Center Symmetry Research Articles

A comprehensive computational investigations on the physical properties of TiXSb (X: Ru, Pt) half‐Heusler alloys and Ti2RuPtSb2 double half‐Heusler

AbstractIn this paper, we have investigated the structural, elastic, optoelectronic and thermoelectric properties of the new half‐Heusler alloys TiXSb (X: Ru, Pt) and Ti2RuPtSb2 double half‐Heusler compound, using the full‐potential linearized augmented plane wave method. Different approximations for the exchange‐correlation functional were performed as generalized gradient approximation + Hubbard potential (GGA + U) and its combination with the modified Becke–Johnson potential. The negative values of the calculated formation energy indicate that these compounds are energetically stable. Both half Heusler alloys are half‐metallic ferromagnetic materials and exhibit an integer magnetic moment of Mt = 1.00 μB. While, the Ti2RuPtSb2 is a direct semiconductor at center symmetry. The calculations of optical properties revealed that Ti2RuPtSb2 compound exhibits an excellent optical efficiency. The thermoelectric properties such as the Seebeck coefficient (S); electronic thermal conductivity (κe/τ), power factor (PF), and figure of merit (ZT) have been studied and discussed in detail. Consequently, the investigated compounds were identified as candidate materials for high technological applications.

Non-invertible topological defects in 4-dimensional $\mathbb {Z}_2$ pure lattice gauge theory

Abstract We explore topological defects in the 4D pure $\mathbb {Z}_2$ lattice gauge theory. This theory has 1-form $\mathbb {Z}_{2}$ center symmetry as well as Kramers–Wannier–Wegner (KWW) duality. We construct the KWW duality topological defects in a similar way to those constructed by Aasen et al. [J. Phys. A 49, 354001 (2016)] for the 2D Ising model. These duality defects turn out to be non-invertible. We also construct 1-form $\mathbb {Z}_{2}$ symmetry defects as well as the junctions between the KWW duality defects and 1-form $\mathbb {Z}_{2}$ center symmetry defects. The crossing relations between these defects are derived. The expectation values of some configurations of these topological defects are calculated by using these crossing relations.

Spectrum of trace deformed Yang-Mills theories

In this paper we study, by means of numerical simulations, the behaviour of the scalar glueball mass and the ground state of the torelon for trace deformed Yang-Mills theory defined on $ \mathbb{R}^3\times S^1$, in which center symmetry is recovered even at small compactification radii. We find, by investigating both $SU(3)$ and $SU(4)$ pure gauge theories, that the glueball mass computed in the deformed theory, when center symmetry is recovered, is compatible with its value at zero temperature and does not show any significant dependence on the compactification radius; moreover, we establish a connection between the deformation parameter and an effective compactification size, which works well at least for small deformations. In addition, we observe that the ground state of the torelon which winds around the small traced deformed circle with size $l$ acquires a pleateau for large values of the strength $h$, with values which are compatible with a $1/l$ behavior but, on the other hand, are still not in complete agreement with the asymptotic semiclassical large-$N$ predictions.

The mixed 0-form/1-form anomaly in Hilbert space: pouring the new wine into old bottles

We study four-dimensional gauge theories with arbitrary simple gauge group with 1-form global center symmetry and 0-form parity or discrete chiral symmetry. We canonically quantize on \U0001d54b3, in a fixed background field gauging the 1-form symmetry. We show that the mixed 0-form/1-form ’t Hooft anomaly results in a central extension of the global-symmetry operator algebra. We determine this algebra in each case and show that the anomaly implies degeneracies in the spectrum of the Hamiltonian at any finite- size torus. We discuss the consistency of these constraints with both older and recent semiclassical calculations in SU(N) theories, with or without adjoint fermions, as well as with their conjectured infrared phases.

