features, Chirality, and Zero Modes.

The discovery of the Hat, an aperiodic monotile, has revealed novel mathematical aspects of aperiodic tilings. However, the physics of particles propagating in such a setting remains unexplored. In this work we study spectral and transport properties of a tight-binding model defined on the Hat. We find that (i)the spectral function displays striking similarities to that of graphene, including sixfold symmetry and Dirac-like features; (ii)unlike graphene, the monotile spectral function is chiral, differing for its two enantiomers; (iii)the spectrum has a macroscopic number of degenerate states at zero energy; (iv)when the magnetic flux per plaquette (ϕ) is half of the flux quantum, zero modes are found localized around the reflected "anti-hats"; and (v)its Hofstadter spectrum is periodic in ϕ, unlike for other quasicrystals. Our work serves as a basis to study wave and electron propagation in possible experimental realizations of the Hat, which we suggest.

Kato's theorem and ultralong-range Rydberg molecules

We consider nonadiabatic coupling in the “trilobite”-like long-range Rydberg molecules created by perturbing degenerate high-ℓ Rydberg states with a ground-state atom. Due to the flexibility granted by the high Rydberg level density, the avoided crossings between relevant potential energy curves can become extremely narrow, leading to highly singular nonadiabatic coupling. We find that the gap between the trilobite potential curve and neighboring “butterfly” or “dragonfly” potential curves can even vanish, as in a conical intersection, if the gap closes at an internuclear distance which matches a node of the s-wave radial wave function. This is an unanticipated outcome of Kato's theorem. Published by the American Physical Society 2024

Pressure control of magnetic order and excitations in the pyrochlore antiferromagnet MgCr2O4

MgCr2O4 is one of the best-known realizations of the pyrochlore-lattice Heisenberg antiferromagnet. The strong antiferromagnetic exchange interactions are perturbed by small further-neighbor exchanges such that this compound may in principle realize a spiral spin liquid (SSL) phase in the zero-temperature limit. However, a spin Jahn-Teller transition below TN≈13 K yields a complicated long-range magnetic order with multiple coexisting propagation vectors. We present neutron scattering and thermomagnetic measurements of MgCr2O4 samples under applied hydrostatic pressure up to P=1.7 GPa demonstrating the existence of multiple close-lying nearly degenerate magnetic ground states. We show that the application of hydrostatic pressure increases the ordering temperature by around 0.8 K per GPa and increases the bandwidth of the magnetic excitations by around 0.5 meV per GPa. We also evidence a strong tendency for the preferential occupation of a subset of magnetic domains under pressure. In particular, we show that the k=(0,0,1) magnetic phase, which is almost negligible at ambient pressure, dramatically increases in spectral weight under pressure. This modifies the spectrum of magnetic excitations, which we interpret unambiguously as spin waves from multiple magnetic domains. Moreover, we report that the application of pressure reveals a feature in the magnetic susceptibility above the magnetostructural transition. We interpret this as the onset of a short-range ordered phase associated with k=(0,0,1), previously not observed in magnetometry measurements. Published by the American Physical Society 2024

Digital twin-driven graph domain adaptation neural network for remaining useful life prediction of rolling bearing

Remaining useful life (RUL) prediction is significant for the healthy operation of machinery. In order to accurately identify the bearing degeneration states, it is necessary to collect massive full lifecycle data. However, the bearing lifecycle data is insufficient for effectively training a RUL prediction model in engineering practice. In this paper, a digital twin-driven graph domain adaptation method is proposed. First, a full lifecycle dynamic twin model of bearings is constructed to generate abundant twin data, in which the surface morphology evolution and roller relative slip at different stages are simulated to generate vibration responses. Second, a novel multi-layered cross-domain gated graph convolutional network (MGGCN) is developed, in which a new graph domain adaptation model is designed to solve the problem that traditional domain adaptation methods are not effective in processing the non-Euclidean data. The spatial and temporal features are extracted by multiple nonlinear transformations and previous time-step hidden state incorporation, respectively. In addition, a graph Laplacian regularized maximum mean discrepancy (GLMMD) is designed and applied in the training of model to enhance the capability of discerning graph domain differences. The experimental results confirm that the proposed method can achieve effective performance even in scenarios with limited actual data.

Modeling the dynamics of quantum systems coupled to large-dimensional baths using effective energy states.

The quantum dynamics of a low-dimensional system in contact with a large but finite harmonic bath is theoretically investigated by coarse-graining the bath into a reduced set of effective energy states. In this model, the couplings between the system and the bath are obtained from statistically averaging over the discrete, degenerate effective states. Our model is aimed at intermediate bath sizes in which non-Markovian processes and energy transfer between the bath and the main system are important. The method is applied to a model system of a Morse oscillator coupled to 40 harmonic modes. The results are found to be in excellent agreement with the direct quantum dynamics simulations presented in the work of Bouakline et al. [J. Phys. Chem. A 116, 11118-11127 (2012)], but at a much lower computational cost. Extension to larger baths is discussed in comparison to the time-convolutionless method. We also extend this study to the case of a microcanonical bath with finite initial internal energies. The computational efficiency and convergence properties of the effective bath states model with respect to relevant parameters are also discussed.

