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DOE OSTI2020

Ronchi shearing interferometry for wavefronts with circular symmetry

Ronchi testing of a focused electromagnetic wave has in the last few years been used extensively at X-ray free-electron laser (FEL) facilities to qualitatively evaluate the wavefront of the beam. It is a quick and straightforward test, is easy to interpret on the fly, and can be used to align phase plates that correct the focus of aberrated beams. In general, a single Ronchigram is not sufficient to gain complete quantitative knowledge of the wavefront. However the compound refractive lenses that are commonly used at X-ray FELs exhibit a strong circular symmetry in their aberration, and this can be exploited. Furthermore, a simple algorithm that uses a single recorded Ronchigram to recover the full wavefront of a nano-focused beam, assuming circular symmetry, is presented, and applied to experimental measurements at the Matter in Extreme Conditions instrument at the Linac Coherent Light Source.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Nematicity with a twist: Rotational symmetry breaking in a moiré superlattice

Motivated by recent reports of nematic order in twisted bilayer graphene (TBG), we investigate the impact of the triangular moiré superlattice degrees of freedom on nematicity. In TBG, the nematic order parameter is not Ising like, as in tetragonal crystals, but has a three-state Potts character related to the threefold rotational symmetry ( C 3 z ) of the moiré superlattice. We find that, even in the presence of static strain that explicitly breaks the C 3 z symmetry, the system can still undergo a nematic-flop phase transition that spontaneously breaks in-plane twofold rotations. Moreover, elastic fluctuations, manifested as acoustic phonons, mediate a nemato-orbital coupling that ties the nematic director orientation to certain soft directions in momentum space, rendering the Potts-nematic transition mean field and first order. In contrast to the case of rigid crystals, the Fermi surface hot spots associated with these soft directions are maximally coupled to low-energy nematic fluctuations in the moiré superlattice case.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Electronic anisotropy and rotational symmetry breaking at a Weyl semimetal/spin ice interface

In magnetic pyrochlore materials, the interplay of spin-orbit coupling, electronic correlations, and geometrical frustration gives rise to exotic quantum phases, including topological semimetals and spin ice. While these phases have been observed in isolation, the interface-driven phenomena emerging from their interaction have never been realized previously. Here, we report on the discovery of interfacial electronic anisotropy and rotational symmetry breaking at a heterostructure consisting of the Weyl semimetal Eu 2 Ir 2 O 7 and spin ice Dy 2 Ti 2 O 7 . Subjected to magnetic fields, we unveil a sixfold anisotropic transport response that is theoretically accounted by a Kondo-coupled heterointerface, where the spin ice’s field-tuned magnetism induces electron scattering in the Weyl semimetal’s topological Fermi-arc states. Furthermore, at elevated magnetic fields, we reveal a twofold anisotropic response indicative of the emergence of a symmetry-broken many-body state. This discovery showcases the potential of pyrochlore frustrated magnet/topological semimetal heterostructures in search of emergent interfacial phenomena.

Science & Technology - Other Topics↗

DOE OSTI2026

$\mathscr{PT}$ symmetry enforced twin exchange as the origin of chirality-induced spin selectivity

Chiral molecules, ubiquitous in chemistry and biology, can differentiate electrons by their spin, a phenomenon known as chirality-induced spin selectivity (CISS). Despite its robustness and technological relevance, CISS has resisted conventional explanation: Spin-orbit coupling (SOC) models cannot fully account for the observed magnitude, room-temperature persistence, or equilibrium signatures. Here, we argue that structural chirality enforces a twin-pair exchange mechanism via the indistinguishability principle, which intrinsically couples spin and spatial degrees of freedom such that wave functions cannot be factorized into spin and spatial components. We derive an effective Hamiltonian that describes both transport and equilibrium CISS phenomena and is non-Hermitian. However, the inherent pseudo-Hermiticity, with $\mathscr{PT}$ symmetry as a special case, ensures real eigenvalues and thermodynamic consistency. We demonstrate that our framework is a step toward resolving long-standing anomalies of CISS. It situates CISS alongside equilibrium symmetry-breaking phenomena such as ferromagnetism and superconductivity, with implications for spintronics, catalysis, and the origins of biological homochirality.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Evidence for a delocalization quantum phase transition without symmetry breaking in CeCoIn 5

