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DOE OSTI2025

Quantum Algorithms for Representation-Theoretic Multiplicities

Kostka, Littlewood-Richardson, Plethysm, and Kronecker coefficients are the multiplicities of irreducible representations in the decomposition of representations of the symmetric group that play an important role in representation theory, geometric complexity, and algebraic combinatorics. We give quantum algorithms for computing these coefficients whenever the ratio of dimensions of the representations is polynomial. We show that there is an efficient classical algorithm for computing the Kostka numbers under this restriction and conjecture the existence of an analogous algorithm for the Littlewood-Richardson coefficients. We argue why such classical algorithm does not straightforwardly work for the Plethysm and Kronecker coefficients and conjecture that our quantum algorithms lead to superpolynomial speedups. The conjecture about Kronecker coefficients was disproved by Panova [Polynomial time classical versus quantum algorithms for representation theoretic multiplicities, arXiv:2502.20253] with a classical algorithm which, if optimal, points to a 𝒪⁡(𝑛 4+2⁢𝑘 ) vs $\tilde{Ω}$⁡(𝑛 4⁢𝑘 2 +1 ) polynomial gap in quantum vs classical computational complexity for an integer parameter 𝑘.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Projective Representations, Bogomolov Multiplier, and Their Applications in Physics

We present a pedagogical review of projective representations of finite groups and their physical applications in quantum many-body systems. Some of our physical results are new. We begin with a self-contained introduction to projective representations, highlighting the role of group cohomology, representation theory, and classification of irreducible projective representations. We then focus on a special subset of cohomology classes, known as the Bogomolov multiplier, which consists of cocycles that are symmetric on commuting pairs but remain nontrivial in group cohomology. Such cocycles have important physical implications: they characterize (1+1)D SPT phases that cannot be detected by string order parameters and give rise, upon gauging, to distinct gapped phases with completely broken non-invertible Rep(G) symmetry. We construct explicit lattice models for these phases and demonstrate how they are distinguished by the fusion rules of local order parameters. We show that a pair of completely broken Rep(G) SSB phases host nontrivial interface modes at their domain walls. As an example, we construct a lattice model where the ground state degeneracy on a ring increases from 32 without interfaces to 56 with interfaces.

Bogomolov multiplier↗

DOE OSTI2025

Orientation reversal and the Chern-Simons natural boundary

We show that the fundamental property of preservation of relations, underlying resurgent analysis, provides a new perspective on crossing a natural boundary, an important general problem in theoretical and mathematical physics. This reveals a deeper rigidity aspect of resurgence in a quantum field theory path integral. The physical context here is the non-perturbative completion of complex Chern-Simons theory that associates to a 3-manifold a collection of q-series invariants labeled by Spinc structures, for which crossing the natural boundary corresponds to orientation reversal of the 3-manifold. Our new resurgent perspective leads to a practical numerical algorithm that generates q-series which are dual to unary q-series composed of false theta functions. Until recently, these duals were only known in a limited number of cases, essentially based on Ramanujan’s mock theta functions, and the common belief was that the duals might not even exist in the general case. Resurgence analysis identifies as primary objects Mordell integrals: up to changes of variables, they are Laplace transforms of resurgent functions. Their unique Borel summed transseries decomposition on either side of the Stokes line is simply the unique decomposition into real and imaginary parts. In turn, the latter are combinations of unary q-series in terms of q and its modular counterpart $\overset{\sim }{q}$ , and are resurgent by construction. The Mordell integral is analytic across the natural boundary of the q and $\overset{\sim }{q}$ series, and uniqueness of a similar decomposition which preserves algebraic relations on the other side of the boundary defines the unique boundary crossing of the q series. We demonstrate that this continuation can be efficiently implemented numerically. In the cases where unique mock modular identities are known, they are found by this numerical procedure, but the procedure can go well beyond the known list of identities. A particularly interesting feature of the resurgent approach is that it reveals new aspects, and is very different from other known approaches based on indefinite theta series, Appell-Lerch sums, and representation theory of logarithmic vertex operator algebras.

