Local Symmetry Research Articles

Classification of Symmetry-Enriched Topological Quantum Spin Liquids

We present a systematic framework to classify symmetry-enriched topological quantum spin liquids in two spatial dimensions. This framework can deal with all topological quantum spin liquids, which may be either Abelian or non-Abelian and chiral or nonchiral. It can systematically treat a general symmetry, which may include both lattice symmetry and internal symmetry, may contain antiunitary symmetry, and may permute anyons. The framework applies to all types of lattices and can systematically distinguish different lattice systems with the same symmetry group using their quantum anomalies, which are sometimes known as Lieb-Schultz-Mattis anomalies. We apply this framework to classify U(1)2N chiral states and non-Abelian Ising(ν) states enriched by a p6×SO(3) or p4×SO(3) symmetry and ZN topological orders and U(1)2N×U(1)−2N topological orders enriched by a p6m×SO(3)×Z2T, p4m×SO(3)×Z2T, p6m×Z2T, or p4m×Z2T symmetry, where p6, p4, p6m, and p4m are lattice symmetries while SO(3) and Z2T are spin rotation and time-reversal symmetries, respectively. In particular, we identify symmetry-enriched topological quantum spin liquids that are not easily captured by the usual parton-mean-field approach, including examples with the familiar Z2 topological order. Published by the American Physical Society 2024

Geometrical interpretation of isospin subalgebras in SU(3)

Ever since new tetrads in four-dimensional Lorentzian curved spacetimes were introduced, many outstanding properties and results have been proven regarding Riemannian geometry, gauge theory or group theory. These tetrads might carry spacetime-kinematic information about particle multiplets. Among other properties, these new tetrads, locally and covariantly diagonalize stress–energy tensors. In the case where particles have an electromagnetic field, the local planes of gauge symmetry served as a tool in order to propose a new gravitational-kinematic interpretation of particle multiplets. The core reason stems from the mathematical fact that all local gauge symmetries associated to the Standard Model have been proven to be isomorphic to local groups of tetrad transformations in four-dimensional Lorentzian spacetimes. Therefore, the different stress–energy tensors have been proven to determine the local gauge geometry as a natural part of Riemannian geometry. The stress–energy tensors determine locally the orthogonal planes such that the rotation on either of them of the local tetrad vectors that span these planes is isomorphic to local tetrad gauge transformations. All these properties put together allow for a reinterpretation presented previously of particle states as particle gravitational-kinematic-spacetime tetrad states in the asymptotically flat limit. We proceed in this paper to study the case where there are [Formula: see text], [Formula: see text] and [Formula: see text] isospin subalgebras or submultiplets within the context of this new Riemannian interpretation of gauge symmetries.

On the geometry and quantum theory of regular and singular spinors

We relate the Lounesto classification of regular and singular spinors to the orbits of the Spin(3,1) group in the space of Dirac spinors. We find that regular spinors are associated with the principal orbits of the spin group while singular spinors are associated with special orbits whose isotropy group is C. We use this to clarify some aspects of the classical and quantum theory of spinors restricted to a class in this classification. In particular, we show that the degrees of freedom of an ELKO field, which has been proposed as a candidate for dark matter, can be reexpressed as a Dirac field preserving locality. Alternatively after introducing the ELKO dual, it can be re-interpreted as four anticommuting Lorentz scalar fields with internal symmetry the spin representation of the Lorentz group. We also propose an interacting Lagrangian which can consistently describe all 6 classes of regular and singular spinors.

Effects of the Substitution of B and C for P on Magnetic Properties of FePCB Amorphous Alloys

In the present study, first-principles molecular dynamics simulations were employed to study the effects of small amounts of B and C substituted for P on the structure and magnetic properties of Fe80P13C7, Fe80P10C7B3, and Fe80P8C9B3 amorphous alloys. A small amount of B and C replacing P atoms increases the icosahedral structure of the amorphous alloys, especially the increase in the regular icosahedral structure. The saturation magnetization of the three kinds of amorphous alloys gradually increases with the addition of B and C atoms, and the results of experimental and simulated calculations show consistent trends. The substitution of P atoms by B and C atoms leads to the aggregation of Fe atoms, which increases the magnetic moment of the iron atoms. In addition, the improvement of local structural symmetry may be one of the reasons for the increase in saturation magnetization of amorphous alloys. The substitution of a small number of B and C atoms plays an important role in improving the saturation magnetization of the amorphous alloy, which has a certain guiding significance for the development of amorphous alloys with excellent soft magnetic properties.

