Full Symmetry Research Articles

Topological classification of higher-order topological phases with nested band inversion surfaces

Higher-order topological phases (HOTPs) hold gapped bulk bands and topological boundary states localized in boundaries with codimension higher than one. In this paper, we provide a unified construction and topological characterization of HOTPs for the full Altland-Zirnbauer tenfold symmetry classes, based on a method known as nested band inversion surfaces (BISs). Specifically, HOTPs built on this method are decomposed into a series of subsystems, and higher-order topological boundary states emerges from the interplay of their first-order topology. Our analysis begins with a general discussion of HOTPs in continuous Hamiltonians for each symmetry class, then moves on to several lattice examples illustrating the topological characterization based on the nested-BIS method. Despite the example minimal models possessing several spatial symmetries, our method does not rely on any spatial symmetry, and can be easily extended into arbitrary orders of topology in dimensions. Furthermore, we extend our discussion to systems with asymmetric boundary states induced by two different mechanisms, namely, crossed BISs that break a $\mathcal{C}_4$ rotation symmetry, and non-Clifford operators that break certain chiral-mirror symmetries of the minimal models.

Exhibition Review: Christina Fernandez: Multiple Exposures

Exhibition Review: <i>Christina Fernandez: Multiple Exposures</i>

Fully Symmetric Cyclodextrin Polycarboxylates: How to Determine Reliable Protonation Constants from NMR Titration Data.

Acid-base properties of cyclodextrins (CDs), persubstituted at C-6 by 3-mercaptopropionic acid, sualphadex (Suα-CD), subetadex (Suβ-CD) and sugammadex (Suγ-CD, the antidote of neuromuscular blocking steroids) were studied by 1H NMR-pH titrations. For each CD, the severe overlap in protonation steps prevented the calculation of macroscopic pKa values using the standard data fitting model. Considering the full symmetry of polycarboxylate structures, we reduced the number of unknown NMR parameters in the "Q-fitting" or the novel "equidistant macroscopic" evaluation approaches. These models already provided pKa values, but some of them proved to be physically unrealistic, deceptively suggesting cooperativity in carboxylate protonations. The latter problem could be circumvented by adapting the microscopic site-binding (cluster expansion) model by Borkovec, which applies pairwise interactivity parameters to quantify the mutual basicity-decreasing effect of carboxylate protonations. Surprisingly, only a single averaged interactivity parameter could be calculated reliably besides the carboxylate 'core' microconstant for each CD derivative. The speciation of protonation isomers hence could not be resolved, but the optimized microscopic basicity parameters could be converted to the following sets of macroscopic pKa values: 3.84, 4.35, 4.81, 5.31, 5.78, 6.28 for Suα-CD; 3.82, 4.31, 4.73, 5.18, 5.64, 6.06, 6.54 for Suβ-CD and 3.83, 4.28, 4.65, 5.03, 5.43, 5.81, 6.18, 6.64 for Suγ-CD. The pH-dependent charge of these compounds can now be accurately calculated, in support of designing new analytical methods to exploit their charge-dependent molecular recognition such as in cyclodextrin-aided chiral capillary electrophoresis.

In Vivo Cherenkov Imaging-Guided FLASH Radiotherapy

<h3>Purpose/Objective(s)</h3> A fast-imaging technique was developed for the first <i>in vivo</i> Cherenkov emission imaging from an ultra-high dose rate (UHDR) electron beam source at single pulse (360 Hz) and submillimeter resolution for beam characterization and real time monitoring during delivery. <h3>Materials/Methods</h3> A CMOS camera, gated to the UHDR LINAC, imaged the Cherenkov emission profiles pulse by pulse during the irradiation of murine limbs and intestinal region and a tissue equivalent phantom. An intensifier's effect on image quality was investigated considering signal to noise and spatial resolution. Pulse by pulse and cumulative Cherenkov emission profiles were quantified spatially and temporally. <h3>Results</h3> An intensifier improved the emission profile's signal to noise ratio from 15 to 280, with reduced spatial resolution (2.8 to 1.0 line pairs/mm). The profile extended beyond the treatment field edge due to the lateral scattering of the electrons and optical photons in tissue. The CMOS camera with an intensifier detected changes of ∼3mm in Cherenkov emission profiles due to expiration and inspiration during the murine respiratory cycle. The intensified camera's spatial resolution facilitated accurate detection of beam parameters as confirmed with radiochromic film (i.e., output, shift, full width half max, symmetry and flatness). The camera resolved the LINAC's ramp up in output during the first 4-6 pulses until stability was reached, agreeing with a photomultiplier tube detected Cherenkov emission during delivery. <h3>Conclusion</h3> This fast-imaging technique can be utilized for in vivo intrafraction monitoring of FLASH patient treatments at single pulse resolution. It can display delivery differences during respiration, and variability in the delivered treatment's surface profile, which may be perturbed from the intended UHDR treatment especially with pencil beam scanning systems. The technique may leverage the Cherenkov emission surface profile to gate the treatment under FLASH conditions while considering beam parameters such as per pulse output or beam steering consistency during delivery.