Chern-Simons theories↗

DOE OSTI2026

Constraints on long-range forces in de Sitter space

The representation theory of de Sitter space admits partially massless (PM) particles, but whether such particles can participate in consistent interacting theories remains unclear. We investigate the consistency of theories containing PM fields, particularly when these fields are coupled to gravity. Our strategy exploits the fact that PM fields correspond to partially conserved currents on the spacetime boundary, which generate symmetries. These symmetries place stringent constraints on correlation functions of charged operators, allowing us to test the consistency of a proposed bulk spectrum. When the assumed operator content violates these constraints, the corresponding bulk theory is ruled out. Applying this framework, we show that, in four-dimensional de Sitter space, PM fields of spin 2 or 3 (at depth 0) cannot couple consistently to gravity: such couplings necessitate additional massive fields, which are inevitably non-unitary. In higher dimensions, however, the constraints can be satisfied without violating unitarity if further PM fields are included. The resulting structure leads to additional charge conservation laws, which suggests that consistency may ultimately require an infinite tower of higher-spin PM fields, akin to the situation for ordinary higher-spin symmetries. The methods developed here provide powerful constraints on possible long-range interactions in de Sitter space and delineate the landscape of consistent quantum field theories in cosmological spacetimes.

AdS-CFT Correspondence↗

DOE OSTI2025

Spectral Bounds on Hyperbolic 3-Manifolds: Associativity and the Trace Formula

We constrain the low-energy spectra of Laplace operators on closed hyperbolic manifolds and orbifolds in three dimensions, including the standard Laplace--Beltrami operator on functions and the Laplacian on powers of the cotangent bundle. Our approach employs linear programming techniques to derive rigorous bounds by leveraging two types of spectral identities. The first type, inspired by the conformal bootstrap, arises from the consistency of the spectral decomposition of the product of Laplace eigensections, and involves the Laplacian spectra as well as integrals of triple products of eigensections. We formulate these conditions in the language of representation theory of PSL 2 (C) and use them to prove upper bounds on the first and second Laplacian eigenvalues. The second type of spectral identities follows from the Selberg trace formula. We use them to find upper bounds on the spectral gap of the Laplace--Beltrami operator on hyperbolic 3-orbifolds, as well as on the systole length of hyperbolic 3-manifolds, as a function of the volume. Further, we prove that the spectral gap λ 1 of the Laplace--Beltrami operator on all closed hyperbolic 3-manifolds satisfies λ 1 < 47.32. Along the way, we use the trace formula to estimate the low-energy spectra of a large set of example orbifolds and compare them with our general bounds, finding that the bounds are nearly sharp in several cases.

Bonifacio, James [University of Mississippi, MS (U↗

DOE OSTI2024

Designs from Local Random Quantum Circuits with SU ( d ) Symmetry

The generation of k -designs (pseudorandom distributions that emulate the Haar measure up to k moments) with local quantum circuit ensembles is a problem of fundamental importance in quantum information and physics. Despite the extensive understanding of this problem for ordinary random circuits, the crucial situations in which symmetries or conservation laws are in play are known to pose fundamental challenges and remain little understood. Here, we construct explicit local unitary ensembles that can achieve high-order unitary k -designs under transversal continuous symmetry, in the particularly important SU ( d ) case. Specifically, we define the convolutional quantum alternating (CQA) group generated by 4-local SU ( d ) -symmetric Hamiltonians as well as associated 4-local SU ( d ) -symmetric random unitary circuit ensembles and prove that they form and converge to SU ( d ) -symmetric k -designs, respectively, for all k < n ( n − 3 ) / 2 , with n being the number of qudits. A key technique that we employ to obtain the results is the Okounkov-Vershik approach to S n representation theory. To study the convergence time of the CQA ensemble, we develop a numerical method using the Young orthogonal form and the S n branching rule. We provide strong evidence for a subconstant spectral gap and certain convergence time scales of various important circuit architectures, which contrast with the symmetry-free case. We also provide comprehensive explanations of the difficulties and limitations in rigorously analyzing the convergence time using methods that have been effective for cases without symmetries, including Knabe’s local gap threshold and Nachtergaele’s martingale methods. This suggests that a novel approach is likely necessary for understanding the convergence time of SU ( d ) -symmetric local random circuits. Published by the American Physical Society 2024