The property of CrCoNiFeMnAl x (x=0, 0.5, and 1) high-entropy alloys on rapid cooling: insights from ab initio molecular dynamics

High-entropy alloys (HEAs) are currently the subject of extensive research. Despite this, the effects of rapid cooling on their performance have yet to be investigated. This study uses ab initio molecular dynamics to investigate the CrCoFeNiMnAl x (x =0, 0.5 and 1) HEAs under a rapid cooling process. It has been observed that the three HEAs all form metallic glass at 300 K under a constant cooling rate of 1.25 × 102 K ps−1, mainly composed of icosahedron and face-centered cubic clusters. Secondly, the glass transition temperatures (T g) are predicted to be 1658 K for CrCoFeNiMn, 1667 K for CrCoFeNiMnAl0.5, and 1687 K for CrCoFeNiMnAl, respectively. It can be seen the T g of HEAs increases with the content of Al increasing. Eventually, a relationship between structure and dynamics is established by using the five-fold local symmetry parameters and shear viscosity, which proves that structural evolution is the fundamental reason for dynamic deceleration. The present results contribute to understanding the evolution of the local structure of CrCoFeNiMnAl x and provide a new perspective for studying the structural mechanism of dynamic retardation in HEAs.

Eu3+ doped Ca3LiSbO6 and Eu3+, Li+ co-doped Ca3LiSbO6 phosphors for white light-emitting diodes

Novel antimonate Ca3LiSbO6: xEu3+ red phosphor was synthesised using a high-temperature solid-phase reaction. The effect of Eu3+ doping concentration on its crystal structure and luminescence performance was investigated. It was found that Eu3+ was at the inversion symmetry site in the lattice of Ca3LiSbO6. To improve the luminescence performance of Ca3LiSbO6: 0.05Eu3+ red phosphor, Ca3LiSbO6: 0.05Eu3+, xLi + red phosphor was synthesised. The doping of Li + can correct the charge difference generated by the substitution of Ca2+ by Eu3+, reduce the generation of defects, enhance the local symmetry of the luminescence centre of Eu3+, improve the structural rigidity, and thus enhance the luminous intensity of the phosphor. At 423 K, the luminous intensity of this phosphor was 68 % of the initial temperature, which was higher than that of the phosphor without the charge compensator Li+ (60 %), indicating that Li+ improved the thermal stability of the phosphor.

Disruption Symmetric Crystal Structure Favoring Photocatalytic CO2 Reduction: Reduced *COOH Formation Energy Barrier on Al Doped CuS/TiO2

AbstractHow to break the C═O bond and reduce the energy barrier of *COOH formation is the key to triggering the photocatalytic CO2 reduction (PCR) reaction and subsequent proton‐electron processes, which is as important as overcoming high recombination rate of photocarriers. In order to solve this issue, the symmetric structure of CuS/TiO2 is destroyed by S vacancy and Al doping (denoted as Al‐CuS/TiO2), which significantly expands the electron localization range and promotes the cis‐coordination splitting of Cu 3d orbits. The experimental results show that the CO yield selectivity of ≈90.68% and yield of ≈335.68 µmol·g−1·h−1 on Al‐CuS/TiO2. The redistribution of Cu electron states in specific d/s/p orbitals increases the adsorption of CO2 and reduces the reaction energy barrier of *COOH intermediates, while effectively breaking the C═O bond. Doped Al atoms also serve as adsorption sites for H2O molecules, effectively interleaving the competition with photocatalytic CO2 reduction at the Cu sites is effectively staggered. This study provides a new approach to reduce the energy barrier of *COOH formation and to accelerate the photocarrier migration by destroying local symmetry to adjust the crystal structure, which is important for further improving the activity and selectivity of PCR.

Bridging Continuous and Lattice-Based Models of Two-Dimensional Diffusion: A Systematic Approach for Estimating Transition Probabilities, Grid Size and Diffusivity

Lattice-based models have been broadly applied in mathematical and computational modeling of biological and biomedical systems for which spatial effects are important. These discrete models commonly include diffusion of mobile constituents as a key underlying mechanism. While the direct simulation of diffusion in continuous (off-lattice) domains is possible, it is computationally intensive, particularly when multiple coupled mechanisms are involved. This study presents a systematic approach for connecting continuous models of two-dimensional diffusion with internal obstacles to discrete, lattice-based (surrogate) models of diffusion. Results from continuous model simulations on a representative domain, and over many realizations, are used to develop accurate lattice-based surrogate models by exploiting internal symmetries. Probabilities determined for the lattice-based surrogate models are also connected to theoretical diffusivities for 2D random walks on a square lattice, necessitating the calibration of a spatial grid size. This approach can facilitate the inclusion of more accurate diffusive transport models of complex media within the general framework of lattice-based models that incorporate multiple coupled mechanisms.