Centrosymmetric‐ and Axisymmetric‐Patterned Flexible Tactile Sensor for Roughness and Slip Intelligent Recognition

Next‐generation robots are being designed to function autonomously in complex and unstructured environments. In particular, based on the real‐time measurement and differentiation of normal pressure and shear force, robots can be equipped with the capabilities of damage‐free grasp within minimum force limits, as well as dexterous operation through surface roughness and slip information. Herein, a flexible tactile sensor with a small cylinder protrusion and four arc‐shaped protrusions is developed. Due to its center symmetry and axisymmetry characteristics, the normal pressure and shear force can be decoupled from the complex stress without any interference from torsion. The flexible tactile sensor exhibits good linearity and superior cycling stability and is capable of determining the magnitude and direction of the applied force accurately. The flexible tactile sensor is comfortable to wear, and it is integrated onto the manipulator to realize various delicate and dexterous tasks, such as pressure detection, interaction with fragile objects, and roughness identification. Moreover, intelligent recognition of the sliding and stationary states can be achieved by decoding signals of sliding friction and static friction from the feedback information, leading to real time and precise adjustment of the grasping state of the manipulator.

Noninvertible 1-form symmetry and Casimir scaling in 2D Yang-Mills theory

Pure Yang-Mills theory in 2 spacetime dimensions shows exact Casimir scaling. Thus there are infinitely many string tensions, and this has been understood as a result of non-propagating gluons in 2 dimensions. From ordinary symmetry considerations, however, this richness in the spectrum of string tensions seems mysterious. Conventional wisdom has it that it is the center symmetry that classifies string tensions, but being finite it cannot explain infinitely many confining strings. In this note, we resolve this discrepancy between dynamics and kinematics by pointing out the existence of a non-invertible 1-form symmetry, which is able to distinguish Wilson loops in different representations. We speculate on possible implications for Yang-Mills theories in 3 and 4 dimensions.

Piezotronics in two‐dimensional materials

AbstractThe fascinating two‐dimensional (2D) materials are being potentially applied in various fields from science to engineering benefitting from the charming physical and chemical properties on optics, electronics, and magnetism, compared with the bulk crystal, while piezotronics is a universal and pervasive phenomenon in the materials with broking center symmetry, promoting the new field and notable achievements of piezotronics in 2D materials with higher accuracy and sensitivity. For example, 20 parts per billion of the detecting limitations in NO2 sensor, 500 μm of spatial strain resolution in flexible devices, and 0.363 eV output voltage in nanogenerators. In this review, three categories of 2D piezotronics materials are first introduced ranging from organic to inorganic data, among which six types of 2D inorganic materials are emphasized based on the geometrical arrangement of different atoms. Then, the microscopic mechanism of carrier transport and separation in 2D piezotronic materials is highlighted, accompanied with the presentation of four measured methods. Subsequently, the developed applications of 2D piezotronics are discussed comprehensively including different kinds of sensors, piezo‐catalysis, nanogenerators and information storage. Ultimately, we suggest the challenges and provide the ideas for qualitative–quantitative research of microscopic mechanism and large‐scale integrated applications of 2D piezotronics.image

Gravitational waves from dark Yang-Mills sectors

Dark Yang-Mills sectors, which are ubiquitous in the string landscape, may be reheated above their critical temperature and subsequently go through a confining first-order phase transition that produces stochastic gravitational waves in the early universe. Taking into account constraints from lattice and from Yang-Mills (center and Weyl) symmetries, we use a phenomenological model to construct an effective potential of the semi quark-gluon plasma phase, from which we compute the gravitational wave signal produced during confinement for numerous gauge groups. The signal is maximized when the dark sector dominates the energy density of the universe at the time of the phase transition. In that case, we find that it is within reach of the next-to-next generation of experiments (BBO, DECIGO) for a range of dark confinement scales near the weak scale.

A Probabilistic Mechanism for Quark Confinement

The confinement of quarks is one of the enduring mysteries of modern physics. There is a longstanding physics heuristic that confinement is a consequence of `unbroken center symmetry'. This article gives mathematical confirmation of this heuristic, by rigorously defining of center symmetry in lattice gauge theories and proving that a theory is confining when center symmetry is unbroken. Furthermore, a sufficient condition for unbroken center symmetry is given: It is shown that if the center of the gauge group is nontrivial, and correlations decay exponentially under arbitrary boundary conditions, then center symmetry does not break.

