Heavy fields and the axion quality problem
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
SEARCH · Engineering Papers
Results for “Continuous symmetries”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Geometric origin of the energy-momentum tensor improvement terms
In a flat background, the canonical energy momentum tensor of Lorentz and conformally invariant matter field theories can be improved to a symmetric and traceless tensor that gives the same conserved charges. We argue that the geometric origin of this improvement process is unveiled when the matter theory is coupled to metric-affine gravity. In particular, we show that the Belinfante-Rosenfeld improvement terms correspond to the matter theory’s hypermomentum. The improvement terms in conformally invariant matter theories are also related to the hypermomentum; however, a general proof would require an extended investigation. We demonstrate our results through various examples, such as the free massless scalar, the Maxwell field, Abelian p-forms, the Dirac field, and a nonunitary massless scalar field. Possible applications of our method for theories that break Lorentz or special conformal invariance are briefly discussed.
classical solutions in field theory↗
ChemEnv : a fast and robust coordination environment identification tool
Coordination or local environments have been used to describe, analyze and understand crystal structures for more than a century. Here, a new tool called ChemEnv, which can identify coordination environments in a fast and robust manner, is presented. In contrast to previous tools, the assessment of the coordination environments is not biased by small distortions of the crystal structure. Its robust and fast implementation enables the analysis of large databases of structures. The code is available open source within the pymatgen package and the software can also be used through a web app available on http://crystaltoolkit.org through the Materials Project.
42 ENGINEERING↗
Operationally induced preferred basis in unitary quantum mechanics
The preferred-basis problem and the definite-outcome aspect of the measurement problem persist even if the detector is modeled unitarily, because experimental data are necessarily represented in a Boolean event algebra of mutually exclusive records whereas the theoretical description is naturally formulated in a noncommutative operator algebra with continuous unitary symmetry. This change of mathematical type constitutes the core of the 'cut': a structurally necessary interface from group-based kinematics to set-based counting. In the presented view the basis relevant for recorded outcomes is not determined by the system Hamiltonian alone; it is induced by the measurement mapping, i.e., by the detector channel together with the coarse-grained readout that defines an instrument. The probabilistic mapping is anchored in symmetry and measure theory: by Gleason-type uniqueness (Gleason for projections in $d>2$ and Busch's extension for Positive Operator-Valued Measures (POVMs) including $d=2$), the trace rule is the unique probability measure consistent with additivity over exclusive events and basis-independence of the unitary sector. A compact qubit--pointer model yields an induced unsharp POVM $E_\pm=\tfrac12(\id\pm η\,σ_z)$ with $η$ fixed by pointer resolution, displaying explicitly how the detector induces the relevant basis. Finally, nested-observer paradoxes are tightened into a non-composability lemma: joint assignment of outcome propositions is obstructed unless a joint instrument exists. This relocates the origin of randomness to the stochasticity of the transition rules.
Pronskikh, Vitaly [Fermilab] (ORCID:00000002518174↗
Smooth periodic gauge satisfying crystal symmetry and periodicity to study high-harmonic generation in solids
Intense lasers can easily drive nonadiabatic transitions of excited electron wave packets across the Brillouin zones, thus transition dipole moments (TDM) between energy bands of solids should be continuous, satisfying crystal symmetry, and periodic at zone boundaries. While current ab initio algorithms are powerful in calculating band structures of solids, they all introduced random phases into the eigenfunctions at each crystal momentum k. In this work, we show how to choose a “smooth-periodic” gauge where TDMs can be smooth versus k, preserving crystal symmetry, as well as maintaining periodic at boundaries. The symmetry properties of TDMs with respect to k ensure the absence of even-order harmonics from MgO with inversion symmetry, while the TDM in the “smooth-periodic” gauge for broken-symmetry ZnO is responsible for even harmonics that were underestimated in previous simulations. These results reveal the importance of correctly treating the complex TDMs that satisfy crystal symmetry and continuous across zone boundaries in nonlinear laser-solid interactions, which has been elusive in most theories so far.