The study of quantum phase transitions that are not clearly associated with broken symmetry is a major effort in condensed matter physics, particularly in regard to the problem of high-temperature superconductivity, for which such transitions are thought to underlie the mechanism of superconductivity itself. Here we argue that the putative quantum critical point in the prototypical unconventional superconductor CeCoIn 5 is characterized by the delocalization of electrons in a transition that connects two Fermi surfaces of different volumes, with no apparent broken symmetry. Drawing on established theory of f-electron metals, we discuss an interpretation for such a transition that involves the fractionalization of spin and charge, a model that effectively describes the anomalous transport behavior we measured for the Hall effect.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Femtosecond symmetry breaking and coherent relaxation of methane cations via x-ray spectroscopy

Understanding the relaxation pathways of photoexcited molecules is essential to gain atomistic-level insight into photochemistry. Here, we performed a time-resolved study of ultrafast molecular symmetry breaking through geometric relaxation (Jahn-Teller distortion) on the methane cation. Attosecond transient absorption spectroscopy with soft x-rays at the carbon K-edge revealed that the distortion occurred within 10 ± 2 femtoseconds after few-femtosecond strong-field ionization of methane. The distortion activated coherent oscillations in the asymmetric scissoring vibrational mode of the symmetry-broken cation, which were detected in the x-ray signal. These oscillations were damped within 58 ± 13 femtoseconds because vibrational coherence was lost with the energy redistributing into lower-frequency vibrational modes. This study completely reconstructs the molecular relaxation dynamics of this prototypical example and opens avenues for exploring complex systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Chiral spin symmetry and the QCD phase diagram

Lattice QCD simulations with chirally symmetric quarks have recently established approximate SU(2) CS and SU(2N F ) symmetries of the quantum effective action in a temperature range above the chiral crossover T ch , in which color-electric interactions between quarks dominate the dynamics. We show that such an intermediate temperature range between the chirally broken and plasma regimes is fully consistent with published screening mass spectra, which demonstrate the breakdown of thermal perturbation theory at the crossover between the partonic and the chiral spin symmetric regime at T s ~(2–3)T ch . From the known behavior of screening masses with baryon chemical potential, we deduce qualitatively how this chiral spin symmetric band extends into the QCD phase diagram. In the cold and dense region, we propose parity doubled baryons as possible candidates for chiral spin symmetric matter. This represents a special case of quarkyonic matter with confinement and restored chiral symmetry, and can smoothly transform to quark matter at sufficiently high densities. Finally, we discuss the potential of dilepton spectra to identify such matter forms.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Data-directed search for new physics based on symmetries of the SM

We propose exploiting symmetries (exact or approximate) of the Standard Model (SM) to search for physics Beyond the Standard Model (BSM) using the data-directed paradigm (DDP). Symmetries are very powerful because they provide two samples that can be compared without requiring simulation. Focusing on the data, exclusive selections which exhibit significant asymmetry can be identified efficiently and marked for further study. Using a simple and generic test statistic which compares two matrices already provides good sensitivity, only slightly worse than that of the profile likelihood ratio test statistic which relies on the exact knowledge of the signal shape. This can be exploited for rapidly scanning large portions of the measured data, in an attempt to identify regions of interest. We also demonstrate that weakly supervised Neural Networks could be used for this purpose as well.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Coupling and recoupling coefficients for Wigner’s U(4) supermultiplet symmetry