Instantons, symmetries and anomalies in five dimensions

All five-dimensional non-abelian gauge theories have a U(1)I global symmetry associated with instantonic particles. We describe an obstruction to coupling U(1)I to a classical background gauge field that occurs whenever the theory has a one-form center symmetry. This is a finite-order mixed ’t Hooft anomaly between the two symmetries. We also show that a similar obstruction takes place in gauge theories with fundamental matter by studying twisted bundles for the ordinary flavor symmetry. We explore some general dynamical properties of the candidate phases implied by the anomaly. Finally, we apply our results to supersymmetric gauge theories in five dimensions and analyze the symmetry enhancement patterns occurring at their conjectured RG fixed points.

Students’ understanding of axial and central symmetry

The paper focuses on students’ understanding of the concepts of axial and central symmetries in a plane. Attention is paid to whether students of various ages identify a non-model of an axially symmetrical figure, know that a line segment has two axes of symmetry and a circle has an infinite number of symmetry axes, and are able to construct an image of a given figure in central symmetry. The results presented here were obtained by a quantitative analysis of tests given to nearly 1,500 Czech students, including pre-service mathematics teachers. The paper presents the statistics of the students’ answers, discusses the students’ thought processes and presents some of the students’ original solutions. The data obtained are also analysed with regard to gender differences and to the type of school that students attend. The results show that students have two principal misconceptions: that a rhomboid is an axially symmetrical figure and that a line segment has just one axis of symmetry. Moreover, many of the tested students confused axial and central symmetry. Finally, the possible causes of these errors are considered and recommendations for preventing these errors are given.

Quark Cluster Expansion Model for Interpreting Finite-T Lattice QCD Thermodynamics

In this work, we present a unified approach to the thermodynamics of hadron–quark–gluon matter at finite temperatures on the basis of a quark cluster expansion in the form of a generalized Beth–Uhlenbeck approach with a generic ansatz for the hadronic phase shifts that fulfills the Levinson theorem. The change in the composition of the system from a hadron resonance gas to a quark–gluon plasma takes place in the narrow temperature interval of 150–190 MeV, where the Mott dissociation of hadrons is triggered by the dropping quark mass as a result of the restoration of chiral symmetry. The deconfinement of quark and gluon degrees of freedom is regulated by the Polyakov loop variable that signals the breaking of the Z(3) center symmetry of the color SU(3) group of QCD. We suggest a Polyakov-loop quark–gluon plasma model with O(αs) virial correction and solve the stationarity condition of the thermodynamic potential (gap equation) for the Polyakov loop. The resulting pressure is in excellent agreement with lattice QCD simulations up to high temperatures.

Condensates and anomaly cascade in vector-like theories

We study the bilinear and higher-order fermion condensates in 4-dimensional SU(N) gauge theories with a single Dirac fermion in a general representation. Augmented with a mixed anomaly between the 0-form discrete chiral, 1-form center, and 0-form baryon number symmetries (BC anomaly), we sort out theories that admit higher-order condensates and vanishing fermion bilinears. Then, the BC anomaly is utilized to prove, in the absence of a topological quantum field theory, that nonvanishing fermion bilinears are inevitable in infrared-gapped theories with 2-index (anti)symmetric fermions. We also contrast the BC anomaly with the 0-form anomalies and show that it is the former anomaly that determines the infrared physics; we argue that the BC anomaly lurks deep to the infrared while the 0-form anomalies are just variations of local terms. We provide evidence of this assertion by studying the BC anomaly in vector-like theories compactified on a small spacial circle. These theories are weakly-coupled, under analytical control, and they admit a dual description in terms of abelian photons that determine the deep infrared dynamics. We show that the dual photons talk directly to the 1-form center symmetry in order to match the BC anomaly, while the 0-form anomalies are variations of local terms and are matched by fiat. Finally, we study the fate of the BC anomaly in the compactified theories when they are held at a finite temperature. The effective field theory that describes the low-energy physics is 2-dimensional. We show that the BC anomaly cascades from 4 to 2 dimensions.

Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond N-ality

We study a 3d lattice gauge theory with gauge group U(1)N−1 ⋊ SN, which is obtained by gauging the SN global symmetry of a pure U(1)N−1 gauge theory, and we call it the semi-Abelian gauge theory. We compute mass gaps and string tensions for both theories using the monopole-gas description. We find that the effective potential receives equal contributions at leading order from monopoles associated with the entire SU(N) root system. Even though the center symmetry of the semi-Abelian gauge theory is given by ℤN, we observe that the string tensions do not obey the N-ality rule and carry more detailed information on the representations of the gauge group. We find that this refinement is due to the presence of non-invertible topological lines as a remnant of U(1)N−1 one-form symmetry in the original Abelian lattice theory. Upon adding charged particles corresponding to W-bosons, such non-invertible symmetries are explicitly broken so that the N-ality rule should emerge in the deep infrared regime.

Reconfinement, localization, and thermal monopoles in SU(3) trace-deformed Yang-Mills theory

We study, by means of numerical lattice simulations, the properties of the reconfinement phase transition taking place in trace deformed $SU(3)$ Yang-Mills theory defined on $\mathbb{R}^3\times S^1$, in which center symmetry is recovered even for small compactification radii. We show, by means of a finite size scaling analysis, that the reconfinement phase transition is first-order, like the usual $SU(3)$ thermal phase transition. We then investigate two different physical phenomena, which are known to characterize the standard confinement/deconfinement phase transition, namely the condensation of thermal magnetic monopoles and the change in the localization properties of the eigenmodes of the Dirac operator. Regarding the latter, we show that the mobility edge signalling the Anderson-like transition in the Dirac spectrum vanishes as one enters the reconfined phase, as it happens in the standard confined phase. Thermal monopoles, instead, show a peculiar behavior: their density decreases going through reconfinement, at odds with the standard thermal theory; nonetheless, they condense at reconfinement, like at the usual confinement transition. The coincidence of monopole condensation and Dirac mode delocalization, even in a framework different from that of the standard confinement transition, suggests the existence of a strict link between them.

Two characterizations of central BMO space via the commutators of Hardy operators

Abstract This article addresses two characterizations of BMO ⁢ ( ℝ n ) {\mathrm{BMO}(\mathbb{R}^{n})} -type space via the commutators of Hardy operators with homogeneous kernels on Lebesgue spaces: (i) characterization of the central BMO ⁢ ( ℝ n ) {\mathrm{BMO}(\mathbb{R}^{n})} space by the boundedness of the commutators; (ii) characterization of the central BMO ⁢ ( ℝ n ) {\mathrm{BMO}(\mathbb{R}^{n})} -closure of C c ∞ ⁢ ( ℝ n ) {C_{c}^{\infty}(\mathbb{R}^{n})} space via the compactness of the commutators. This is done by exploiting the center symmetry of Hardy operator deeply and by a more explicit decomposition of the operator and the kernel function.

Deconfinement critical point of lattice QCD with Nf=2 Wilson fermions

The ${\rm SU}(3)$ pure gauge theory exhibits a first-order thermal deconfinement transition due to spontaneous breaking of its global $Z_3$ center symmetry. When heavy dynamical quarks are added, this symmetry is broken explicitly and the transition weakens with decreasing quark mass until it disappears at a critical point. We compute the critical hopping parameter and the associated pion mass for lattice QCD with $N_f=2$ degenerate standard Wilson fermions on $N_\tau\in\{6,8,10\}$ lattices, corresponding to lattice spacings $a=0.12\, {\rm fm}$, $a=0.09\, {\rm fm}$, $a=0.07\, {\rm fm}$, respectively. Significant cut-off effects are observed, with the first-order region growing as the lattice gets finer. While current lattices are still too coarse for a continuum extrapolation, we estimate $m_\pi^c\approx 4 {\rm GeV}$ with a remaining systematic error of $\sim 20\%$. Our results allow to assess the accuracy of the LO and NLO hopping expanded fermion determinant used in the literature for various purposes. We also provide a detailed investigation of the statistics required for this type of calculation, which is useful for similar investigations of the chiral transition.

