Parity Inversion Research Articles

A coherent microscopic picture for the exotic structure of 11Be

The neutron-rich nucleus 11Be is one of the most enigmatic exotic nuclei in the periodic table. It exhibits a multitude of unique and intriguing phenomena within a single nucleus, including the halo phenomenon, clustering structure, and parity inversion. A unified description of these exotic properties represents a significant challenge for the nuclear physics field. By employing the axially deformed relativistic Hartree-Fock-Bogoliubov (D-RHFB) model, we have successfully reproduced the parity inversion and the one-neutron halo in 11Be, and revealed the underlying cluster structure. It is found that the intrusion of the sd-shell, which results in the parity inversion, is coherently connected with the halo and cluster structures. In particular, the s-wave is responsible for the halo formation, and the mixing of 2s1/2- and 1d5/2-waves enhances the cluster structure. This work elucidates the coherence between the parity inversion and the halo/cluster structures of 11Be, and addresses the long-standing challenge of providing a unified explanation for the multiple exotic phenomena observed in 11Be.

Quantum Conductance within Luttinger Liquid from Parity Inversion and Time Rversal Symmetryic Interaction

Quantum Conductance within Luttinger Liquid from Parity Inversion and Time Rversal Symmetryic Interaction

Symmetry-Projected Nuclear-Electronic Hartree-Fock: Eliminating Rotational Energy Contamination.

We present a symmetry projection technique for enforcing rotational and parity symmetries in nuclear-electronic Hartree-Fock wave functions, which treat electrons and nuclei on equal footing. The molecular Hamiltonian obeys rotational and parity inversion symmetries, which are, however, broken by expanding in Gaussian basis sets that are fixed in space. We generate a trial wave function with the correct symmetry properties by projecting the wave function onto representations of the three-dimensional rotation group, i.e., the special orthogonal group in three dimensions SO(3). As a consequence, the wave function becomes an eigenfunction of the angular momentum operator which (i) eliminates the contamination of the ground-state wave function by highly excited rotational states arising from the broken rotational symmetry and (ii) enables the targeting of specific rotational states of the molecule. We demonstrate the efficiency of the symmetry projection technique by calculating the energies of the low-lying rotational states of the H2 and H3+ molecules.

Mirror Symmetry for New Physics beyond the Standard Model in 4D Spacetime

The two discrete generators of the full Lorentz group O(1,3) in 4D spacetime are typically chosen to be parity inversion symmetry P and time reversal symmetry T, which are responsible for the four topologically separate components of O(1,3). Under general considerations of quantum field theory (QFT) with internal degrees of freedom, mirror symmetry is a natural extension of P, while CP symmetry resembles T in spacetime. In particular, mirror symmetry is critical as it doubles the full Dirac fermion representation in QFT and essentially introduces a new sector of mirror particles. Its close connection to T-duality and Calabi–Yau mirror symmetry in string theory is clarified. Extension beyond the Standard Model can then be constructed using both left- and right-handed heterotic strings guided by mirror symmetry. Many important implications such as supersymmetry, chiral anomalies, topological transitions, Higgs, neutrinos, and dark energy are discussed.

Fixed points on band structures of non-Hermitian models: Extended states in the bandgap and ideal superluminal tunneling

Space-time reflection symmetry (PT symmetry) in non-Hermitian electronic models has drawn much attention over the past decade mainly because it guarantees that the band structures calculated under open boundary conditions be the same as those calculated under periodic boundary conditions. PT symmetry in electromagnetic (EM) models, which are usually borrowed from electronic models, has also been of immense interest, mainly because it leads to ``exceptional'' parameter values below which non-Hermitian operators have real eigenvalues, although PT symmetry is not the sole symmetry that allows such exceptional parameter values. In this work, we examine one-dimensional PT-symmetric non-Hermitian EM models to introduce novel concepts and phenomena. We introduce the band-structure concept of ``fixed points,'' which leads to ``bidirectional'' reflection zeros in the corresponding finite structures, contrary to a common belief about the EM structures with PT symmetry (and without parity inversion and time-reversal symmetries). Some of the fixed points manifest themselves as, what we name, ``extended states in the bandgap'' on the band structure while some other fixed points are the ``turning points'' of the band structure. The extended states in the bandgap are in fact the dual of the well-known ``bound states in the continuum,'' while the turning points allow us to observe ``ideal'' superluminal tunneling in the corresponding finite structures. By ``ideal'' superluminal tunneling, we mean the case where not only the transmission coefficient has an almost uniform phase over a broad bandwidth, but also the magnitudes of the transmission and reflection coefficients are almost equal to unity and zero, respectively, over the bandwidth.