Decoding Reed-Muller Codes With Successive Codeword Permutations

A novel recursive list decoding (RLD) algorithm for Reed-Muller (RM) codes based on successive permutations (SP) of the codeword is presented. A low-complexity SP scheme applied to a subset of the symmetry group of RM codes is first proposed to carefully select a good codeword permutation on the fly. Then, the proposed SP technique is integrated into an improved RLD algorithm that initializes different decoding paths with random codeword permutations, which are sampled from the full symmetry group of RM codes. Finally, efficient latency and complexity reduction schemes are introduced that virtually preserve the error-correction performance of the proposed decoder. Simulation results demonstrate that at the target frame error rate of 10−3 for the RM code of length 256 with 163 information bits, the proposed decoder reduces 6% of the computational complexity and 22% of the decoding latency of the state-of-the-art semi-parallel simplified successive-cancellation decoder with fast Hadamard transform (SSC-FHT) that uses 96 permutations from the full symmetry group of RM codes, while relatively maintaining the error-correction performance and memory consumption of the semi-parallel permuted SSC-FHT decoder.

Effects of gravity on the capillary flow of a molten metal

Repair and construction in space by means of brazing requires understanding of the effect of gravity on the capillary flow of a molten metal. We perform two sets of experiments: (1) spreading of a sessile drop of liquid aluminum-silicon-flux (Al-Si-KxAlyFz) composite braze on a horizontal alumina (Al2O3) substrate (a non-wetting surface), and (2) capillary flow of the same braze alloy on an inclined aluminum-manganese (AA3003) substrate (a wetting surface). We vary the mass of the brazing liquid and the inclination of the substrate (i.e., the relative direction of gravity).In the composite metal/flux sessile drop experiments, we observe a secondary liquid flux meniscus forming at the contact line between the liquid Al-Si and the alumina substrate. We demonstrate that the equilibrium contact angle appears to be close to 180°, while the apparent contact angle depends on the mass of the braze. In the second set of experiments, we study the molten braze alloy on different inclinations of AA3003 in a wedge-T wetting/non-wetting assembly. As the inclination angle decreases, the wetting distance increases and the surface profile changes from a non-symmetric bag-like shape to a more symmetric pancake shape. With the mass decreasing, the surface profile on the vertical substrate approaches a symmetric shape when the wetting distance is equal or smaller than the capillary length. While the non-homogeneous melting and hence, the non-homogeneous microstructure of the melt, may prevent a full symmetry. Computational predictions of equilibrium shapes are in good agreement with experimental results.

Massless fermions on a half-space: the curious case of 2+1-dimensions

Boundary conditions for a massless Dirac fermion in 2+1 dimensions where the space is a half-plane are discussed in detail. It is argued that linear boundary conditions that leave the Hamiltonian Hermitian generically break C P and T symmetries as well as Lorentz and conformal symmetry. We show that there is essentially one special case where a single species of fermion has C PT and the full Poincare and conformal symmetry of the boundary. We show that, with doubled fermions, there is a second special case which respects C PT but still violates Lorentz and conformal symmetry. This second special case is essentially the unique boundary condition where the Dirac operator has fermion zero mode edge states. We discuss how the edge states lead to exotic representations of scale, phase and translation symmetries and how imposing a symmetry requirement leads to edge ferromagnetism of the system. We prove that the exotic ferromagnetic representations are indeed carried by the ground states of the system perturbed by a class of interaction Hamiltonians which includes the non-relativistic Coulomb interaction.