The quantum Carnot-like heat engine: The level degenerate case

The two-level quantum heat engines have been studied extensively. Before that, the optimization of most heat engines was mainly concentrated in non-degenerate cases. We consider the level degeneracy, then calculate the maximum operation time and the irreversible dissipation coefficient of the two-level system under the scheme of linear tuned levels. In the high-temperature limit, we find that the level degeneracy affects the maximum power of the two-level heat engine. Especially in the case of the same degeneracy of the ground state and the excited state, the influence is the greatest. In addition, we also show that the degeneracy does not affect the efficiency at maximum power and the consistent relation of the two-level Carnot-like heat engine.

Degeneracy and Photon Trapping in a Dissipationless Two-Mode Optomechanical Model.

In this work, we theoretically study a finite and undamped two-mode optomechanical model consisting of a high quality optical cavity containing a thin, elastic, and dielectric membrane. The main objective is to investigate the precursors of quantum phase transition in such a model by studying the behavior of some observables in the ground state. By controlling the coupling between membrane and modes, we find that the two lowest energy eigenstates become degenerate, as is indicated by the behavior of the mean value of some operators and by other quantifiers as a function of the coupling. Such degenerate states are characterized by a coherent superposition of eigenstates describing one of the two modes preferentially populated and the membrane dislocated from its equilibrium position due the radiation pressure (Schrödinger's cat states). The delocalization of the compound system photons+membrane results in an increase in fluctuations as measured by Robertson-Schrödinger uncertainty relations.

Quantum Vibronic Effects on the Excitation Energies of the Nitrogen-Vacancy Center in Diamond.

We investigated the impact of quantum vibronic coupling on the electronic properties of solid-state spin defects using stochastic methods and first-principles molecular dynamics with a quantum thermostat. Focusing on the negatively charged nitrogen-vacancy center in diamond as an exemplary case, we found a significant dynamic Jahn-Teller splitting of the doubly degenerate single-particle levels within the diamond's band gap, even at 0 K, with a magnitude exceeding 180 meV. This pronounced splitting leads to substantial renormalizations of these levels and, subsequently, of the vertical excitation energies of the doubly degenerate singlet and triplet excited states. Our findings underscore the pressing need to incorporate quantum vibronic effects into first-principles calculations, particularly when comparing computed vertical excitation energies with experimental data. Our study also reveals the efficiency of stochastic thermal line sampling for studying phonon renormalizations of solid-state spin defects.

Investigation of Floquet engineered non-Abelian geometric phase for holonomic quantum computing

Holonomic quantum computing functions by transporting an adiabatically degenerate manifold of computational states around a closed loop in a control-parameter space; this cyclic evolution results in a non-Abelian geometric phase which may couple states within the manifold. Realizing the required degeneracy is challenging and typically requires auxiliary levels or intermediate-level couplings. One potential way to circumvent this is through Floquet engineering, where the periodic driving of a nondegenerate Hamiltonian leads to degenerate Floquet bands, and subsequently non-Abelian gauge structures may emerge. Here we present an experiment in ultracold Rb87 atoms where atomic spin states are dressed by modulated RF fields to induce periodic driving of a family of Hamiltonians linked through a fully tuneable parameter space. The adiabatic motion through this parameter space leads to the holonomic evolution of the degenerate spin states in SU(2), characterized by a non-Abelian connection. We study the holonomic transformations of spin eigenstates in the presence of a background magnetic field, characterizing the fidelity of these single-qubit gate operations. Results indicate that while the Floquet engineering technique removes the need for explicit degeneracies, it inherits many of the same limitations present in degenerate systems. Published by the American Physical Society 2024

Electron confinement study in a double quantum dot by means of Shannon entropy information

In this work, we use the Shannon informational entropies to study an electron confined in a double quantum dot; we mean the entropy in the space of positions, Sr, in the space of momentum, Sp, and the total entropy, St=Sr+Sp. We obtain Sr, Sp and St as a function of the parameters A2 and k which rules the height and the width, respectively, of the internal barrier of the confinement potential. We conjecture that the entropy Sr maps the degeneracy of states when we vary A2 and also is an indicator of the level of decoupling/coupling of the double quantum dot. We study the quantities Sr and Sp as measures of delocalization/localization of the probability distribution. Furthermore, we analyze the behaviors of the quantities Sp and St as a function of A2 and k. Finally, we carried out an energy analysis and, when possible, compared our results with work published in the literature.