Unified mechanism behind the even-parity ground state and neutron halo of 11Be* *This work was partly supported by the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34000000), the National Natural Science Foundation of China (12275111) and the Fundamental Research Funds for the Central Universities (lzujbky-2021–sp41, lzujbky-2021–sp36)

Using the axially deformed relativistic Hartree-Fock-Bogoliubov (D-RHFB) model, we explore the mechanism behind the parity inversion and halo occurrence in 11Be, which are well reproduced by the RHF Lagrangian PKA1. It is illustrated that evidently enhanced deformation effects by the π-pseudo-vector and ρ-tensor couplings in PKA1 are crucial for correctly describing both the even-parity ground state (GS) and the neutron halo of 11Be. Coupling with the deformation, the intrude component largely enhances the couplings between the even-parity orbit and the nuclear core to ensure an even-parity GS, whereas the component therein dominates the halo formation in 11Be. Moreover, the deformed halo in 11Be is found to be stabilized by the attractive inherent correlations between the and components of the halo orbit , instead of pairing correlations, which paves a new way for understanding the halo pictures in deformed unstable nuclei.

Exploring strong and weak topological states on isostructural substitutions in TlBiSe_2

Topological Insulators (TIs) are unique materials where insulating bulk hosts linearly dispersing surface states protected by the Time-Reversal Symmetry. These states lead to dissipationless current flow, which makes this class of materials highly promising for spintronic applications. Here, we predict TIs by employing state-of-the-art first-principles based methodologies, viz., density functional theory and many-body perturbation theory (G_0W_0) combined with spin-orbit coupling effects. For this, we take a well-known 3D TI, TlBiSe_2 and perform complete substitution with suitable materials at different sites to check if the obtained isostructural materials exhibit topological properties. Subsequently, we scan these materials based on SOC-induced parity inversion at Time-Reversal Invariant Momenta. Later, to confirm the topological nature of selected materials, we plot their surface states along with calculation of Z_2 invariants. Our results show that GaBiSe_2 is a strong Topological Insulator, besides, we report six weak Topological Insulators, viz., PbBiSe_2, SnBiSe_2, SbBiSe_2, Bi_2Se_2, TlSnSe_2 and PbSbSe_2. We have further verified that all the reported TIs are dynamically stable, showing all real phonon modes of vibration.

Ta2NiSe5 : A candidate topological excitonic insulator with multiple band inversions

The electronic structures and topological properties of the orthorhombic and monoclinic phases of the quasi-one-dimensional excitonic insulator Ta2NiSe5 are investigated based on density functional theory. In contrast to a single parity or band inversion across the Fermi level in many topological insulators studied previously, there are multiple parity and band inversions with or without spin-orbit coupling in both phases of Ta2NiSe5, resulting in more complex and topologically nontrivial electronic structures. The Dirac cone type surface states of the low-temperature monoclinic phase are also obtained. In this paper, we demonstrate that Ta2NiSe5 is a promising candidate as a three-dimensional topological excitonic insulator.