36 MATERIALS SCIENCE↗
2-Group global symmetries and anomalies in six-dimensional quantum field theories
We examine six-dimensional quantum field theories through the lens of higher-form global symmetries. Every Yang-Mills gauge theory in six dimensions, with field strength ƒ (2) , naturally gives rise to a continuous 1-form global symmetry associated with the 2-form instanton current J (2) ~ * Tr (ƒ (2) $\wedge$ ƒ (2) ). We show that suitable mixed anomalies involving the gauge field ƒ (2) and ordinary 0-form global symmetries, such as flavor or Poincaré symmetries, lead to continuous 2-group global symmetries, which allow two flavor currents or two stress tensors to fuse into the 2-form current J (2) . We discuss several features of 2-group symmetry in six dimensions, many of which parallel the four-dimensional case. The majority of six-dimensional supersymmetric conformal field theories (SCFTs) and little string theories have infrared phases with non-abelian gauge fields. We show that the mixed anomalies leading to 2-group symmetries can be present in little string theories, but that they are necessarily absent in SCFTs. This allows us to establish a previously conjectured algorithm for computing the ’t Hooft anomalies of most SCFTs from the spectrum of weakly-coupled massless particles on the tensor branch of these theories. We then apply this understanding to prove that the a -type Weyl anomaly of all SCFTs with a tensor branch must be positive, a > 0.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Landau-Forbidden Quantum Criticality in Rydberg Quantum Simulators
The Landau-Ginzburg-Wilson theory of phase transitions precludes a continuous transition between two phases that spontaneously break distinct symmetries. However, quantum mechanical effects can intertwine the symmetries, giving rise to an exotic phenomenon called deconfined quantum criticality (DQC). Here, in this Letter, we study the ground state phase diagram of a one-dimensional array of individually trapped neutral atoms interacting strongly via Rydberg states, and demonstrate through extensive numerical simulations that it hosts a variety of symmetry-breaking phases and their transitions including DQC. We show how an enlarged, emergent continuous symmetry arises at the DQCs, which can be experimentally observed in the joint distribution of two distinct order parameters, obtained within measurement snapshots in the standard computational basis. Our findings highlight quantum simulators of Rydberg atoms not only as promising platforms to experimentally realize such exotic phenomena, but also as unique ones allowing access to physical properties not obtainable in traditional experiments.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Twisted bilayer graphene. II. Stable symmetry anomaly
We show that the entire continuous model of twisted bilayer graphene (TBG) (and not just the two active bands) with particle-hole symmetry is anomalous and hence incompatible with lattice models. Previous works [e.g., Z. Song, Z. Wang, W. Shi, G. Li, C. Fang, and B. A. Bernevig, Phys. Rev. Lett. 123, 036401 (2019); J. Ahn, S. Park, and B.-J. Yang, Phys. Rev. X 9, 021013 (2019); H. C. Po, L. Zou, T. Senthil, and A. Vishwanath, Phys. Rev. B 99, 195455 (2019); J. Kang and O. Vafek, Phys. Rev. X 8, 031088 (2018); M. Koshino, N. F. Q. Yuan, T. Koretsune, M. Ochi, K. Kuroki, and L. Fu, Phys. Rev. X 8, 031087 (2018); J. Liu, J. Liu, and X. Dai, Phys. Rev. B 99, 155415 (2019); L. Zou, H. C. Po, A. Vishwanath, and T. Senthil, Phys. Rev. B 98, 085435 (2018)] found that the two flatbands in TBG possess a fragile topology protected by the C 2z T symmetry. Song et al. [Z. Song, Z. Wang, W. Shi, G. Li, C. Fang, and B. A. Bernevig, Phys. Rev. Lett. 123, 036401 (2019)] also pointed out an approximate particle-hole symmetry (P) in the continuous model of TBG. In this paper, we numerically confirm that P is indeed a good approximation for TBG and show that the fragile topology of the two flatbands is enhanced to a P-protected stable topology. This stable topology implies 4l + 2 (l ϵ N) Dirac points between the middle two bands. The P-protected stable topology is robust against arbitrary gap closings between the middle two bands and the other bands. We also show that, remarkably, this P-protected stable topology, as well as the corresponding 4l + 2 Dirac points, cannot be realized in lattice models that preserve both C 2z T and P symmetries. In other words, the continuous model of TBG is anomalous and cannot be realized on lattices. Two other topology related topics, with consequences for the interacting TBG problem, i.e., the choice of Chern band basis in the two flatbands and the perfect metal phase of TBG in the so-called second chiral limit, are also discussed.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Deep learning symmetries and their Lie groups, algebras, and subalgebras from first principles
Abstract We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding generators. The constructed loss functions ensure that the applied transformations are symmetries and the corresponding set of generators forms a closed (sub)algebra. Our procedure is validated with several examples illustrating different types of conserved quantities preserved by symmetry. In the process of deriving the full set of symmetries, we analyze the complete subgroup structure of the rotation groups SO (2), SO (3), and SO (4), and of the Lorentz group S O ( 1 , 3 ) . Other examples include squeeze mapping, piecewise discontinuous labels, and SO (10), demonstrating that our method is completely general, with many possible applications in physics and data science. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.