Minimal consistent Dark Matter models for systematic experimental characterisation: fermion Dark Matter

The search for a Dark Matter particle is the new grail and hard-sought nirvana of the particle physics community. From the theoretical side, it is the main challenge to provide a consistent and model-independent tool for comparing the bounds and reach of the diverse experiments. We propose a first complete classification of minimal consistent Dark Matter models, abbreviated as MCDMs, that are defined by one Dark Matter weak multiplet with up to one mediator multiplet. This classification provides the missing link between experiments and top-down models. Consistency is achieved by imposing renormalisability and invariance under the full Standard Model symmetries. We apply this paradigm to the fermionic Dark Matter case. We also reconsider the one-loop contributions to direct detection, including the relevant effect of (small) mass splits in the Dark multiplet. Our work highlights the presence of unexplored viable models, and paves the way for the ultimate systematic hunt for the Dark Matter particle.

Ring-Opening Dynamics of the Cyclopropyl Radical and Cation: the Transition State Nature of the Cyclopropyl Cation.

We provide compelling experimental and theoretical evidence for the transition state nature of the cyclopropyl cation. Synchrotron photoionization spectroscopy employing coincidence techniques together with a novel simulation based on high-accuracy ab initio calculations reveal that the cation is unstable via its allowed disrotatory ring-opening path. The ring strains of the cation and the radical are similar, but both ring opening paths for the radical are forbidden when the full electronic symmetries are considered. These findings are discussed in light of the early predictions by Longuet-Higgins alongside Woodward and Hoffman; we also propose a simple phase space explanation for the appearance of the cyclopropyl photoionization spectrum. The results of this work allow the refinement of the cyclopropane C-H bond dissociation energy, in addition to the cyclopropyl radical and cation cyclization energies, via the Active Thermochemical Tables approach.

Altermagnetism and magnetic groups with pseudoscalar electron spin

We revise existing group-theoretical approaches for a treatment of nonrelativistic collinear magnetic systems with perfect translation invariance. We show that full symmetry groups of these systems, which contain elements with independent rotations in the spin and configuration spaces (spin groups), can be replaced by magnetic groups consisting of elements with rotations acting only on position vectors. This reduction follows from modified transformation properties of electron spin, which in the considered systems becomes effectively a pseudoscalar quantity remaining unchanged upon spatial operations but changing its sign due to an operation of antisymmetry. We introduce a unitary representation of the relevant magnetic point groups and use it for a classification of collinear magnets from the viewpoint of antiferromagnetism-induced spin splitting of electron bands near the center of Brillouin zone. We prove that the recently revealed different altermagnetic classes correspond in a unique way to all nontrivial magnetic Laue classes, i.e., to the Laue groups containing the operation of antisymmetry only in combination with a spatial rotation. Four of these Laue classes are found compatible with a nonzero spin conductivity. Subsequent inspection of a simple model allows us to address briefly the physical mechanisms responsible for the spin splitting in real systems.

Symmetry breaking yields chimeras in two small populations of Kuramoto-type oscillators.

Despite their simplicity, networks of coupled phase oscillators can give rise to intriguing collective dynamical phenomena. However, the symmetries of globally and identically coupled identical units do not allow solutions where distinct oscillators are frequency-unlocked-a necessary condition for the emergence of chimeras. Thus, forced symmetry breaking is necessary to observe chimera-type solutions. Here, we consider the bifurcations that arise when full permutational symmetry is broken for the network to consist of coupled populations. We consider the smallest possible network composed of four phase oscillators and elucidate the phase space structure, (partial) integrability for some parameter values, and how the bifurcations away from full symmetry lead to frequency-unlocked weak chimera solutions. Since such solutions wind around a torus they must arise in a global bifurcation scenario. Moreover, periodic weak chimeras undergo a period-doubling cascade leading to chaos. The resulting chaotic dynamics with distinct frequencies do not rely on amplitude variation and arise in the smallest networks that support chaos.