Experimental observation of chiral inversion at exceptional points of non-Hermitian systems

Based on the quantum mechanics, the physical observables are represented by Hermitian linear operators. Derived from the conservation of energy, these Hermitian operators exhibit real eigenvalues. However, when a closed system described by an effective Hamiltonian is coupled with the surrounding environment, the dynamics of the system itself becomes non-Hermitian dynamic. In general, the eigenvalues of an open optical non-Hermitian system are complex. Parity-time symmetric structure is the system composed of complex potentials, which is neither parity symmetric nor time reversal symmetric alone but is symmetric after operations of parity inversion and time reversal have been combined. The eigenvalue of the parity-time symmetric Hamiltonian can be found to be real, despite the non-Hermitian nature of the system. One of the most attractive properties of non-Hermitian system is the exceptional point, which is degenerate at which two or more eigenvalues and eigenstates of a non-Hermitian physical system coalesce. The unique topological features of EPs, forming a self-intersecting Riemann surface, have given rise to several exotic physical properties. As a kind of phase singularity in a physical system, exceptional point of non-Hermitian system gives rise to a plethora of counterintuitive phenomenon, such as the loss-induced transmission enhancement, unidirectional reflection and asymmetric state transfer. Especially, the eigenvectors of exceptional point are self-orthogonal and an inherent chirality can be determined because of the missing dimension. Chirality lies at the heart of the most fascinating and fundamental phenomena in modern physics, and how to impose a strong chirality and a switchable direction of light propagation in an optical system by steering it to an exceptional point is an interesting research topic. In this work, a non-Hermitian system is constructed based on the special metamaterial resonator of split-ring resonator, in which the sign of coupling coefficient can be flexibly controlled. Especially, the chiral inversion at an exceptional point of non-Hermitian system is observed experimentally. This sign of coupling coefficient controlled exceptional point not only paves a new way for studying the fundamental non-Hermitian physics in an open system, but also holds great potential in the applied photonic devices such as the efficient chiral mode converter and chiral antennas.

A hyperbolic analogue of the Atiyah-Hitchin manifold

The Atiyah-Hitchin manifold is the moduli space of parity inversion symmetric charge two SU(2) monopoles in Euclidean space. Here a hyperbolic analogue is presented, by calculating the boundary metric on the moduli space of parity inversion symmetric charge two SU(2) monopoles in hyperbolic space. The calculation of the metric is performed using a twistor description of the moduli space and the result is presented in terms of standard elliptic integrals.

Symmetry and Quantum Features in Optical Vortices

Optical vortices are beams of laser light with screw symmetry in their wavefront. With a corresponding azimuthal dependence in optical phase, they convey orbital angular momentum, and their methods of production and applications have become one of the most rapidly accelerating areas in optical physics and technology. It has been established that the quantum nature of electromagnetic radiation extends to properties conveyed by each individual photon in such beams. It is therefore of interest to identify and characterize the symmetry aspects of the quantized fields of vortex radiation that relate to the beam and become manifest in its interactions with matter. Chirality is a prominent example of one such aspect; many other facets also invite attention. Fundamental CPT symmetry is satisfied throughout the field of optics, and it plays significantly into manifestations of chirality where spatial parity is broken; duality symmetry between electric and magnetic fields is also involved in the detailed representation. From more specific considerations of spatial inversion, amongst which it emerges that the topological charge has the character of a pseudoscalar, other elements of spatial symmetry, beyond simple parity inversion, prove to repay additional scrutiny. A photon-based perspective on these features enables regard to be given to the salient quantum operators, paying heed to quantum uncertainty limits of observables. The analysis supports a persistence in features of significance for the material interactions of vortex beams, which may indicate further scope for suitably tailored experimental design.

Electric dipole response of low-lying excitations in the two-neutron halo nucleus F29