Li, Zimu (ORCID:0000000314736492)↗

DOE OSTI2024

Enhancing Lattice Kinetic Schemes for Fluid Dynamics with Lattice-Equivariant Neural Networks

A new class of equivariant neural networks is presented, hereby dubbed lattice-equivariant neural networks (LENNs), designed to satisfy local symmetries of a lattice structure. The approach develops within a recently introduced framework aimed at learning neural network-based surrogate models’ lattice Boltzmann collision operators. Whenever neural networks are employed to model physical systems, respecting symmetries and equivariance properties has been shown to be key for accuracy, numerical stability, and performance. Here, hinging on ideas from group representation theory, trainable layers are defined whose algebraic structure is equivariant with respect to the symmetries of the lattice cell. In this work, the presented method naturally allows for efficient implementations, in terms of both memory usage and computational costs, supporting scalable training/testing for lattices in two spatial dimensions and higher (in which the size of symmetry group grows). The approach is validated and tested considering 2D and 3D flowing dynamics, both in laminar and turbulent regimes. It is compared with group-averaged-based symmetric networks and with plain, nonsymmetric, networks, showing how the presented approach unlocks the (a posteriori) accuracy and training stability of the former models and the train/inference speed of the latter networks. (LENNs are about one order of magnitude faster than group-averaged networks in 3D.) The work in this paper opens toward practical use of machine learning-augmented lattice Boltzmann CFD in real-world simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

All-electron molecular tunnel ionization based on the weak-field asymptotic theory in the integral representation

Tunnel ionization (TI) underlies many important ultrafast processes, such as high-harmonic generation andstrong-field ionization. Among the existing theories for TI, many-electron weak-field asymptotic theory (ME-WFAT) is by design capable of accurately treating many-electron effects in TI. An earlier version of ME-WFATrelied on an accurate representation of the asymptotic tail of the orbitals, which hindered its implementation inGaussian-basis-set-based quantum chemistry programs. In this work, we reformulate ME-WFAT in the integralrepresentation, which makes the quality of the asymptotic tail much less critical, hence greatly facilitating itsimplementation in standard quantum chemistry packages. The integral reformulation introduced here is thereforemuch more robust when applied to molecules with arbitrary geometry. Here, we present several case studies, amongwhich is the CO molecule where some earlier theories disagree with experiments. Here we find that ME-WFATproduces the largest ionization probability when the field points from C to O, as experiments suggest. Anattractive feature of ME-WFAT is that it can be used with various types of multielectron methods whether ofdensity functional or multiconfiguration types, this inturn facilitates tunnel ionization calculation in systems exhibiting a strong multireference character.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2026

Relativistic Exact Two-Component Theory in the Generalized Pseudospectral Representation

We present a formulation and implementation of exact two-component (X2C) relativistic theory in the generalized pseudospectral representation. When combined with the Hartree-Fock-Slater framework, this approach enables efficient and accurate treatments of scalar-relativistic and spin-orbit effects in atomic electronic structures without the computational overhead of four-component methods. Benchmark calculations across light and heavy elements demonstrate that the our X2C scheme yields substantially more accurate relativistic corrections to core-electron binding energies than perturbational Breit-Pauli treatments while converging more rapidly with respect to basis size. The method provides an improved computational framework for modeling ultrafast x-ray-induced processes in heavy-element systems.