Stabilizing lattice gauge theories through simplified local pseudogenerators

The postulate of gauge invariance in nature does not lend itself directly to implementations of lattice gauge theories in modern setups of quantum synthetic matter. Unavoidable gauge-breaking errors in such devices require gauge invariance to be enforced for faithful quantum simulation of gauge-theory physics. This poses major experimental challenges, in large part due to the complexity of the gauge-symmetry generators. Here, we show that gauge invariance can be reliably stabilized by employing simplified local pseudogenerators designed such that within the physical sector they act identically to the actual local generator. Dynamically, they give rise to emergent exact gauge theories up to time scales polynomial and even exponential in the protection strength. This obviates the need for implementing often complex multibody full gauge symmetries, thereby further reducing experimental overhead in physical realizations. We showcase our method in the ${\mathbb{Z}}_{2}$ lattice gauge theory, and discuss experimental considerations for its realization in modern ultracold-atom setups.

A symmetry-based approach to the characterization of complex surface morphologies: Application in CuO and NiO nanostructures

In recent years, bottom-up nanofabrication techniques and especially solution-based ones have gained significant popularity due to their relatively facile implementation, low-cost and design flexibility that allows the development of a plethora of three-dimensional nanostructures and nanoarchitectures. Nonetheless, despite the apparent simplicity of the methods, the resulting nanostructures are often morphologically and hierarchically complex with no apparent way of appropriately describing their features in a quantifiable and methodological way. In this work, we propose a symmetry-based approach for the quantitative characterization of the morphology of nanostructured surfaces. The key idea is to characterize the morphology of nanostructures by means of the fundamental spatial symmetry metrics and the deviations from the fully symmetrical counterparts. The focus of the proposed methodology is on the translational and scaling symmetry, which are investigated through the mathematical tools of Fourier and (multi)fractal analysis, respectively. The calculated metrics characterizing these symmetries are the period and the fractal dimension of surfaces while the deviations are quantified by the disorder parameter ω d related to the FWHM of Fourier peak and by the asymmetry of the multifractal spectrum for the translational and scaling symmetry respectively. As an initial study case and in order to demonstrate its suitability, the developed symmetry-based methodology was applied to nickel oxide (NiO) and copper oxide (CuO) nanostructures hydrothermally-grown on silicon substrates. The results show that even in the cases where the surfaces display similar symmetry metrics (period, fractal dimension) the symmetry-based approach reveals subtle, but quantifiable differences in the deviations from full symmetries which are not easily identified by other approaches. • A symmetry-based method for nanometrological analysis of complex nanomorphologies is developed and implemented. • It detects and quantifies the spatial symmetries in surfaces and the deviations from these (surface disorder). • Fourier, correlation and (multi) fractal analysis are used. • The method is successfully applied in CuO and NiO nanostructures hydrothermally grown on silicon substrates. • It captures subtle differences in nanosurface translational and scaling disorder and evaluates material/process origins.

Integrals of Legendre polynomials over half range and their relation to the electrostatic potential in hemispherical geometry

Spherical symmetry is often encountered in many problems in mathematics and physical sciences. On the other hand, cases that involve hemispherical geometry lead to much less studied mathematical situations. In this work, we consider a case study that arises from potential theory where absence of a full spherical symmetry gives rise to expressions involving Legendre polynomials constrained in an interval that is different from the usual range in which they are orthogonal. We use exact mathematical results for the integrals of Legendre polynomials of arbitrary order over half range to obtain analytic expressions for the electrostatic potential created by a solid hemisphere with uniform volume charge density.

BIGDML—Towards accurate quantum machine learning force fields for materials

Machine-learning force fields (MLFF) should be accurate, computationally and data efficient, and applicable to molecules, materials, and interfaces thereof. Currently, MLFFs often introduce tradeoffs that restrict their practical applicability to small subsets of chemical space or require exhaustive datasets for training. Here, we introduce the Bravais-Inspired Gradient-Domain Machine Learning (BIGDML) approach and demonstrate its ability to construct reliable force fields using a training set with just 10–200 geometries for materials including pristine and defect-containing 2D and 3D semiconductors and metals, as well as chemisorbed and physisorbed atomic and molecular adsorbates on surfaces. The BIGDML model employs the full relevant symmetry group for a given material, does not assume artificial atom types or localization of atomic interactions and exhibits high data efficiency and state-of-the-art energy accuracies (errors substantially below 1 meV per atom) for an extended set of materials. Extensive path-integral molecular dynamics carried out with BIGDML models demonstrate the counterintuitive localization of benzene–graphene dynamics induced by nuclear quantum effects and their strong contributions to the hydrogen diffusion coefficient in a Pd crystal for a wide range of temperatures.