Full-color, time-valve controllable and Janus-type long-persistent luminescence from all-inorganic halide perovskites

Long persistent luminescence (LPL) has gained considerable attention for the applications in decoration, emergency signage, information encryption and biomedicine. However, recently developed LPL materials – encompassing inorganics, organics and inorganic-organic hybrids – often display monochromatic afterglow with limited functionality. Furthermore, triplet exciton-based phosphors are prone to thermal quenching, significantly restricting their high emission efficiency. Here, we show a straightforward wet-chemistry approach for fabricating multimode LPL materials by introducing both anion (Br−) and cation (Sn2+) doping into hexagonal CsCdCl3 all-inorganic perovskites. This process involves establishing new trapping centers from [CdCl6-nBrn]4− and/or [Sn2-nCdnCl9]5− linker units, disrupting the local symmetry in the host framework. These halide perovskites demonstrate afterglow duration time ( > 2,000 s), nearly full-color coverage, high photoluminescence quantum yield ( ~ 84.47%), and the anti-thermal quenching temperature up to 377 K. Particularly, CsCdCl3:x%Br display temperature-dependent LPL and time-valve controllable time-dependent luminescence, while CsCdCl3:x%Sn exhibit forward and reverse excitation-dependent Janus-type luminescence. Combining both experimental and computational studies, this finding not only introduces a local-symmetry breaking strategy for simultaneously enhancing afterglow lifetime and efficiency, but also provides new insights into the multimode LPL materials with dynamic tunability for applications in luminescence, photonics, high-security anti-counterfeiting and information storage.

Reduced Tensor Network Formulation for Non-Abelian Gauge Theories in Arbitrary Dimensions

Abstract Formulating non-Abelian gauge theories as a tensor network is known to be challenging due to the internal degrees of freedom that result in the degeneracy in the singular value spectrum. In two dimensions, it is straightforward to “trace out” these degrees of freedom with the use of character expansion, giving a reduced tensor network where the degeneracy associated with the internal symmetry is eliminated. In this work, we show that such an index loop also exists in higher dimensions in the form of a closed tensor network that we call the “armillary sphere”. This allows us to completely eliminate the matrix indices and reduce the overall size of the tensors in the same way as is possible in two dimensions. This formulation allows us to include significantly more representations with the same tensor size, thus making it possible to reach a greater level of numerical accuracy in the tensor renormalization group computations.

Topological solitons in coupled Su-Schrieffer-Heeger waveguide arrays.

We investigate the formation of multipole topological solitons at the edges of two and three coupled parallel Su-Schrieffer-Heeger (SSH) waveguide arrays. We show that independent variations of waveguide spacing in the unit cells (dimers) in coupled waveguide arrays result in the emergence at their edges of several topological edge states with different internal symmetries. The number of emerging edge states is determined by how many arrays are in topologically nontrivial phase. In the presence of nonlinearity, such edge states give rise to families of multipole topological edge solitons with distinct stability properties. Our results illustrate that coupling between quasi-one-dimensional topological structures substantially enriches the variety of stable topological edge solitons existing in them.

D * s0(2317) and B*s0 as Molecular States

Abstract We investigate the dynamical generation of the $D_{s0}^{*}(2317)$ and $B_{s0}^{*}$ mesons using a meson-exchange model with a coupled-channel formalism. Our primary focus is on the $D_s^+\pi ^0$ channel below the $DK$ threshold. First, we construct the invariant kernel amplitudes, incorporating effective Lagrangians based on heavy-quark symmetry, flavor SU(3) symmetry, and hidden local symmetry. Since the $D_{s0}^{*}(2317)$ state implies isospin symmetry breaking, we introduce $\pi ^0\!-\!\eta$ isospin mixing. We subsequently solve the coupled-channel integral equations, which include four different channels, i.e. $D_s^+\pi ^0$, $D^0 K^+$, $D^+ K^0$, and $D_s^+\eta$. We carefully analyze how the pole corresponding to the $D_{s0}^{*}(2317)$ state emerges from the coupled channels. Our findings reveal that the pole positions of the $D_{s0}^{*}(2317)$ meson are at $\sqrt{s_R}=(2317.9 - i 0.0593)$ MeV and those of the $\bar{B}_{s0}^{*}$ meson are at $(5756.43-i0.0215)$ MeV, respectively. We also discuss their decay widths and destructive interference of the two sources. In conclusion, our current results provide a clear indication supporting the interpretation of the $D_{s0}^{*}(2317)$ meson as a $DK$ molecular state within the present coupled-channel formalism. In addition, we discuss the possible existence of $\bar{B}_{s0}^{*}$.