Wang, Xubo↗

DOE OSTI2025

A flavor of SO(10) unification with a spinor Higgs

We investigate Higgs Parity unification — a realization of SO(10) grand unification based on the Higgs Parity mechanism in which the Standard Model (SM) Higgs resides in a spinor representation. The theory has an intermediate left-right symmetric stage where the SU(2)R symmetry breaking scale is fixed by the vanishing of the SM Higgs quartic coupling. The strong CP problem is solved by parity. Gauge coupling unification successfully predicts αs(MZ) to within 1%. The spinor Higgs naturally leads to a seesaw origin for SM flavor observables. We identify a novel mechanism where large mixing of third generation fermions with additional heavy vector-like fermions accounts for the anarchical nature of the PMNS matrix and the lack of hierarchy in the neutrino mass spectrum, relative to the up-quarks. A fit to quark and lepton masses and mixings, with a minimal parameter set, predicts 1) A testable relation between the top quark mass and αs(MZ) which is about (1 – 2)σ from current best fit values, 2) The order of magnitude of the baryon asymmetry of the universe, via leptogenesis from second-generation right-handed neutrino decays. 3) The proton decay and the neutron EDM are likely observable in next generation experiments, and 4) A normal ordered neutrino mass spectrum where 0νββ decay and the mass of the lightest neutrino are out of reach of next generation experiments.

Baryo-and Leptogenesis↗

DOE OSTI2025

Gauge loop-string-hadron formulation on general graphs and applications to fully gauge fixed Hamiltonian lattice gauge theory

We develop a gauge invariant, Loop-String-Hadron (LSH) based representation of SU(2) Yang-Mills theory defined on a general graph consisting of vertices and half-links. Inspired by weak coupling studies, we apply this technique to maximal tree gauge fixing. This allows us to develop a fully gauge-fixed representation of the theory in terms of LSH quantum numbers. We explicitly show how the quantum numbers in this formulation directly relate to the variables in the magnetic description. In doing so, we will also explain in detail how the Kogut-Susskind formulation, prepotentials, and point splitting work for general graphs. In the appendix of this work, we provide a self-contained exposition of the mathematical details of Hamiltonian pure gauge theories defined on general graphs.

Algorithms and Theoretical Developments↗

DOE OSTI2025

Efficient sampling of free energy landscapes with functions in Sobolev spaces

Molecular simulations of biological and physical phenomena generally involve sampling complicated, rough energy landscapes characterized by multiple local minima. In this work, we introduce a new family of methods for advanced sampling that draw inspiration from functional representations used in machine learning and approximation theory. As shown here, such representations are particularly well suited for learning free energies using artificial neural networks. As a system evolves through phase space, the proposed methods gradually build a model for the free energy as a function of one or more collective variables, from both the frequency of visits to distinct states and generalized force estimates corresponding to such states. Implementation of the methods is relatively simple and, more importantly, for the representative examples considered in this work, they provide computational efficiency gains of up to several orders of magnitude over other widely used simulation techniques.

Approximation theory↗

DOE OSTI2026

A physically based mechanical model for Mullins effect in thermoplastic polyurethanes

Despite decades of research, connecting the chemical and physical structure of thermoplastic polyurethanes to their mechanical properties remains highly challenging. Of particular note are their large-deformation and rate-dependent behaviors, which vary greatly with molecular chemistry, including the type and relative content of soft and hard segments. In this work, we develop a physically motivated mechanical theory for predicting the behavior of thermoplastic polyurethanes. The theory incorporates a representation of microstructural evolution during mechanical deformation, which captures the signatures of stress softening over cyclic loading (commonly referred to as the Mullins effect). There are only eight physically motivated fitting parameters, including a direct dependence on the hard segment fraction. The model predicts that increasing the hard segment fraction leads to higher stiffness and greater energy dissipation, in quantitative agreement with published experimental data. Furthermore, we provide a comprehensive analysis of the model and validate its predictions across several independent datasets focused on mechanical characterization. Direct comparisons to experimental data demonstrate its predictive capability on the effect of loading rate, cyclic deformations, and applied tension or compression. Altogether, this work establishes a predictive framework that connects polymer chemistry and microstructure to emergent mechanical behaviors.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Circles and triangles, the NLSM and Tr(Φ 3 )

