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DOE OSTI2025

(SPT-)LSM theorems from projective non-invertible symmetries

Projective symmetries are ubiquitous in quantum lattice models and can be leveraged to constrain their phase diagram and entanglement structure. In this paper, we investigate the consequences of projective algebras formed by non-invertible symmetries and lattice translations in a generalized 1+1 1 + 1 D quantum XY model based on group-valued qudits. This model is specified by a finite group G G and enjoys a projective \mathsf{Rep}(G)× Z(G) 𝖱 𝖾 𝗉 ( G ) × Z ( G ) and translation symmetry, where symmetry operators obey a projective algebra in the presence of symmetry defects. For invertible symmetries, such projective algebras imply Lieb-Schultz-Mattis (LSM) anomalies. However, this is not generally true for non-invertible symmetries, and we derive a condition on G G for the existence of an LSM anomaly. When this condition is not met, we prove an SPT-LSM theorem: any unique and gapped ground state is necessarily a non-invertible weak symmetry protected topological (SPT) state with non-trivial entanglement, for which we construct an example fixed-point Hamiltonian. The projectivity also affects the dual symmetries after gauging \mathsf{Rep}(G)× Z(G) 𝖱 𝖾 𝗉 ( G ) × Z ( G ) sub-symmetries, giving rise to non-Abelian and non-invertible dipole symmetries, as well as non-invertible translations. We complement our analysis with the SymTFT, where the projectivity causes it to be a topological order non-trivially enriched by translations. Throughout the paper, we develop techniques for gauging \mathsf{Rep}(G) 𝖱 𝖾 𝗉 ( G ) symmetry and inserting its symmetry defects on the lattice, which are applicable to other non-invertible symmetries.

Pace, Salvatore D. (ORCID:0000000306093335)↗
DOE OSTI2023

How does your gyroid grow? A mesoatomic perspective on supramolecular, soft matter network crystals

We propose and describe a framework to understand the structure of supramolecular network crystals formed in soft matter in terms of mesoatomic building blocks, collective groupings of amphiphilic molecules that play a role analogous to atomic or molecular subunits of hard matter crystals. While the concept of mesoatoms is intuitive and widely invoked in crystalline arrangements of spherelike or cylinderlike (micellelike) domains, analogous notions of natural and physically meaningful building blocks of triply periodic network (TPN) crystals, like the double-gyroid or double-diamond structures are obscured by the complex, bicontinuous domain shapes and intercatenated topologies of the double networks. Focusing on the specific example of diblock copolymer melts, we propose generic rules for decomposing TPN crystals into a unique set of mesoatomic building blocks. Based on physically motivated principles, the combination of symmetries and topologies of these structures point to mesoatomic elements associated with the nodal connections, leading to mesoatomic volumes that are nonconvex and bound by smoothly curved faces, unlike the more familiar Voronoi polyhedral shapes associated with spherelike and cylinderlike mesoatoms. We analyze the shapes of these mesoatoms, their internal structure, and importantly, their local packing with neighbor mesoatomic units. Importantly, we hypothesize that mesoatoms are kinetically favored intermediate structures whose local shapes and packing template network crystal assembly on long time scales. We propose and study a minimal energetic model of mesoatom assembly for three different cubic double-network crystals, based on local shape packing, which predicts a detailed picture for kinetics of intercatenation and surface growth. Based on these analyses, we discuss several possible extensions and elaborations of the mesoatomic description of supramolecular soft matter network crystals, most notably the implications of mesoatomic malleability, a feature that distinguishes soft matter from hard matter crystals. We describe experimental observations of malleable mesoatomic units in the precursor sponge phase as well as in ordered cubic networks and suggest possibilities for observing mesoatoms in primordial, precrystalline states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Spin Berry points as crucial for ultrafast demagnetization

Laser-induced ultrafast demagnetization has puzzled researchers around the world for over two decades. Intrinsic complexity in electronic, magnetic and phononic subsystems is difficult to understand microscopically. So far, it is not possible to explain demagnetization using a single mechanism, which suggests a crucial piece of information still missing. In this paper, we return to a fundamental aspect of physics: spin and its change within each band in the entire Brillouin zone. We employ face-centered cubic (fcc) Ni as an example and use an extremely dense k mesh to map out spin changes for every band close to the Fermi level along all the high symmetry lines. To our surprise, spin angular momentum at some special k points abruptly changes from [Formula: see text] to [Formula: see text] simply by moving from one crystal momentum point to the next. This explains why intraband transitions, which the spin superdiffusion model is based upon, can induce a sharp spin moment reduction, and why electric current can change spin orientation in spintronics. These special k points, which are called spin Berry points [M. V. Berry, Proc. R. Soc. Lond. A 393 (1984) 45], are not random and appear when several bands are close to each other, so the Berry potential of spin majority states is different from that of spin minority states. Although within a single band, spin Berry points jump, when we group several neighboring bands together, they form distinctive smooth spin Berry lines. It is the band structure that disrupts those lines. Spin Berry points are crucial to laser-induced ultrafast demagnetization and spintronics.