Engineering and revealing Dirac strings in spinor condensates

Artificial monopoles have been engineered in various systems, yet there has been no systematic study of the singular vector potentials associated with the monopole field. We show that the Dirac string, the line singularity of the vector potential, can be engineered, manipulated, and made manifest in a spinor atomic condensate. We elucidate the connection among spin, orbital degrees of freedom, and the artificial gauge, and show that there exists a mapping between the vortex filament and the Dirac string. We also devise a proposal where preparing initial spin states with relevant symmetries can result in different vortex patterns, revealing an underlying correspondence between the internal spin states and the spherical vortex structures. Such a mapping also leads to a new way of constructing spherical Landau levels, and monopole harmonics. Our observation provides insights into the behavior of quantum matter possessing internal symmetries in curved spaces. Published by the American Physical Society 2024

Protection of entanglement in two independently decohering qubits via local prior and post parity-time symmetry operations

Protection of entanglement of two qubits undergoing two independent amplitude damping channels using a local parity-time ( PT ) symmetric operation is exactly studied. First, the explicit expressions of concurrence quantifying the entanglement of two qubits with both local PT symmetric operation and two amplitude damping channels are obtained. Then, we give two schemes, i.e. prior and post PT symmetric operations, to show the performance of PT symmetric operation on entanglement dynamics of two qubits. By investigation, we find that the effect of prior PT symmetric operation schemes on the protection of entanglement of two qubits in the double channel case is superior to that of the single channel case. Conversely, the effect of post PT symmetric operation scheme on the protection of entanglement of two qubits in the single channel case is better than that in the double channel case. In other words, the local PT symmetric operation approach may have potential applications in combating amplitude damping decoherence.

Fibration symmetry-breaking supports functional transitions in a brain network engaged in language.

In his book 'A Beautiful Question' 1, physicist Frank Wilczek argues that symmetry is 'nature's deep design,' governing the behavior of the universe, from the smallest particles to the largest structures 1-4. While symmetry is a cornerstone of physics, it has not yet been found widespread applicability to describe biological systems 5, particularly the human brain. In this context, we study the human brain network engaged in language and explore the relationship between the structural connectivity (connectome or structural network) and the emergent synchronization of the mesoscopic regions of interest (functional network). We explain this relationship through a different kind of symmetry than physical symmetry, derived from the categorical notion of Grothendieck fibrations 6. This introduces a new understanding of the human brain by proposing a local symmetry theory of the connectome, which accounts for how the structure of the brain's network determines its coherent activity. Among the allowed patterns of structural connectivity, synchronization elicits different symmetry subsets according to the functional engagement of the brain. We show that the resting state is a particular realization of the cerebral synchronization pattern characterized by a fibration symmetry that is broken 7 in the transition from rest to language. Our findings suggest that the brain's network symmetry at the local level determines its coherent function, and we can understand this relationship from theoretical principles.

Does the accounting of the local symmetry fragments in quasi-SMILES improve the predictive potential of the QSAR models of toxicity toward tadpoles?

Models of toxicity to tadpoles have been developed as single parameters based on special descriptors which are sums of correlation weights, molecular features, and experimental conditions. This information is presented by quasi-SMILES. Fragments of local symmetry (FLS) are involved in the development of the model and the use of FLS correlation weights improves their predictive potential. In addition, the index of ideality correlation (IIC) and correlation intensity index (CII) are compared. These two potential predictive criteria were tested in models built through Monte Carlo optimization. The CII was more effective than IIC for the models considered here.

The Schwinger-Keldysh coset construction

The coset construction is a tool for systematically building low energy effective actions for Nambu-Goldstone modes. This technique is typically used to compute time-ordered correlators appropriate for S-matrix computations for systems in their ground state. In this paper, we extend this technique to the Schwinger-Keldysh formalism, which enables one to calculate a wider variety of correlators and applies also to systems in a mixed state. We focus our attention on internal symmetries and demonstrate that, after identifying the appropriate symmetry breaking pattern, Schwinger-Keldysh effective actions for Nambu-Goldstone modes can be constructed using the standard rules of the coset construction. Particular emphasis is placed on the thermal state and ensuring that correlators satisfy the KMS relation. We also discuss explicitly the power counting scheme underlying our effective actions. We comment on the similarities and differences between our approach and others that have previously appeared in the literature. In particular, our prescription does not require the introduction of additional “diffusive” symmetries and retains the full non-linear structure generated by the coset construction. We conclude with a series of explicit examples, including a computation of the finite-temperature two-point functions of conserved spin currents in non-relativistic paramagnets, antiferromagnets, and ferromagnets. Along the way, we also clarify the discrete symmetries that set antiferromagnets apart from ferromagnets, and point out that the dynamical KMS symmetry must be implemented in different ways in these two systems.

