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DOE OSTI2025

Odd-Parity Magnetism Driven by Antiferromagnetic Exchange

Realizing odd-parity, time-reversal-preserving, nonrelativistic spin splitting is a central goal for spintronics applications. We propose a group-theory-based microscopic framework to induce odd-parity spin splitting from coplanar antiferromagnetic (AFM) states without spin-orbit coupling (SOC). We develop phenomenological models for 421 conventional period-doubling AFM systems in nonsymmorphic space groups and construct minimal microscopic models for 119 of these. We find that these AFM states can attain three possible competing ground states. These ground states all break symmetries in addition to those broken by the usual AFM order. Specifically, they give rise to either odd-parity spin-splitting, nematic order, or scalar odd-parity order related to multiferroicity. Our microscopic theories reveal that the odd-parity spin-splitting energy scale is generically large and further reveal that the scalar odd-parity order gives a nonzero Berry curvature dipole without SOC. We identify 67 materials in the Magndata database for which our theory applies. We provide density-functional theory (DFT) calculations on Fe-based materials that reveal an ℎ-wave spin splitting consistent with our symmetry arguments and apply our microscopic model to determine the nonrelativistic Edelstein response for CeNiAsO.

Antiferromagnets↗

DOE OSTI2020

Molecule Origins of Dipolar Character in Excited Electronic States

The molecular level origins for symmetry breaking in the excited state of symmetrical quadrupolar molecules, particularly in polar solvents, was investigated using time-dependent density functional theory approaches. Molecules of the form ADA (A/D electron accepting/donating respectively), have been shown to break their symmetry upon excitation, producing an intramolecular charge transfer event and permanent dipole. Current research indicates that polar solvents stabilize the charge transfer event thereby producing asymmetrical solvent dynamics on opposite ends of the molecules. In this work key structural features of the molecule were identified including (1) incorporation of cyano groups, (2) rotation of grafted phenyl rings, and (3) the length of the conjugated R group chain. More specifically, incorporation of cyano groups appears to decrease the magnitude of the dipole in the excited state, thereby indicating that solvent interactions at these groups do not stabilize the charge transfer. While the rotation of the phenyl groups appears to be necessary to break the symmetry of the excited state in the molecule.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Dynamic, symmetry-preserving, and hardware-adaptable circuits for quantum computing many-body states and correlators of the Anderson impurity model

We present a hardware-reconfigurable ansatz on N q -qubits for the variational preparation of many-body states of the Anderson impurity model (AIM) with N imp + N bath = N q /2 sites, which conserves total charge and spin z component within each variational search subspace. The many-body ground state of the AIM is determined as the minimum over all minima of O(N$^2_ q$) distinct charge-spin sectors. Hamiltonian expectation values are shown to require ω(N q ) < N meas. $\leqslant$ O(N imp N bath ) symmetry-preserving, parallelizable measurement circuits, each amenable to postselection. To obtain the one-particle impurity Green’s function we show how initial Krylov vectors can be computed via midcircuit measurement and how Lanczos iterations can be computed using the symmetry-preserving ansatz. For a single-impurity Anderson model with a number of bath sites increasing from one to seven, we show using numerical emulation that the ease of variational ground-state preparation is suggestive of linear scaling in circuit depth and subquartic scaling in optimizer complexity. We therefore expect that, combined with time-dependent methods for Green’s function computation, our ansatz provides a useful tool to account for electronic correlations on early fault-tolerant processors. Finally, with a view towards computing real materials properties of interest like magnetic susceptibilities and electron-hole propagators, we provide a straightforward method to compute many-body, time-dependent correlation functions using a combination of time evolution, midcircuit measurement-conditioned operations, and the Hadamard test.

36 MATERIALS SCIENCE↗

DOE OSTI2022

SU(4) Symmetry in Twisted Bilayer Graphene: An Itinerant Perspective

We study symmetry-broken phases in twisted bilayer graphene at small filling above charge neutrality and at van Hove filling. We argue that the Landau functionals for the particle-hole order parameters at these fillings both have an approximate SU(4) symmetry, but differ in the sign of quartic terms. We determine the order parameter manifold of the ground state and analyze its excitations. For small fillings, we find a strong first-order transition to an SU(3) Ⓧ U(1) manifold of orders that break spin-valley symmetry and induce a 3-1 splitting of fermionic excitations. For van Hove filling, we find a weak first-order transition to an SU(2) Ⓧ SU(2) Ⓧ U(1) manifold of orders that preserves the twofold band degeneracy. Here, we discuss the effect of particle-hole orders on superconductivity and compare with strong-coupling approaches.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Spectroscopic factors, overlaps, and isospin symmetry from an R -matrix point of view