Physics↗
DOE OSTI2023

Multichannel Topological Kondo Effect

A Coulomb blockaded M-Majorana island coupled to normal metal leads realizes a novel type of Kondo effect where the effective impurity “spin” transforms under the orthogonal group SO⁡(M). The impurity spin stems from the nonlocal topological ground state degeneracy of the island and thus the effect is known as the topological Kondo effect. We introduce a physically motivated N-channel generalization of the topological Kondo model. Starting from the simplest case N =2, we conjecture a stable intermediate coupling fixed point and evaluate the resulting low-temperature impurity entropy. The impurity entropy indicates that an emergent Fibonacci anyon can be realized in the N =2 model. We also map the case N =2, M =4 to the conventional four-channel Kondo model and find the conductance at the intermediate fixed point. By using the perturbative renormalization group, we also analyze the large-N limit, where the fixed point moves to weak coupling. In the isotropic limit, we find an intermediate stable fixed point, which is stable to “exchange” coupling anisotropies, but unstable to channel anisotropy. We evaluate the fixed point impurity entropy and conductance to obtain experimentally observable signatures of our results. Here, in the large-N limit, we evaluate the full crossover function describing the temperature-dependent conductance.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Asymptotic gauge symmetry and UV extension of the nonperturbative coupling in holographic QCD

We extend our recent analytic study of the strong coupling 𝛼 eff in the nonperturbative and near-perturbative regimes [Phys. Rev. Lett. 133, 181901 (2024)] by imposing rigorous renormalization-group constraints from asymptotically free gauge theories at 𝑄 2 → ∞. The asymptotic boundary conditions modify the scaling properties of 𝛼eff at large values of the momentum transfer 𝑄 2 and lead to a scale-dependent confinement strength 𝜅⁡(𝑄 2 ). This requires that both 𝜅⁡(𝑄 2 ) and 𝛼 eff⁡ (𝑄 2 , 𝜅⁡(𝑄 2 )) remain holomorphic in the complex 𝑄 2 plane, except at the physical cuts associated with the heavy-quark thresholds and the singularity flow trajectory studied in our previous Letter. For color SU(3), a precise connection is found between the scaling exponent of 𝜅⁡(𝑄 2 ) in the ultraviolet, the value of the infrared fixed point of the strong coupling, and the number of flavors in agreement with observations. The nonperturbative analytic model gives an accurate description of the strong coupling across all scales, up to the highest available data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Yb Substitution and Ultralow Thermal Conductivity of the Ca 3– x Yb x AlSb 3 (0 ≤ x ≤ 0.81(1)) System

Here, a series of Yb-substituted Zintl phases in the Ca 3–x Yb x AlSb 3 (0 ≤ x ≤ 0.81(1)) system has been synthesized by initial arc melting and post-heat treatment, and their isotypic crystal structures were characterized by both powder and single crystal X-ray diffraction analysis. All four title compounds adopted the Ca 3 AlAs 3 -type structure (space group Pnma, Pearson code oP28, Z = 4). The overall structure can be described as a combination of the 1-dimensional (1D) infinite chain of ∞ 1 [Al(Sb 2 Sb 2/2 )] formed by two vertices sharing [AlSb 4 ] tetrahedral moieties and three Ca 2+ /Yb 2+ mixed sites located in between these 1D chains. The charge balance and the resultant independency of the 1D chains in the title system were explained by the Zintl-Klemm formalism [Ca 2+ /Yb 2+ ] 3 [(4b-Al 1– )(1b-Sb 2– ) 2 (2b-Sb 1– ) 2/2 ]. A series of DFT calculations proved that (1) the band overlap between the d-orbital states from two types of cations and the p-orbital states from Sb at the high symmetry Γ point implied a heavily doped degenerate semiconducting behavior of the quaternary Ca 2 YbAlSb 3 model and (2) the site preference of Yb for the M1 site was due to the electronic-factor criterion based on the Q values of each atomic site. The electron localization function calculations also proved that the two different shapes of lone pairs of the Sb atoms—the “umbrella-shape” and the “C-shape”—are determined by local geometry and the coordination environment on the anionic frameworks. Thermoelectric measurements of the quaternary title compound Ca 2.19(1) Yb 0.81 AlSb 3 showed an approximately two times larger ZT value than that of ternary Ca 3 AlSb 3 at 623 K due to increased electrical conductivity and ultralow thermal conductivity originated from Yb substitution for Ca.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Easy-plane anisotropic-exchange magnets on a honeycomb lattice: Quantum effects and dealing with them