ЗВ’ЯЗОК ГРУПИ СИМЕТРІЇ ОРНАМЕНТУ НА ЕСКІЗІ М. К. ЕШЕРА «МОРСЬКІ КОНИКИ» З РУХАМИ ПЛОЩИНИ, ЩО ОПИСУЮТЬ ПОБУДОВУ ЙОГО ФІГУРНОЇ ПЛИТКИ

Перше, що кидається в очі, коли розглядаєш ескіз М. К. Ешера «Морські коники», − її особливість, яка полягає в тому, що якщо прийняти будь-яку зооморфну форму за оригінал, то, щоб отримати її копії, необхідно виконати центральні симетрії оригіналу та його паралельні перенесення, причому паралельні перенесення здійснюються в шести напрямках. Ми припускаємо, що такими ж центральними симетріями і паралельними перенесеннями пов’язані між собою окремі частини контуру зооморфної форми, що цілком заповнює площину. Наше припущення ґрунтується на тому, що зв’язок між групою симетрії орнаменту і групою рухів площині, яка описує побудову фігурних плиток, що заповнюють площину без накладень і пропусків, була виявлена нами і в гравюрі М. К. Ешера «Вершники», і в його літографії «Ящірки». Таким чином, наша мета полягає в тому, щоб класифікувати орнаменти за кристалографічними групами симетрії на площині, відкритими російським вченим Є. С. Федоровим, і зв’язати групи симетрії орнаментів з групами рухів площині, що описують побудову їх фігур, що повторюються. Запропоновано правило побудови фігурної плитки, що стилізує зображення рослин і тварин і заповнює площину без накладень і пропусків при паралельних перенесеннях і обертаннях її повторень, зокрема фігурної плитки, що узагальнює зображення зооморфною форми на ескізі М. К. Ешера «Морські коники». Запропоноване правило було застосовано для побудови орнаменту, що стилізує ескіз М. К. Ешера «Морські коники». Показано, що даний орнамент має множину центрів симетрії і шість векторів трансляції. Виявлено зв’язок між групою симетрії орнаменту і рухами площині, що приводять до утворення його фігурної плитки. Показано, що якщо будь-якій фігурі відповідає будь-яка група перетворень площини, то такій же групі перетворень площини буде відповідати орнамент, отриманий паралельними переносами і обертаннями її повторень. Припущено, що предметом подальших досліджень буде застосування однієї з кристалографічних груп симетрії Є. С. Федорова до побудови фігурної плитки, що стилізує зооморфну форму на одній з гравюр М. К. Ешера.

Deconfinement and the Explicit Center Symmetry Breaking in a Strong Magnetic Field

Deconfinement and the Explicit Center Symmetry Breaking in a Strong Magnetic Field

Higher form symmetries and M-theory

We discuss the geometric origin of discrete higher form symmetries of quantum field theories in terms of defect groups from geometric engineering in M-theory. The flux non-commutativity in M-theory gives rise to (mixed) ’t Hooft anomalies for the defect group which constrains the corresponding global structures of the associated quantum fields. We analyze the example of 4d mathcal{N} = 1 SYM gauge theory in four dimensions, and we reproduce the well-known classification of global structures from reading between its lines. We extend this analysis to the case of 7d mathcal{N} = 1 SYM theory, where we recover it from a mixed ’t Hooft anomaly among the electric 1-form center symmetry and the magnetic 4-form center symmetry in the defect group. The case of five-dimensional SCFTs from M-theory on toric singularities is discussed in detail. In that context we determine the corresponding 1-form and 2-form defect groups and we explain how to determine the corresponding mixed ’t Hooft anomalies from flux non-commutativity. Several predictions for non-conventional 5d SCFTs are obtained. The matching of discrete higher-form symmetries and their anomalies provides an interesting consistency check for 5d dualities.