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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Symmetry-projected spin-AGP methods applied to spin systems

Symmetry-projected wave function methods capture static correlation by breaking and restoring the symmetries of a system. In this article, we present the symmetry-projected spin antisymmetrized geminal power (spin-AGP) state projected onto space group symmetry as well as complex conjugation, spin-flip, and time-reversal symmetries. The method is benchmarked on the 1D XXZ model and the 2D J 1 − J 2 model with square and triangular lattices. Our results indicate that symmetry projection methods provide a powerful tool for frustrated spin systems.

Antisymmetrized geminal power↗
DOE OSTI2023

Symmetry-projected cluster mean-field theory applied to spin systems

We introduce S z spin-projection based on cluster mean-field theory and apply it to the ground state of strongly correlated spin systems. In cluster mean-fields, the ground state wavefunction is written as a factorized tensor product of optimized cluster states. In previous work, we have focused on unrestricted cluster mean-field, where each cluster is S z symmetry adapted. We here remove this restriction by introducing a generalized cluster mean-field (GcMF) theory, where each cluster is allowed to access all S z sectors, breaking S z symmetry. In addition, a projection scheme is used to restore global S z , which gives rise to the S z spin-projected generalized cluster mean-field (S z GcMF). Both of these extensions contribute to accounting for inter-cluster correlations. We benchmark these methods on the 1D, quasi-2D, and 2D J 1 – J 2 and XXZ Heisenberg models. Furthermore, our results indicate that the new methods (GcMF and S z GcMF) provide a qualitative and semi-quantitative description of the Heisenberg lattices in the regimes considered, suggesting them as useful references for further inter-cluster correlations, which are discussed in this work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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 OSTI2025

Multiscale Physics of Atomic Nuclei from First Principles

Atomic nuclei exhibit multiple energy scales ranging from hundreds of MeV in binding energies to fractions of an MeV for low-lying collective excitations. As the limits of nuclear binding are approached near the neutron and proton drip lines, traditional shell structure starts to melt with an onset of deformation and an emergence of coexisting shapes. It is a long-standing challenge to describe this multiscale physics starting from nuclear forces with roots in quantum chromodynamics. Here, we achieve this within a unified and nonperturbative quantum many-body framework that captures both short- and long-range correlations starting from modern nucleon-nucleon and three-nucleon forces from chiral effective field theory. The short-range (dynamic) correlations which account for the bulk of the binding energy are included within a symmetry-breaking framework, while long-range (static) correlations (and fine details about the collective structure) are included by employing symmetry projection techniques. Our calculations accurately reproduce—within theoretical error bars—available experimental data for low-lying collective states and the electromagnetic quadrupole transitions in 20−30 Ne. In addition, we reveal coexisting spherical and deformed shapes in 30 Ne, which indicates the breakdown of the magic neutron number 𝑁 = 20 as the key nucleus 28 O is approached, and we predict that the drip line nuclei 32,34 Ne are strongly deformed and collective. By developing reduced-order models for symmetry-projected states, we perform a global sensitivity analysis and find that the subleading singlet 𝑆-wave contact and a pion-nucleon coupling strongly impact nuclear deformation in chiral effective field theory. The techniques developed in this work clarify how microscopic nuclear forces generate the multiscale physics of nuclei spanning collective phenomena as well as short-range correlations and allow one to capture emergent and dynamical phenomena in finite fermion systems such as atom clusters, molecules, and atomic nuclei.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Scattering solution of an interacting Hamiltonian for the electronic control of molecular spin qubits

We theoretically study how a scattered electron can entangle molecular spin qubits (MSQs). This requires solving the inelastic transport of a single electron through a scattering region described by a tight-binding interacting Hamiltonian. We accomplish this using a Green's-function solution. We can model realistic physical implementations of MSQs by parametrizing the tight-binding Hamiltonian with first-principles descriptions of magnetic anisotropy and exchange interactions. As a result, we find that, for two-MSQ systems with inversion symmetry, projective measurement of the spin degree of freedom of the scattered electron offers probabilistic control of the degree of entanglement between the MSQs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Low-energy edge signatures of the Kitaev spin liquid

Recent experimental work indicates that the Kitaev spin liquid may be realizable close to zero magnetic field in exfoliated 𝛼−RuCl 3 flakes, thus providing a more versatile setting for studying non-Abelian anyons. Here, we propose a robust nanoscale signature of the Kitaev spin liquid that results from its edge states and manifests in the low-energy spin dynamics. In particular, we highlight a singular peak in the dynamical spin structure factor of a zigzag edge whose energy scales linearly with only one component of the magnetic field. This sharp feature in the local spin dynamics directly reflects the bond-directional Kitaev spin interactions and, more generally, the projective symmetries of the Kitaev spin liquid. In conclusion, we demonstrate that our proposed signature survives in the presence of edge disorder as well as non-Kitaev interactions, and provide detailed guidelines for experimentally observing it using inelastic electron tunneling spectroscopy and color-center relaxometry.