A novel procedure for evaluating Wigner coupling coefficients and Racah recoupling coefficients for U(4) in two group–subgroup chains is presented. The canonical U(4) > U(3) > U(2) > U(1) coupling and recoupling coefficients are applicable to any system that possesses U(4) symmetry, while the physical U(4) coupling coefficients are more specific to nuclear structure studies that utilize Wigner’s supermultiplet symmetry concept. The procedure that is proposed sidesteps the use of binomial coefficients and alternating sum series and consequently enables fast and accurate computation of any and all U(4)-underpinned features. The inner multiplicity of a (S, T) pair within a single U(4) > SU S (2) Ⓧ SU T (2) irreducible representation is obtained from the dimension of the null space of the SU(2) raising generators, while the resolution for the outer multiplicity follows from the work of Alex et al. on U(N) . It is anticipated that a C++ library will ultimately be available for determining generic coupling and recoupling coefficients associated with both the canonical and the physical group–subgroup chains of U(4).

Cross-Coupling Reaction↗

DOE OSTI2023

Superdiffusion from Nonabelian Symmetries in Nearly Integrable Systems

The Heisenberg spin chain is a canonical integrable model. As such, it features stable ballistically propagating quasiparticles, but spin transport is subballistic at any nonzero temperature: An initially localized spin fluctuation spreads in time t to a width t 2/3 . This exponent as well as the functional form of the dynamical spin correlation function suggest that spin transport is in the Kardar–Parisi–Zhang (KPZ) universality class. However, the full counting statistics of magnetization is manifestly incompatible with KPZ scaling. A simple two-mode hydrodynamic description, derivable from microscopic principles, captures both the KPZ scaling of the correlation function and the coarse features of the full counting statistics, but remains to be numerically validated. These results generalize to any integrable spin chain invariant under a continuous nonabelian symmetry and are surprisingly robust against moderately strong integrability-breaking perturbations that respect the nonabelian symmetry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

The Cosmological Bootstrap: Spinning correlators from symmetries and factorization

We extend the cosmological bootstrap to correlators involving massless spinning particles, focusing on spin-1 and spin-2. In de Sitter space, these correlators are constrained both by symmetries and by locality. In particular, the de Sitter isometries become conformal symmetries on the future boundary of the spacetime, which are reflected in a set of Ward identities that the boundary correlators must satisfy. We solve these Ward identities by acting with weight-shifting operators on scalar seed solutions. Using this weight-shifting approach, we derive three- and four-point correlators of massless spin-1 and spin-2 fields with conformally coupled scalars. Four-point functions arising from tree-level exchange are singular in particular kinematic configurations, and the coefficients of these singularities satisfy certain factorization properties. We show that in many cases these factorization limits fix the structure of the correlators uniquely, without having to solve the conformal Ward identities. The additional constraint of locality for massless spinning particles manifests itself as current conservation on the boundary. We find that the four-point functions only satisfy current conservation if the s, t, and u-channels are related to each other, leading to nontrivial constraints on the couplings between the conserved currents and other operators in the theory. For spin-1 currents this implies charge conservation, while for spin-2 currents we recover the equivalence principle from a purely boundary perspective. For multiple spin-1 fields, we recover the structure of Yang--Mills theory. Finally, we apply our methods to slow-roll inflation and derive a few phenomenologically relevant scalar-tensor three-point functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

A symmetry algebra in double-scaled SYK

The double-scaled limit of the Sachdev-Ye-Kitaev (SYK) model takes the number of fermions and their interaction number to infinity in a coordinated way. In this limit, two entangled copies of the SYK model have a bulk description of sorts known as the “chord Hilbert space”. We analyze a symmetry algebra acting on this Hilbert space, generated by the two Hamiltonians together with a two-sided operator known as the chord number. This algebra is a deformation of the JT gravitational algebra, and it contains a subalgebra that is a deformation of the \mathfrak{sl}_2 𝔰 𝔩 2 near-horizon symmetries. The subalgebra has finite-dimensional unitary representations corresponding to matter moving around in a discrete Einstein-Rosen bridge. In a semiclassical limit the discreteness disappears and the subalgebra simplifies to \mathfrak{sl}_2 𝔰 𝔩 2 , but with a non-standard action on the boundary time coordinate. One can make the action of \mathfrak{sl}_2 𝔰 𝔩 2 algebra more standard at the cost of extending the boundary circle to include some “fake” portions. Such fake portions also accommodate certain subtle states that survive the semi-classical limit, despite oscillating on the scale of discreteness. We discuss applications of this algebra, including sub-maximal chaos, the traversable wormhole protocol, and a two-sided OPE.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Apparent fine tunings for field theories with broken space-time symmetries