A surprising connection has recently been made between the amplitudes for Tr(Φ 3 ) theory and the non-linear sigma model (NLSM). A simple shift of kinematic variables naturally suggested by the associahedron/stringy representation of Tr(Φ 3 ) theory yields pion amplitudes at all loops. In this note we provide an elementary motivation and proof for this link going in the opposite direction, starting from the non-linear sigma model and discovering its formulation as a sum over triangulations of surfaces with simple numerator factors. This uses an ancient connection between “circles” and “triangles”, interpreting the equation y = $\sqrt{1 – x^2}$ both as parametrizing points a circle as well as generating the number of triangulations of polygons. A further simplification of the numerator factors exposes them as arising from the kinematically shifted Tr(Φ3) theory, and gives rise to novel tropical representations of NLSM amplitudes. The connection to Tr(Φ 3 ) theory defines a natural notion of “surface-soft limit” intrinsic to curves on surfaces. Remarkably, with this definition, the soft limit of pion amplitudes vanishes directly at the level of the integrand, via obvious pairwise cancellations. We also give simple, explicit expressions for the multi-soft factors for tree and loop-level integrands in the limit as any number of pions are taken “surface-soft”.

Scattering Amplitudes↗

DOE OSTI2025

Direct detection of dark baryons naturally suppressed by ℋ-parity

We identify symmetries in a broad class of vectorlike confining dark sectors that forbid the leading electromagnetic moments that would ordinarily mediate dark baryon scattering with the Standard Model. The absence of these operators implies dark baryon dark matter has much smaller cross sections for elastic scattering off nuclei, leading to suppressed direct detection signals. In the confined description, we identify an “ℋ-parity” symmetry that exists in any dark sector with dark quarks transforming under a vectorlike representation of a new confining SU(𝑁 𝑐 ) gauge theory as well as a vectorlike representation of the electroweak group SU⁡(2) 𝐿 . The parity is independent of 𝑁 𝑐 and 𝑁 𝑓 , though it is essential that the dark quarks are neutral under hypercharge. This parity forbids dark hadron electric and magnetic dipole moments, charge radius, and anapole moment, while permitting dimension-7 operators that include polarizability, electroweak loop-induced interactions, and lower-dimensional electromagnetic transition moments between different neutral dark baryon states. We work out an explicit example, 𝑁 𝑐 = 𝑁 𝑓 = 3, that is the most minimal theory with fermionic dark baryons. In this specific model, we use the nonrelativistic quark model to show the magnetic dipole moment and charge radius vanish, while the transition moments are nonzero, consistent with ℋ-parity. We discuss the implications of a suppressed direct detection signal, emphasizing that this broad class of models provide a well-motivated target for future colliders.

composite models↗

DOE OSTI2025

Bounds on spectral gaps of Hyperbolic spin surfaces

We describe a method for constraining Laplacian and Dirac spectra of two dimensional compact orientable hyperbolic spin manifolds and orbifolds. The key ingredient is an infinite family of identities satisfied by the spectra. These spectral identities follow from the consistency between 1) the spectral decomposition of functions on the spin bundle into irreducible representations of SL(2,R) and 2) associativity of pointwise multiplication of functions. Applying semidefinite programming methods to our identities produces rigorous upper bounds on the Laplacian spectral gap as well as on the Dirac spectral gap conditioned on the former. In several examples, our bounds are nearly sharp; a numerical algorithm based on the Selberg trace formula shows that the [0;3,3,5] orbifold, a particular surface with signature [1;3], and the Bolza surface nearly saturate the bounds at genus 0, 1 and 2 respectively. Under additional assumptions on the number of harmonic spinors carried by the spin-surface, we obtain more restrictive bounds on the Laplacian spectral gap. In particular, these bounds apply to hyperelliptic surfaces. We also determine the set of Laplacian spectral gaps attained by all compact orientable two-dimensional hyperbolic spin orbifolds. We show that this set is upper bounded by 12.13798; this bound is nearly saturated by the [0;3,3,5] orbifold, whose first non-zero Laplacian eigenvalue is λ^(0)_1 ≈ 12.13623.