Achieving ultrahigh energy density and efficiency simultaneously in (Na, K)NbO3-based lead-free relaxor ferroelectrics via a collaborative design

Relaxor ferroelectrics have garnered enormous attention for their great application potential in pulsed power energy-storage capacitors, while simultaneously achieving large recoverable energy density (Wrec) and high efficiency (η) remains a formidable challenge. Through collaboratively controlling multiscale structure via a combination of composition design and processing improvement, polar nanodomains with multiple local symmetries were engineered in ultrafine grains, enabling significantly reduced polarization hysteresis, delayed saturation polarization, maintained high polarization, and enhanced breakdown strength. As a result, an excellent comprehensive energy-storage performance of Wrec ∼11.8 J/cm3 and η ∼88.7 % is achieved in the (Na, K)NbO3-based spark-plasma-sintered lead-free ceramics, together with stable charge-discharge properties of power density ∼176.3 MW/cm3, discharge energy density ∼3.2 J/cm3, and discharge time ∼43 ns over a wide temperature range of 20–140 °C. The studied ceramic demonstrates great advantages in advanced capacitive energy-storage applications.

Breaking the mirror symmetry of photonic spin-orbit interaction using a geometrically symmetric chiral resonator

The symmetries of photonic spin-orbit interaction (PSOI) at waveguide interfaces provide flexible modulation capability but limit their practical implementation due to the stringent requirements of excitation conditions. This limitation can be mitigated by intentionally breaking local symmetries, offering a novel platform for achieving directional coupling and optical isolation with PSOI-based interfaces. For example, breaking the inversion symmetry of a nanofiber PSOI interface using a nanosphere scatterer reduces the required accuracy in the size and position of excitation spots. This study introduces a novel approach to break the mirror symmetry of a PSOI-based nanofiber waveguide by coupling it with a geometrically symmetric chiral gold nanohelicoid (GNH) resonator, which relaxes the original requirement of circularly polarized excitations. Finite-difference time-domain simulations demonstrate unidirectional light coupling and propagation under both circularly and linearly polarized excitations, showcasing the versatility of this hybrid symmetry-broken system. The Fano-like features observed in directionality spectra align with the GNH’s circular dichroism spectrum, emphasizing an intricate correlation between plasmonic near-field chirality and far-field scattering dichroism. This work paves the way for enhancing the functionalities of PSOI-based waveguide interfaces through locally coupling them with nanoscale chiral resonators, thereby expanding their application in quantum photonics, information transport and plasmonic nanophotonics.

Local Isomeric Polar Nanoclusters Enabled Superior Capacitive Energy Storage Under Moderate Fields in NaNbO3-Based Lead-Free Ceramics.

The high-field energy-storage performance of dielectric capacitors has been significantly improved in recent years, yet the high voltage risks of device failure and large cost of insulation technology increase the demand for high-performance dielectric capacitors at finite electric fields. Herein, a unique superparaelectric state filled with polar nanoclusters with various local symmetries for lead-free relaxor ferroelectric capacitors is subtly designed through a simple chemical modification method, successfully realizing a collaborative improvement of polarization hysteresis, maximum polarization, and polarization saturation at moderate electric fields of 20-30kVmm-1. Therefore, a giant recoverable energy density of ≈5.0Jcm-3 and a high efficiency of ≈82.1% are simultaneously achieved at 30kVmm-1 in (0.9-x)NaNbO3-0.1BaTiO3-xBiFeO3 lead-free ceramics, showing a breakthrough progress in moderate-field comprehensive energy-storage performances. Moreover, superior charge-discharge performances of high-power density ≈182MWcm-3, high discharge energy density ≈4.3Jcm-3 and ultra-short discharge time <70ns as well as excellent temperature stability demonstrate great application potentials for dielectric energy-storage capacitors in pulsed power devices. This work provides an effective and paradigmatic strategy for developing novel lead-free dielectrics with high energy-storage performance under finite electric fields.