We provide analytical and numerical insights into the phase diagram and other properties of the extended Kitaev-Heisenberg model on the honeycomb lattice in the easy-plane limit, in which interactions are only between spin components that belong to the plane of magnetic ions. This parameter subspace allows for a much-needed systematic quantitative investigation of spin excitations in the ordered phases and of their generic features. Specifically, we demonstrate that in this limit one can consistently take into account magnon interactions in both zero-field zigzag and field-polarized phases. For the nominally polarized phase, we propose a regularization of the unphysical divergences that occur at the critical field and are plaguing the 1/S approximation in this class of models. For the explored parameter subspace, all symmetry-allowed terms of the standard parametrization of the extended Kitaev-Heisenberg model, such as K, J, and Γ, are significant, making the offered consideration relevant to a much wider parameter space. Furthermore, the dynamical structure factor near the paramagnetic critical point illustrates this relevance by showing features that are reminiscent of the ones observed in α–RuCl 3 , underscoring that they are not unique and should be common to a wide range of parameters of the model and, by extension, to other materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Physics of the Inverted Harmonic Oscillator: From the lowest Landau level to event horizons

In this work, we present the inverted harmonic oscillator (IHO) Hamiltonian as a paradigm to understand the quantum mechanics of scattering and time-decay in a diverse set of physical systems. As one of the generators of area preserving transformations, the IHO Hamiltonian can be studied as a dilatation generator, squeeze generator, a Lorentz boost generator, or a scattering potential. In establishing these different forms, we demonstrate the physics of the IHO that underlies phenomena as disparate as the Hawking–Unruh effect and scattering in the lowest Landau level (LLL) in quantum Hall systems. We derive the emergence of the IHO Hamiltonian in the LLL in a gauge invariant way and show its exact parallels with the Rindler Hamiltonian that describes quantum mechanics near event horizons. This approach of studying distinct physical systems with symmetries described by isomorphic Lie algebras through the emergent IHO Hamiltonian enables us to reinterpret geometric response in the lowest Landau level in terms of relativistic effects such as Wigner rotation. Further, the analytic scattering matrix of the IHO points to the existence of quasinormal modes (QNMs) in the spectrum, which have quantized time-decay rates. We present a way to access these QNMs through wave packet scattering, thus proposing a novel effect in quantum Hall point contact geometries that parallels those found in black holes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Form factors and spectral densities from Lightcone Conformal Truncation

We use the method of Lightcone Conformal Truncation (LCT) to obtain form factors and spectral densities of local operators $\mathcal{O}$ in $\phi^4$ theory in two dimensions. We show how to use the Hamiltonian eigenstates from LCT to obtain form factors that are matrix elements of a local operator $\mathcal{O}$ between single-particle bra and ket states, and we develop methods that significantly reduce errors resulting from the finite truncation of the Hilbert space. We extrapolate these form factors as a function of momentum to the regime where, by crossing symmetry, they are form factors of $\mathcal{O}$ between the vacuum and a two-particle asymptotic scattering state. We also compute the momentum-space time-ordered two-point functions of local operators in LCT. These converge quickly at momenta away from branch cuts, allowing us to indirectly obtain the time-ordered correlator and the spectral density at the branch cuts. We focus on the case where the local operator $\mathcal{O}$ is the trace Θ of the stress tensor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Short-Range Order in VI 3

We present a detailed investigation of the crystal structure of VI 3 , a two-dimensional van der Waals material of interest for studies of low-dimensional magnetism. As opposed to the average crystal structure that features $R\bar{3}$ symmetry of the unit cell, our Raman scattering and X-ray atomic pair distribution function analysis supported by density functional theory calculations point to the coexistence of short-range ordered $P\bar{3}$1c and long-range ordered $R\bar{3}$phases. The highest-intensity peak, A 1g 3 , exhibits a moderate asymmetry that might be traced back to the spin–phonon interactions, as in the case of CrI 3 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Two-loop beta function for complex scalar electroweak multiplets