The neutron-rich $^{28,29}$F isotopes have been recently studied via knockout and interaction cross-section measurements. The $2n$ halo in $^{29}$F has been linked to the occupancy of $pf$ intruder configurations. We investigate bound and continuum states in $^{29}$F, focusing on the $E1$ response of low-lying excitations and the effect of dipole couplings on nuclear reactions. $^{29}\text{F}$ ($^{27}\text{F}+n+n$) wave functions are built within the hyperspherical harmonics formalism, and reaction cross sections are calculated using the Glauber theory. Continuum states and $B(E1)$ transition probabilities are described in a pseudostate approach using the analytical THO basis. The corresponding structure form factors are used in CDCC calculations to describe low-energy scattering. Parity inversion in $^{28}$F leads to a $^{29}$F ground state characterized by 57.5% of $(p_{3/2})^2$ intruder components, a strong dineutron configuration, and an increase of the matter radius with respect to the core radius of $\Delta R=0.20$ fm. Glauber-model calculations for a carbon target at 240 MeV/nucleon provide a total reaction cross section of 1370 mb, in agreement with recent data. The model produces also a barely bound excited state corresponding to a quadrupole excitation. $B(E1)$ calculations into the continuum yield a total strength of 1.59 e$^2$fm$^2$ up to 6 MeV, and the $E1$ distribution exhibits a resonance at $\approx$ 0.85 MeV. Results using a standard shell-model order for $^{28}$F lead to a considerable reduction of the $B(E1)$ distribution. The four-body CDCC calculations for $^{29}\text{F}+^{120}\text{Sn}$ around the Coulomb barrier are dominated by dipole couplings, which totally cancel the Fresnel peak in the elastic cross section. These results are consistent with a two-neutron halo and may guide future experimental campaigns.

Elementary band representations for (double)-line groups

Quantized topological invariants characterizing topological phases in quasi-1D materials are usually considered only on the basis of spatial inversion parity eigenvalues. However, symmetry of quasi-1D systems is far more complex and their complete topological characterisation can be obtained only on the basis of elementary band representations (EBRs) for the relevant symmetry groups. We derive complete sets of inequivalent EBRs for line groups (LG), the symmetry groups of all quasi-1D systems with either translational or helical periodicity. Besides, we determine also EBRs for double-LGs, accounting for spin degree of freedom. In order to illustrate applicability of the results obtained, we analyze electronic-band topology of a chiral single-wall carbon nanotube, using EBRs for relevant (double)-LG and discuss Su-Schrieffer–Heeger model from EBR-perspective.

Ideal type-II Weyl points in topological circuits.

Weyl points (WPs), nodal degenerate points in three-dimensional (3D) momentum space, are said to be ‘ideal’ if they are symmetry-related and well-separated, and reside at the same energy and far from nontopological bands. Although type-II WPs have unique spectral characteristics compared with type-I counterparts, ideal type-II WPs have not yet been reported because of a lack of an experimental platform with enough flexibility to produce strongly tilted dispersion bands. Here, we experimentally realize a topological circuit that hosts only topological bands with a minimal number of four ideal type-II WPs. By stacking two-dimensional (2D) layers of inductor-capacitor (LC) resonator dimers with the broken parity inversion symmetry (P), we achieve a strongly tilted band structure with two group velocities in the same direction, and topological surface states in an incomplete bandgap. Our results establish an ideal system for the further study of Weyl physics and other exotic topological phenomena.

Symmetry-controlled edge states in graphene-like topological sonic crystal**Project supported by the National Key R&D Program of China (Grant No. 2017YFA0303700), the National Natural Science Foundation of China (Grant Nos. 11634006, 11934009, and 11690030), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20191245), the Fundamental Research Funds for the Central Universities, China (Grant No. 020414380131), and the State Key

Unique topological states emerged in various topological insulators (TI) have been proved with great application value for robust wave regulation. In this work, we demonstrate the parity inversion related to the definition of the primitive cell in one common lattice, and realize a type of symmetry-controlled edge states confined on the zigzag interfaces of the graphene-like sonic topological crystal. By simply sliding the selected ‘layer’ near the interface, the coupling of the pseudospin states induced by the multiple scattering for the C6v lattice results in the adjustment of the edge states. Based on the physics of the states, we experimentally propose a prototype of acoustic topological filter hosting multiple channels with independent adjustable edge states and realize the selective high transmission. Our work diversifies the prospects for the applications of the gapped edge states in the robust wave regulation, and proposes a frame to design new topological devices.