We exhibit a class of effective field theories that have hierarchically small Wilson coefficients for operators that are not protected by symmetries but are not finely tuned. These theories possess bounded target spaces and vacua that break space-time symmetries. We give a physical interpretation of these theories as generalized solids with open boundary conditions. We show that these theories realize unusual RG flows where higher dimensional (seemingly irrelevant) operators become relevant even at weak coupling. Finally, we present an example of a field theory whose vacuum energy relaxes to a hierarchically small value compared to the UV cut-off.

Physics↗

DOE OSTI2020

Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D

Motivated by applications to critical phenomena and open theoretical questions, we study conformal field theories with O(m)\times O(n) O ( m ) × O ( n ) global symmetry in d=3 d = 3 spacetime dimensions. We use both analytic and numerical bootstrap techniques. Using the analytic bootstrap, we calculate anomalous dimensions and OPE coefficients as power series in \varepsilon=4-d ε = 4 − d and in 1/n 1 / n , with a method that generalizes to arbitrary global symmetry. Whenever comparison is possible, our results agree with earlier results obtained with diagrammatic methods in the literature. Using the numerical bootstrap, we obtain a wide variety of operator dimension bounds, and we find several islands (isolated allowed regions) in parameter space for O(2)\times O(n) O ( 2 ) × O ( n ) theories for various values of n n . Some of these islands can be attributed to fixed points predicted by perturbative methods like the \varepsilon ε and large- n n expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Abelian combinatorial gauge symmetry

Combinatorial gauge symmetry is a principle that allows us to construct lattice gauge theories with two key and distinguishing properties: a) only one- and two-body interactions are needed; and b) the symmetry is exact rather than emergent in an effective or perturbative limit. The ground state exhibits topological order for a range of parameters. This paper is a generalization of the construction to any finite Abelian group. In addition to the general mathematical construction, we present a physical implementation in superconducting wire arrays, which offers a route to the experimental realization of lattice gauge theories with static Hamiltonians.

Yu, Hongji↗

DOE OSTI2023

Spectroscopic Investigations of Molecular Symmetry Breakdown

This project addressed precise measurements of the spectra of molecules to address fundamental questions in chemical physics in the realm of nuclear spin symmetries and their breakdown in molecules, and parity non-conservation caused by the weak nuclear force. Nuclear spin symmetry is intimately connected to parity in symmetrical molecules and plays a central role in the physical and chemical properties of symmetric molecules, their collisional relaxation, and the establishment of thermodynamic equilibrium in an ensemble. Such effects are present in every molecular system or process, but their small size means they are often only directly observable under special conditions. However, their measurement is of fundamental, and often practical importance, and strongly relates to the themes of coherence in light and matter in the recent Basic Energy Sciences Advisory Committee (BESAC) report “Challenges at the Frontiers of Matter and Energy: Transformative Opportunities for Discovery Science”. We begin by addressing lifetime broadening of spectroscopic lines caused by self-collisions in acetylene, where efficient resonant rotational energy transfer between a pair of molecules separated in energy by rotational quantum number ΔJ = ± 2, can result in a different pressure broadening for ortho- and para- nuclear spin state molecules. This work was prompted by a controversial report [Iwakuni et al. Phys. Rev Letts. 117 (2016) 143902] of the observation of such an effect in the v 1 +v 3 combination band transition of acetylene discussed in the original proposal. After delays caused by the COVID-19 pandemic, we have completed these measurements and a paper was published in the Journal of Chemical Physics describing the work. The measurements pointed out that the use of an approximate model in the analysis of the original work was the cause of the erroneous conclusion that ortho and para acetylene molecules had substantially different collisional lifetime broadening. In the process, much improved broadening measurements have been made that will permit more reliable modeling of the effects in the future. Subsequently, we have completed a new set of measurements of self- and nitrogen-collisional broadening at a series of low and intermediate temperatures to characterize the temperature dependence of the effects in the molecule. This work is currently being analyzed and will be the subject of a paper to be published in the relatively near future. In addition, some very preliminary measurements of CH 4 as described in the proposal, have been completed. If facilities and time permit, these will continue as an undergraduate research project.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2025