Spectral theory↗

DOE OSTI2025

Facet-dependent structure and dissociation of water at pristine IrO 2 /water interfaces

Understanding the microscopic structure of water at metal oxide interfaces is crucial for advancing electrocatalysis. IrO 2 , specifically, has shown exceptional activity for electrochemical water oxidation, but we currently lack a fundamental understanding of how the surface structure of IrO 2 impacts water reactivity. In this work, we developed a machine learning potential trained to first-principles accuracy for modeling IrO 2 /water interfaces across different facets: (110), (100), (101), and (001). Using extensive machine learning molecular dynamics simulations, we investigated the spontaneous dissociation of water molecules at these interfaces. Our results reveal a distinct dissociation probability trend: (110) > (100) ≈ (101) > (001), which we attribute primarily to the reaction thermodynamics of surface water dissociation. A strong correlation is observed between the surface Ir–O bond distances and the dissociation probabilities, highlighting the role of surface geometry in modulating reactivity. As a consequence, the interfacial solvation structures and hydrogen bonding environments are dynamically tuned by the varying water dissociation capabilities across facets. This work elucidates how water dissociation energetics depend on surface orientation and interfacial structure, offering atomistic insights into manipulating reaction chemistry at electrocatalytic interfaces.

organic↗

DOE OSTI2025

Applications of Nickelate perovskites for neuromorphic computing from electronic structure and Machine Learning

While the limit of Moore's law is presently being reached with current microelectronic technologies, we need to develop new paradigms that overcome this limitation. In that respect, neuromorphic computing is a concept that emulates the neural behavior and response of the human brain, and it has been recognized as a promising alternative approach. In this research project, we will perform multi-fidelity scale bridging to explore the potential use of materials with metal to insulator transition for neuromorphic applications. In particular, rare earth nickelates are promising for such purposes, as the transition in these materials is quite sensitive to a broad set of different external stimuli. Our multi-fidelity approach will bridge the high-fidelity electronic structure calculations with classical potentials. We will bridge dynamical mean field theory with a classical atomistic representation via a deep learning force field. The neural network is trained with energies, charges, and forces obtained by accurate electronic structure theories based on Dynamical Mean Field Theory. The configurational space is generated from known crystal phases, ab initio molecular dynamics with exchange-correlation functionals corrected with the Hubbard model, disordered phases with different concentrations of oxygen vacancies, and nonsymmetrical positions and induced strain by grain interfaces or contact with a substrate. Strategies to train the model with a reduced number of training examples are obtained from active learning methods, and new structures for improving the learning process are generated by using machine learning autoencoders. This classical potential will be validated through a diversity of electronic structure methods and represents an important step to combine the flexibility and accuracy of first-principles with the speed of classical potentials. The generated multi-fidelity surrogate model will be used to understand the role of strain, oxygen vacancies, proton doping, the variation of the crystal phase, substrate effects, vibrational effects as the octahedral rotation, grain boundaries and defect effects on the response of a Metal to Insulator Transition (MIT) in correlated materials. Long time and large-scale simulations will help understand the role of different stimuli to control the hysteresis of the MIT, as it has been experimentally suggested. Selected configurations will be analyzed with higher-level theories to provide an accurate electronic description and to study how the orbitals and charges are rearranged under different conditions.

36 MATERIALS SCIENCE↗