We present the general form of the renormalizable four-point interactions of a complex scalar field furnishing an irreducible representation of SU(2), and derive a set of algebraic identities that facilitates the calculation of higher-order radiative corrections. As an application, we calculate the two-loop beta function for the SM extended by a scalar multiplet, and provide the result explicitly in terms of the group invariants. Our results include the evolution of the Higgs-portal couplings, as well as scalar “minimal dark matter”. We present numerical results for the two-loop evolution of the various couplings.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Flavor Fragmentation Function Factorization

A definition of partonic jet flavor that is both theoretically well-defined and experimentally robust would have profound implications for measurements and predictions especially for heavy flavor applications. Recently, a definition of jet flavor was introduced as the net flavor flowing along the direction of the Winner-Take-All axis of a jet which is soft safe to all orders, but not collinear safe. Here, we exploit the lack of collinear safety and propose a factorization theorem of perturbative flavor fragmentation functions that resum collinear divergences and describe the evolution of flavor from the short distance of jet production to the long distance at which hadronization occurs. Collinear flavor evolution is governed by a small modification of the DGLAP equations. We present a detailed all-orders analysis and identify exact relations that must hold amongst the various anomalous dimensions by probability conservation and the existence of fixed points of the renormalization group flow. We explicitly validate the factorization theorem at one-loop order, and demonstrate its consistency at two loops in particular flavor channels. Starting at two-loops, constraints on phase space imposed by flavor measurements potentially allow for non-trivial soft contributions, but we demonstrate that they are scaleless and so explicitly vanish, ensuring that soft particles are summed inclusively and all divergences are exclusively collinear in nature. This factorization theorem opens the door to precision calculations with identified flavor in the infrared.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Gravitational Waves and Proton Decay: Complementary Windows into Grand Unified Theories

Proton decay is a smoking gun signature of grand unified theories (GUTs). Searches by Super-Kamiokande have resulted in stringent limits on the GUT symmetry-breaking scale. The large-scale multipurpose neutrino experiments DUNE, Hyper-Kamiokande, and JUNO will either discover proton decay or further push the symmetry-breaking scale above 10 16 GeV. Another possible observational consequence of GUTs is the formation of a cosmic string network produced during the breaking of the GUT to the standard model gauge group. The evolution of such a string network in the expanding Universe produces a stochastic background of gravitational waves which will be tested by a number of gravitational wave detectors over a wide frequency range. We demonstrate the nontrivial complementarity between the observation of proton decay and gravitational waves produced from cosmic strings in determining SO(10) GUT-breaking chains. We show that such observations could exclude SO(10) breaking via flipped SU(5) × U(1) or standard SU(5), while breaking via a Pati-Salam intermediate symmetry, or standard SU(5) × U(1), may be favored if a large separation of energy scales associated with proton decay and cosmic strings is indicated. We note that recent results by the NANOGrav experiment have been interpreted as evidence for cosmic strings at a scale of ~10 14 GeV. This would strongly point toward the existence of GUTs, with SO(10) being the prime candidate. We show that the combination with already available constraints from proton decay allows us to identify preferred symmetry-breaking routes to the standard model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Flavor fragmentation function factorization

A definition of partonic jet flavor that is both theoretically well-defined and experimentally robust would have profound implications for measurements and predictions especially for heavy flavor applications. Recently, a definition of jet flavor was introduced as the net flavor flowing along the direction of the Winner-Take-All axis of a jet which is soft safe to all orders, but not collinear safe. Here, we exploit the lack of collinear safety and propose a factorization theorem of perturbative flavor fragmentation functions that resum collinear divergences and describe the evolution of flavor from the short distance of jet production to the long distance at which hadronization occurs. Collinear flavor evolution is governed by a small modification of the DGLAP equations. We present a detailed all-orders analysis and identify exact relations that must hold amongst the various anomalous dimensions by probability conservation and the existence of fixed points of the renormalization group flow. We explicitly validate the factorization theorem at one-loop order, and demonstrate its consistency at two loops in particular flavor channels. Starting at two-loops, constraints on phase space imposed by flavor measurements potentially allow for non-trivial soft contributions, but we demonstrate that they are scaleless and so explicitly vanish, ensuring that soft particles are summed inclusively and all divergences are exclusively collinear in nature. This factorization theorem opens the door to precision calculations with identified flavor in the infrared.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Non-Gaussianities in collider energy flux