Li9(d,p) reaction as a specific probe of Li10 , the paradigm of parity-inverted nuclei around the N=6 closed shell

We show, within the framework of renormalized nuclear field theory and of the induced reaction surrogate formalism, that the highly debated $^{10}\mathrm{Li}$ structure, studied in a recent high statistics $^{9}\mathrm{Li}(d,p)\phantom{\rule{0.16em}{0ex}}^{10}\mathrm{Li}$ one-neutron transfer experiment, is consistent with, or better, requires, the presence of a virtual $1/{2}^{+}$ state of similar single-particle strength than that of the $1/{2}^{\ensuremath{-}}$ resonance at $0.45\ifmmode\pm\else\textpm\fi{}0.03\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$. Based on continuum spectroscopy self-energy techniques, we find that the physical mechanism responsible for parity inversion in $_{3}^{10}\mathrm{Li}$ is the same as that at the basis of the similar phenomenon observed in $_{4}^{11}\mathrm{Be}$ and as that needed in $^{11}\mathrm{Li}$ to have an important $s$-wave ground-state component. In particular the strong dynamical coupling between the ${s}_{1/2}$ and the ${d}_{5/2}$ states, mediated by the quadrupole vibration of the core $^{9}\mathrm{Li}$. A phenomenon which also affects the strength distribution of the ${d}_{5/2}$ state, in particular, in the energy range of 3--4.5 MeV. Furthermore, this mechanism is also consistent with the (normal) sequence of the $1{p}_{1/2}$ and $2{s}_{1/2}$ levels in the $N=7$ isotones $_{5}^{12}\mathrm{B}$ and $_{6}^{13}\mathrm{C}$. The main aim of the present Rapid Communication is that of treating structure and reactions on equal footing and in a common language. In other words, the calculation of the $^{9}\mathrm{Li}(d,p)^{10}\mathrm{Li}$ reaction as a single conceptual step from individual single-particle motion and collective vibrations to absolute double differential cross sections of renormalized virtual and resonant final states, which can be directly compared with experiment.

Scalar fields and the FLRW singularity

The dynamics of multiple scalar fields on a flat FLRW spacetime can be described entirely as a relational system in terms of the matter alone. The matter dynamics is an autonomous system from which the geometrical dynamics can be inferred, and this autonomous system remains deterministic at the point corresponding to the singularity of the cosmology. We show the continuation of this system corresponds to a parity inversion at the singularity, and that the singularity itself is a surface on which the space-time manifold becomes non-orientable.

About Chirality in Minkowski Spacetime

In this paper, we show that Lorentz boosts are direct isometries according to the recent mathematical definitions of direct and indirect isometries and of chirality, working for any metric space. Here, these definitions are extended to the Minkowski spacetime. We also show that the composition of parity inversion and time reversal is an indirect isometry, which is the opposite of what could be expected in Euclidean spaces. It is expected that the extended mathematical definition of chirality presented here can contribute to the unification of several definitions of chirality in space and in spacetime, and that it helps clarify the ubiquitous concept of chirality.

Scattering of partially coherent radiation by non-Hermitian localized structures having parity-time symmetry

A theoretical model based on two-point scatterers is suggested to investigate scattering of partially coherent radiation by a non-Hermitian localized structure, invariant under the simultaneous symmetry operations of parity inversion and time reversal. Within the first-order Born approximation, and the formalism of classical coherence theory, the spectral density of the scattered field in the far zone is obtained analytically. We find that the unidirectional character of the scattered radiation, which is one of the principal effects present in non-Hermitian structures, may be suppressed due to the coherence properties of the radiation without changing the geometry of the structure. Asymmetric spectral changes of the scattered radiation due to the non-Hermitian character of the material are also observed.

Non-Hermitian spectral changes in the scatteringof partially coherent radiation byperiodic structures.

The physical aspects of partially coherent radiation interacting with deterministic non-Hermitian periodic materials remain largely unexplored in the statistical optics literature. Here, we consider the scattering of partially coherent radiation by a deterministic periodic medium, symmetric under the simultaneous transformations of parity inversion and time reversal, i.e., a parity-time-symmetric periodic medium. Taking into account light fluctuations, one is able to describe the spectrum changes on propagation and the influence of the coherence-driven angular divergence effect. The far-field spectral density profile is found to depend crucially on the loss/gain properties of the material, giving rise to unexpected and contrasting spectral diffraction profiles when compared to the Hermitian ones.