Gauge symmetry of the 3BF theory for a generic semistrict Lie three-group

The higher category theory can be employed to generalize the BF action to the so-called 3BF action, by passing from the notion of a gauge group to the notion of a gauge three-group. In this work we determine the full gauge symmetry of the 3BF action. To that end, the complete Hamiltonian analysis of the 3BF action for an arbitrary semistrict Lie three-group is performed, by using the Dirac procedure. The Hamiltonian analysis is the first step towards a canonical quantization of a 3BF theory. This is an important stepping-stone for the quantization of the complete standard model of elementary particles coupled to Einstein–Cartan gravity, formulated as a 3BF action with suitable simplicity constraints. We show that the resulting gauge symmetry group consists of the familiar G-, H-, and L-gauge transformations, as well as additional M- and N-gauge transformations, which have not been discussed in the existing literature.

A model of persistent breaking of continuous symmetry

We consider a UV-complete field-theoretic model in general dimensions, including d=2+1, which consists of two copies of the long-range vector models, with O(m) and O(N-m) global symmetry groups, perturbed by double-trace operators. Using conformal perturbation theory we find weakly-coupled IR fixed points for N\geq 6N≥6 that reveal a spontaneous breaking of global symmetry. Namely, at finite temperature the lower rank group is broken, with the pattern persisting at all temperatures due to scale-invariance. We provide evidence that the models in question are unitary and invariant under full conformal symmetry. Furthermore, we show that this model exhibits a continuous family of weakly interacting field theories at finite N.

Lattice models from CFT on surfaces with holes: I. Torus partition function via two lattice cells

We construct a one-parameter family of lattice models starting from a two-dimensional rational conformal field theory on a torus with a regular lattice of holes, each of which is equipped with a conformal boundary condition. The lattice model is obtained by cutting the surface into triangles with clipped-off edges using open channel factorisation. The parameter is given by the hole radius. At finite radius, high energy states are suppressed and the model is effectively finite. In the zero-radius limit, it recovers the CFT amplitude exactly. In the touching hole limit, one obtains a topological field theory. If one chooses a special conformal boundary condition which we call ‘cloaking boundary condition’, then for each value of the radius the fusion category of topological line defects of the CFT is contained in the lattice model. The fact that the full topological symmetry of the initial CFT is realised exactly is a key feature of our lattice models. We provide an explicit recursive procedure to evaluate the interaction vertex on arbitrary states. As an example, we study the lattice model obtained from the Ising CFT on a torus with one hole, decomposed into two lattice cells. We numerically compare the truncated lattice model to the CFT expression obtained from expanding the boundary state in terms of the hole radius and we find good agreement at intermediate values of the radius.

Role of anomalous symmetry in 0−π qubits

We present an exact full symmetry analysis of the 0-$\pi$ superconducting circuit. We identify points in control parameter space of enhanced anomalous symmetry, which imposes robust twofold degeneracy of its ground state, that is for all values of the energy parameters of the model. We show, both analytically and numerically, how this anomalous symmetry is maintained in the low-energy sector, thus providing us with a strong candidate for robust qubit engineering.

Marginal stability of soft anharmonic mean field spin glasses

We investigate the properties of the glass phase of a recently introduced spin glass model of soft spins subjected to an anharmonic quartic local potential, which serves as a model of low temperature molecular or soft glasses. We solve the model using mean field theory and show that, at low temperatures, it is described by full replica symmetry breaking. As a consequence, at zero temperature the glass phase is marginally stable. We show that in this case, marginal stability comes from a combination of both soft linear excitations—appearing in a gapless spectrum of the Hessian of linear excitations—and pseudogapped non-linear excitations—corresponding to nearly degenerate two level systems. Therefore, this model is a natural candidate to describe what happens in soft glasses, where quasi localized soft modes in the density of states appear together with non-linear modes triggering avalanches and conjectured to be essential to describe the universal low temperature anomalies of glasses.