97 MATHEMATICS AND COMPUTING↗
Novel Wavefunction Approaches for Studying Actinides and Other Heavy Elements (Final Report (2012-2020))
The theoretical characterization of actinide molecules is a crucial complement to their experimental study; actinides are vital to issues of national security and energy, but they are expensive and hazardous to study experimentally. However, because actinides contain a large number of electrons and are often strongly correlated, their theoretical description is difficult. We have had success studying actinide chemistry and physics using density functional theoretical approaches over the past several years, but we have found that such methods are incapable of treating strong correlations adequately. We thus shifted our research focus to the development of tractable wavefunction methods for strong correlations of actinides. Our early wavefunction-based approaches focused on extending symmetry-adapted, single-reference coupled cluster for treating strong correlations with feasible computational cost. While we have had some success along these lines, we have recently developed spin-projected unrestricted coupled cluster, which is essentially a black-box multi-reference coupled cluster theory that is superior to unrestricted coupled cluster for small- to medium-sized systems across practically all physical correlation strengths, yet preserves good quantum numbers. For actinides, however, where spin-orbit coupling is often nonnegligible, spin is no longer a fundamental symmetry. We thus propose to develop time reversal and point group projected coupled cluster, which will preserve the fundamental symmetries for actinides. Time reversal projection is achieved via the product of half-spin projection, or spin flip, and complex conjugation projection. Along with point group, these are discrete symmetries, i.e. non-continuous quantum numbers, which, in addition to being the correct symmetries for actinides, can be implemented in lower computational cost than full spin projection. We propose the development of these theories within a synergistic collaboration to use the new methods to elucidate difficult actinide chemistry.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Electron-phonon coupling induced intrinsic Floquet electronic structure
Floquet states are a topic of intense contemporary interest, which is often induced by coherent external oscillating perturbation (e.g., laser, or microwave) which breaks the continuous time translational symmetry of the systems. Usually, electron–phonon coupling modifies the electronic structure of a crystal as a non-coherent perturbation and seems difficult to form Floquet states. Surprisingly, we found that the thermal equilibrium electron–phonon coupling in M(MoS) 3 and M(MoSe) 3 (where M is a metallic element) exhibits a coherent behavior, and the electronic structure can be described by the Floquet theorem. Such a coherent Floquet state is caused by a selective giant electron–phonon coupling, with thermodynamic phonon oscillation serving as a driving force on the electronic part of the system. The quasi-1D Dirac cone at the Fermi energy has its band gap open and close regularly. Similarly, the electric current will oscillate even under a constant voltage.
36 MATERIALS SCIENCE↗
On the morphological development of second-phase particles in elastically-stressed solids
We examine the equilibrium shape and the dynamics of the morphological evolution of a coherent misfitting particle in an elastically anisotropic medium. No a priori assumptions are made on the possible particle morphologies; the particle evolves in a manner consistent with both the diffusion and elastic fields surrounding the particle and the thermodynamics of interfaces in stressed solids. Through these calculations we find the thermodynamically stable equilibrium shape of a misfitting particle. By thermodynamically stable we mean that all the equilibrium conditions, elastic, chemical and interfacial are satisfied simultaneously, in contrast to previous treatments which determined the equilibrium shape by minimizing the sum of the elastic and interfacial energies for certain classes of particle shapes. We find that the equilibrium particle morphologies are not simple geometric shapes, have fourfold symmetry and a continuously varying interfacial curvature with position along the interface. Furthermore, the results show that the times required for a particle to evolve to its equilibrium morphology are likely to be within those which are accessible experimentally. In addition, we develop a general approach for determining the equilibrium shape of a particle in an elastically stressed solid.