Color centers↗
DOE OSTI2024

A method for crystallographic mapping of an alpha-beta titanium alloy with nanometre resolution using scanning precession electron diffraction and open-source software libraries

An approach for the crystallographic mapping of two-phase alloys on the nanoscale using a combination of scanned precession electron diffraction and open-source python libraries is introduced in this paper. This method is demonstrated using the example of a two-phase α/β titanium alloy. The data were recorded using a direct electron detector to collect the patterns, and recently developed algorithms to perform automated indexing and analyse the crystallography from the results. Very high-quality mapping is achieved at a 3 nm step size. The results show the expected Burgers orientation relationships between the α laths and β matrix, as well as the expected misorientations between α laths. A minor issue was found that one area was affected by 180° ambiguities in indexing occur due to this area being aligned too close to a zone axis of the α with twofold projection symmetry (not present in 3D) in the zero-order Laue Zone, and this should be avoided in data acquisition in the future. Nevertheless, this study demonstrates a good workflow for the analysis of nanocrystalline two- or multi-phase materials, which will be of widespread use in analysing two-phase titanium and other systems and how they evolve as a function of thermomechanical treatments.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Engineering micromotion in Floquet prethermalization via space-time symmetries

We present a systematic framework for Floquet prethermalization under strong resonant driving, emphasizing the pivotal role of dynamical space-time symmetries. Our approach demonstrates how dynamical space-time symmetries map onto the projective static symmetry group of the prethermal Hamiltonian governing the prethermal regime. We introduce techniques for detecting dynamical symmetries through the time evolution of local observables, facilitating a detailed analysis of micromotion within each period and surpassing the limitations of conventional stroboscopic Floquet prethermal dynamics. To implement this framework, we present a prethermal protocol that preserves order-2 dynamical symmetry in a spin-ladder model, confirming the predicted relationships between the expectation values of local observables at distinct temporal points in the Floquet cycle, linked by this symmetry.

floquet systems↗
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 OSTI2024

Mixed gauge-global symmetries, elliptic modes, and black hole thermodynamics in Hořava-Lifshitz gravity

In Hořava-Lifshitz gravity, a putative consistent theory of quantum gravity for which there is evidence for both black hole thermodynamics and a holographic construction, spacetime is endowed with a preferred dynamical spacelike foliation. The theory has a leaf reparameterization symmetry that is neither global nor local gauge, hyperbolic and elliptic equations of motion, a lack of splittability, and universal horizon black hole solutions. The reparameterization symmetry is “mixed”: it is a local symmetry in one coordinate yet global on each leaf. More broadly it is an example of both unfree and projectable gauge symmetries. The mixed symmetry and associated charge has not yet been accounted for in calculations of universal horizon thermodynamics in Hořava-Lifshitz gravity. This has led to problems, in particular the failure of the first law in a class of asymptotically AdS solutions where the normal to the leaves of the foliation is not aligned with the time translation Killing vector at infinity. We show how the dynamics of the charge corresponding to this symmetry coupled with the other features above resolves this issue. We then briefly comment how this mixed symmetry, the corresponding charge, and the elliptic equations of motion also conspire to evade recent holographic arguments for only local gauge fields in consistent theories of quantum gravity due to the lack of splittability of the elliptic equation and associated mode.

Global Symmetries↗
NASA NTRS1991

Program Computes Universal Transverse Mercator Projection

Computer program produces Gauss-Kruger (constant meridional scale) transverse Mercator projection, used to construct U.S. Army's universal transverse Mercator (UTM) grid system. Capable of mapping entire Northern Hemisphere of Earth (and, by symmetry of projection, entire Earth) accurately with respect to single principal meridian. Mathematically insensitive to proximity to pole or equator and insensitive to departure of meridian from central meridian. Useful to any mapmaking agency. FORTRAN 77 program developed on IBM PC-series computer equipped with Intel Math Coprocessor.