The microscopic dynamics of particle collisions is imprinted into the statistical properties of asymptotic energy flux, much like the dynamics of inflation is imprinted into the cosmic microwave background. This energy flux is characterized by correlation functions < E(n → 1 )…E(n → k ) > of energy flow operators E(n → ). There has been significant recent progress in studying energy flux, including the calculation of multi-point correlation functions and their direct measurement inside high-energy jets at the Large Hadron Collider (LHC). In this paper, we build on these advances by defining a notion of “celestial non-gaussianity” as a ratio of the three-point function to a product of two-point functions. We show that this celestial non-gaussianity is under perturbative control within jets at the LHC, allowing us to cleanly access the non-gaussian interactions of quarks and gluons. We find good agreement between perturbative calculations of the non-gaussianity and a charged-particle-based analysis using CMS Open Data, and we observe a strong non-gaussianity peaked in the “flattened triangle” regime. The ability to robustly study three-point correlations is a significant step in advancing our understanding of jet substructure at the LHC. We anticipate that the celestial non-gaussianity, and its generalizations, will play an important role in the development of higher-order parton showers simulations and in the hunt for ever more subtle signals of potential new physics within jets.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Topological and nematic superconductivity mediated by ferro-SU(4) fluctuations in twisted bilayer graphene

We propose an SU(4) spin-valley-fermion model to investigate the superconducting instabilities of twisted bilayer graphene (TBG). In this approach, bosonic fluctuations associated with an emergent SU(4) symmetry, corresponding to combined rotations in valley and spin spaces, couple to the low-energy fermions that comprise the flat bands. These fluctuations are peaked at zero wave vector, reflecting the “ferromagnetic-like” SU(4) ground state recently found in strong-coupling solutions of microscopic models for TBG. Focusing on electronic states related to symmetry-imposed points of the Fermi surface, dubbed here “valley hot-spots” and “van Hove hot-spots,” we find that the coupling to the itinerant electrons partially lifts the huge degeneracy of the ferro-SU(4) ground state manifold, favoring intervalley order, spin-valley coupled order, ferromagnetic order, spin-current order, and valley-polarized order, depending on details of the band structure. Here, these fluctuations, in turn, promote attractive pairing interactions in a variety of closely competing channels, including a nodeless f-wave state, a nodal i-wave state, and topological d+id and p+ip states with unusual Chern numbers 2 and 4, respectively. Nematic superconductivity, although not realized as a primary instability of the system, appears as a consequence of the near-degeneracy of superconducting order parameters that transform as one-dimensional and two-dimensional irreducible representations of the point group D 6 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Stacking Fault Induced Symmetry Breaking in van der Waals Nanowires

While traditional ferroelectrics are based on polar crystals in bulk or thin film form, two-dimensional and layered materials can support mechanisms for symmetry breaking between centrosymmetric building blocks, e.g., by creating low-symmetry interfaces in van der Waals stacks. Here, we introduce an approach toward symmetry breaking in van der Waals crystals that relies on the spontaneous incorporation of stacking faults in a nonpolar bulk layer sequence. The concept is realized in nanowires consisting of Se-rich group IV monochalcogenide (GeSe 1–x S x ) alloys, obtained by vapor–liquid–solid growth. The single crystalline wires adopt a layered structure in which the nonpolar A-B bulk stacking along the nanowire axis is interrupted by single-layer stacking faults with local A-A' stacking. Density functional theory explains this behavior by a reduced stacking fault formation energy in GeSe (or Se-rich GeSe 1–x S x alloys). Computations demonstrate that, similar to monochalcogenide monolayers, the inserted A-layers should show a spontaneous electric polarization with a switching barrier consistent with a Curie temperature above room temperature. Second-harmonic generation signals are consistent with a variable density of stacking faults along the wires. Here, our results point to possible routes for designing ferroelectrics via the layer stacking in van der Waals crystals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Loop-level double-copy for massive fermions in the fundamental

We find that unitarity cuts and the duality between color and kinematics are sufficient constraints to bootstrap D-dimensional QCD scattering amplitudes starting from three-particle tree-level. Specifically, we calculate tree level amplitudes through six-points, as well as the four-point one-loop correction for massive fermions in the fundamental representation of the gauge group — constructing a color-dual representation of the latter for the first time. To do so we clarify a prescription for functional kinematic ansatze involving fermionic matter. The advantages of color-dual calculation, familiar from particles in the adjoint, also apply here: only a small number of basis topologies must be constrained via physical information of the theory, and algebraic relations propagate this to a full solution. As all the QCD amplitudes we construct here are color-dual, they trivially generate D-dimensional amplitudes in gravitational theories via double-copy construction.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