Voorhees, P. W.↗
Consistency of chiral symmetry breaking in chiral Yang-Mills theory with adiabatic continuity
Not Available
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Fluxbranes, generalized symmetries, and Verlinde’s metastable monopole
The stringy realization of generalized symmetry operators involves wrapping “branes at infinity”. We argue that in the case of continuous (as opposed to discrete) symmetries, the appropriate objects are fluxbranes. We use this perspective to revisit the phase structure of Verlinde’s monopole, a proposed particle satisfies the Bogomol’nyi-Prasad-Sommerfield (BPS) condition when gravity is decoupled, but is non-BPS and metastable when gravity is switched on. Geometrically, this monopole is obtained from branes wrapped on locally stable but globally trivial cycles of a compactification geometry. The fluxbrane picture allows us to characterize electric (respectively magnetic) confinement (respectively screening) in the 4D theory as a result of monopole decay. In the presence of the fluxbrane, this decay also creates lower-dimensional fluxbranes, which in the field theory is interpreted as the creation of an additional topological field theory sector. Published by the American Physical Society 2024
Astronomy & Astrophysics↗
Space-time crystals from particle-like topological solitons
Time crystals are unexpected states of matter that spontaneously break time-translation symmetry either in a discrete or continuous manner. However, spatially mesoscale space-time crystals that break both space and time symmetries have not been reported. Here we report a continuous space-time crystal in a nematic liquid crystal driven by ambient-power, constant-intensity unstructured light. Our numerically constructed four-dimensional configurations exhibit good agreement with these experimental findings. Although meeting the established criteria to identify time-crystalline order, both experiments and computer simulations reveal a space-time crystallization phase formed by particle-like topological solitons. The robustness against temporal perturbations and spatiotemporal dislocations shows the stability and rigidity of the studied space-time crystals, which relates to their locally topological nature and many-body interactions between emergent spontaneously twisted, particle-like solitonic building blocks. Their potential technological utility includes optical devices, photonic space-time crystal generators, telecommunications and anti-counterfeiting designs, among others.
Liquid crystals↗
Rotational symmetry protected edge and corner states in Abelian topological phases
Spatial symmetries can enrich the topological classification of interacting quantum matter and endow systems with non-trivial strong topological invariants (protected by internal symmetries) with additional "weak" topological indices. In this paper, we study the edge physics of systems with a non-trivial shift invariant, which is protected by either a continuous $\text{U}(1)_r$ or discrete $\text{C}_n$ rotation symmetry, along with internal $\text{U}(1)_c$ charge conservation. Specifically, we construct an interface between two systems which have the same Chern number but are distinguished by their Wen-Zee shift and, through analytic arguments supported by numerics, show that the interface hosts counter-propagating gapless edge modes which cannot be gapped by arbitrary local symmetry-preserving perturbations. Using the Chern-Simons field theory description of two-dimensional Abelian topological orders, we then prove sufficient conditions for continuous rotation symmetry protected gapless edge states using two complementary approaches. One relies on the algebraic Lagrangian sub-algebra framework for gapped boundaries while the other uses a more physical flux insertion argument. For the case of discrete rotation symmetries, we extend the field theory approach to show the presence of fractional corner charges for Abelian topological orders with gappable edges, and compute them in the case where the Abelian topological order is placed on the two-dimensional surface of a Platonic solid. Finally, our work paves the way for studying the edge physics associated with spatial symmetries in symmetry enriched topological phases.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Emergent tetragonality in a fundamentally orthorhombic material
Symmetry plays a key role in determining the physical properties of materials. By Neumann’s principle, the properties of a material remain invariant under the symmetry operations of the space group to which the material belongs. Continuous phase transitions are associated with a spontaneous reduction in symmetry. Less common are examples where proximity to a continuous phase transition leads to an increase in symmetry. We find signatures of an emergent tetragonal symmetry close to a charge density wave (CDW) bicritical point in a fundamentally orthorhombic material, ErTe 3 , for which the two distinct CDW phase transitions are tuned via anisotropic strain. We first establish that tension along the a axis favors an abrupt rotation of the CDW wave vector from the c to a axis and infer the presence of a bicritical point where the two continuous phase transitions meet. We then observe a divergence of the nematic elastoresistivity approaching this putative bicritical point, indicating an emergent tetragonality in the critical behavior.
36 MATERIALS SCIENCE↗
Symmetries of all lines in monolayer crystals
As `2D' materials (i.e. materials just a few atoms thick) continue to gain prominence, understanding their symmetries is critical for unlocking their full potential. In this work, we present comprehensive tables that tabulate the rod group symmetries of all crystallographic lines in all 80 layer groups, which describe the symmetries of 2D materials. These tables are analogous to the scanning tables for space groups found in Volume E of the International Tables for Crystallography, but are specifically tailored for layer groups and their applications to 2D materials. This resource will aid in the analysis of line defects, such as domain walls, which play a crucial role in determining the properties and functionality of 2D materials.
2D materials↗