Wallis, David E.↗
DOE OSTI2024

Emerging Functionality in Transition-Metal Compounds Driven by Spatial Confinement and Broken Symmetry

This research project investigates the emerging functionality in transition-metal-compounds (TMCs) driven by spatial confinement and broken symmetry. It combines advanced growth capabilities with cutting-edge characterization and first principles theory to probe and control the properties of TMC interfaces, including the utilization and development of state-of-the-art atomically resolved electron microscopy and spectroscopy to determine the structure, composition, and bonding at TMC interfaces. The proposed research will focus on four challenging areas: 1) manipulate interfaces to design new material phases such as magnetic metals with unique polar structure (net dipole) to achieve multiple functionality; 2) explore electronic mismatch or screening at interfaces of insulating/poor metal TMCs to produce novel electronic and magnetic properties; 3) elucidate and exploit the role of defects, both point and extended, on the functionality of interfaces; 4) develop advanced electron microscopy/spectroscopy techniques to explore temperature dependent phase transitions and couple these structural tools with new nonlinear optical probes of the electronic structure. The research team aims to close the materials-by-design loop of make, measure, model, and modify. The program promises to enhance our ability to engineer the desired physical properties at interfaces, superlattices (periodic arrays of films of different compounds), and heterostructures of TMCs.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Unification of finite symmetries in the simulation of many-body systems on quantum computers

Symmetry is fundamental in the description and simulation of quantum systems. Leveraging symmetries in classical simulations of many-body quantum systems can result in significant overhead due to the exponentially growing size of some symmetry groups as the number of particles increases. Quantum computers hold the promise of achieving exponential speedup in simulating quantum many-body systems; however, a general method for utilizing symmetries in quantum simulations has not yet been established. In this work, we present a unified framework for incorporating symmetry group transforms on quantum computers to simulate many-body systems. The core of our approach lies in the development of efficient quantum circuits for symmetry-adapted projection onto irreducible representations of a group or pairs of commuting groups. We provide resource estimations for common groups, including the cyclic and permutation groups. Our algorithms demonstrate the capability to prepare coherent superpositions of symmetry-adapted states and to perform quantum evolution across a wide range of models in condensed-matter physics and ab initio electronic structure in quantum chemistry. Specifically, we execute a symmetry-adapted quantum subroutine for small molecules in first-quantization on noisy hardware and demonstrate the emulation of symmetry-adapted quantum phase estimation for preparing coherent superpositions of quantum states in various irreducible representations of a symmetry group. In addition, we present a discussion of open problems regarding treating symmetries in digital quantum simulations of many-body systems, paving the way for future systematic investigations into leveraging symmetries quantumly for practical quantum advantage. The broad applicability and rigorous resource estimation for symmetry transformations make our framework appealing for achieving provable quantum advantage on fault-tolerant quantum computers, especially for symmetry-related properties.

quantum algorithms↗
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 OSTI2024

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”.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Lifetime measurements of 0 + states in Er 168 with the Doppler-shift attenuation method

Here, the lowest-lying shape oscillations of deformed nuclei have been described as quadrupole in nature (λ = 2), resulting in two types of vibrations or oscillations: β vibrations with oscillations along the symmetry axis (K π = 0 + ) and γ vibrations breaking axial symmetry with a projection of K π = 2 + on the symmetry axis. The γ vibration seems to be well characterized as the first K π = $2^+_1$ (or $2^+_γ$) band in deformed nuclei and exhibits a systematic behavior across the region. The nature of the K π = 0 + excitations, however, has remained poorly understood and has been open to debate for some decades. The goal of this work is to understand the nature of 0 + states observed in 168 Er through measurements of the lifetimes of these states and to determine if they are consistent with oscillations built on a deformed ground state, the minima of other coexisting shapes, single-particle states, or a mixture of effects. Lifetimes of excited states in the 168 Er nucleus were measured with the Doppler Shift Attenuation Method (DSAM) and the inelastic neutron scattering reaction, (n, n'γ), at the University of Kentucky Accelerator Laboratory. Numerous 0 + states had been observed by the (p, t) reaction. We confirm the 0 + states at 1217.2, 1421.5, 1833.6, 2364.9, 2392.1, and 2643.0 keV in 168 Er. We could not, however, support the previous assignments of 0 + levels at 2114.1, 2200.6, 2572.5, and 2617.4 keV. We report measured lifetimes for six confirmed 0 + excitations and additional members of 0 + bands. The results for 168 Er show that it is the third excited K π = 0 + ($0^+_4$) excitation that carries the collective strength and, therefore, the potential to be an oscillation on the ground state. This result is similar to the case in 166 Er, where it was also the $0^+_4$ state that exhibited greater collectivity than the first excited K π = 0 + band. The Delaroche et al. prediction for a collective K π = 0 + band is at E T =1.818 MeV which corresponds the third excited K π = 0 + band.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