Symmetry Determining Equations of the Rankine-Hugoniot Equations for Variable Velocity Shock Waves

The “constant velocity piston” problem (Fig. 1), also known as the “piston problem,” is a standard model for a one dimensional, in our case linear, symmetric shock wave moving through an inviscid, perfect gas. The model can be divided into two regions - a perturbed section on the left and an unperturbed section on the right - by a moving shock wave moving left to right. Both the perturbed and unperturbed sections, i.e. the shocked and unshocked regions, respectively, obey the Eulerian conservation equations; however, at the exact location of the shock, there is a mathematical discontinuity not satisfied by the Euler equations. To ensure continuity and conservation of certain quantities when crossing between the unshocked and shocked regions, we evoke a series of equations derived from the Eulerian conservation equations, called the Rankine-Hugoniot equations, or “jump” equations as it is often referred to in the literature on the topic. The classical constant-velocity piston problem assumes the piston features a constant driving velocity (among many other willing suspensions of belief required in the pursuit of a first principles equation model); consequent to this assumption is a constant-velocity shock and a constant-velocity shocked flow state. However, using Lie Group Theory (LGT), also known as symmetry analysis, we can attempt to reinterpret the model with a shock wave of variable velocity in time and space. An extension of the model in this way opens up the possibility for obtaining new analytical solutions to the piston problem for certain shock velocity models. In this report, we use LGT to derive the symmetry determining equations (SDEs), whose solutions are Lie groups, which permit analytical solutions. In the future, we can then use the SDEs to define constraint equations on the shock velocity model and what the successive solutions to the Euler equations might be based off such constraints. This report is structured as follows: Section 2 provides a brief derivation of the Rankine-Hugoniot (“jump”) equations; Section 3 gives an overview of Lie group theory; Section 4 derives the SDEs of the jump equations; Section 5 derives the Euler conservation equations for fluids; and Section 6 presents concluding remarks and opportunities for future studies.

42 ENGINEERING↗

DOE OSTI2026

Extending Symmetry-Preserving Attention Networks (SPANet) for Jet Assignment in Fully Hadronic $t\bar{t}$ Events

Fully hadronic $t\bar{t}$ reconstruction requires assigning reconstructed jets to the two top-quark decay branches, $t\bar{t}\to(Wb)(Wb)\to(qqb)(qqb)$. This is a combinatorially large, symmetry-rich, and frequently underconstrained set-assignment problem due to detector effects and partial reconstructability. SPANet provides a strong symmetry-preserving baseline for this task, but its standard inference eagerly commits to a single hypothesis and does not explicitly treat branch-level reconstructability decisions. We present a two-stage extension of the SPANet pipeline for fully hadronic $t\bar{t}$ events: (i) SPANet is modified into a proposal model that generates a shortlist of candidate jet assignments; (ii) a custom dual-head set transformer is trained to re-rank these candidates and identify reconstructible branches. Our extension gives modest improvements in candidate-selection efficiency, with SPANet achieving $69.9\%$ and our extension achieving $71.1\%$. Finally, an oracle study of the generated shortlist shows a substantial upper bound of $88.5\%$ on the evaluated fully reconstructable subset, suggesting that the shortlist contains significant residual information that is not fully exploited.

Lisondodi Tada, Mateo [Puerto Rico U., Mayaguez] (↗