Background: Spectroscopic factors, overlaps, and isospin symmetry are often used in conjunction with single-particle wave functions for the phenomenological analysis of nuclear structure and reactions. Many differing prescriptions for connecting these quantities to physically relevant asymptotic normalization constants or widths are available in the literature, but their relationship and degree of validity are not always clear. Purpose: This paper derives relationships among the above quantities of interest using well-defined methodology and starting assumptions. Method: R -matrix theory is used as the primary tool to interoperate among the quantities of interest to this work. Particular attention is paid to effects arising from beyond the nuclear surface, where isospin symmetry is strongly violated. Results: Relationships between the quantities of interest are derived. Example applications of these methods to mirror levels in nucleon + 12 C, nucleon + 16 O, and nucleon + 26 Al are presented. A new approach to multilevel mirror symmetry is derived and applied to the first three 2 + states of 18 O and 18 Ne. Conclusions: In this work, the relationship between the quantities of interest is clarified and certain procedures are recommended. It is found that the asymptotic normalization constant of the second 2 + state in 18 Ne deduced from the mirror state in 18 O is significantly larger than found in previous work. This finding has the effect of increasing the 17 F($\textit{p,γ}$) 18 Ne reaction rate in novae.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

On ambiguities and divergences in perturbative renormalization group functions

There is an ambiguity in choosing field-strength renormalization factors in the $ \overline{\mathrm{MS}} $ scheme starting from the 3-loop order in perturbation theory. More concerning, trivially choosing Hermitian factors has been shown to produce divergent renormalization group functions, which are commonly understood to be finite quantities. We demonstrate that the divergences of the RG functions are such that they vanish in the RG equation due to the Ward identity associated with the flavor symmetry. It turns out that any such divergences can be removed using the renormalization ambiguity and that the use of the flavor-improved β-function is preferred. We show how our observations resolve the issue of divergences appearing in previous calculations of the 3-loop SM Yukawa β-functions and provide the first calculation of the flavor-improved 3-loop SM β-functions in the gaugeless limit.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Nonperturbative dynamics of (2+1)d φ 4 -theory from Hamiltonian truncation

We use Lightcone Conformal Truncation (LCT) - a version of Hamiltonian truncation - to study the nonperturbative, real-time dynamics of φ 4 -theory in 2+1 dimensions. This theory has UV divergences that need to be regulated. We review how, in a Hamiltonian framework with a total energy cutoff, renormalization is necessarily state-dependent, and UV sensitivity cannot be canceled with standard local operator counter-terms. To overcome this problem, we present a prescription for constructing the appropriate state-dependent counterterms for (2+1)d φ 4 -theory in lightcone quantization. We then use LCT with this counterterm prescription to study φ 4 -theory, focusing on the $\mathbb{Z}$ 2 symmetry-preserving phase. Specifically, we compute the spectrum as a function of the coupling and demonstrate the closing of the mass gap at a (scheme-dependent) critical coupling. We also compute Lorentz-invariant two-point functions, both at generic strong coupling and near the critical point, where we demonstrate IR universality and the vanishing of the trace of the stress tensor.

field theories in lower dimensions↗

DOE OSTI2022

Light-front holography model of the EMC effect

A new two-component model of the EMC effect based on Light-Front Holographic QCD (LFHQCD) is presented. The model suggests the EMC effect is the result of the nuclear potential breaking SU(6) symmetry. The model separates the $F_{2}^{A}$ nuclear structure function into two parts: a free contribution, involving the addition of proton and neutron structure functions weighted by the number of protons and neutrons respectively, and a nuclear/medium modified contribution that involves a universal function for all nuceli. Further, the model displays a connection with the correlation between the size of the EMC effect and the SRC pair density, a 2 - extracted from kinematic plateaus at around x > 1 in inclusive quasi-elastic (QE) scattering.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Inclusive curvaturelike framework for describing dissipation: Metriplectic 4-bracket dynamics

An inclusive framework for joined Hamiltonian and dissipative dynamical systems that are thermodynamically consistent, i.e., preserve energy and produce entropy, is given. The dissipative dynamics of the framework is based on the metriplectic 4-bracket , a quantity like the Poisson bracket defined on phase space functions, but unlike the Poisson bracket has four slots with symmetries and properties motivated by Riemannian curvature. Metriplectic 4-bracket dynamics is generated using two generators, the Hamiltonian and the entropy, with the entropy being a Casimir of the Hamiltonian part of the system. The formalism includes known previous binary bracket theories for dissipation or relaxation as special cases. Rich geometrical significance of the formalism and methods for constructing metriplectic 4-brackets are explored. Many examples of both finite and infinite dimensions are given.

Physics↗

DOE OSTI2023

Functional Renormalization Group Study of Superconductivity in Rhombohedral Trilayer Graphene

We employ a functional renormalization group approach to ascertain the pairing mechanism and symmetry of the superconducting phase observed in rhombohedral trilayer graphene. Superconductivity in this system occurs in a regime of carrier density and displacement field with a weakly distorted annular Fermi sea. We find that repulsive Coulomb interactions can induce electron pairing on the Fermi surface by taking advantage of momentum-space structure associated with the finite width of the Fermi sea annulus. Furthermore, the degeneracy between spin-singlet and spin-triplet pairing is lifted by valley-exchange interactions that strengthen under the RG flow and develop nontrivial momentum-space structure. We find that the leading pairing instability is d-wave-like and spin-singlet, and that the theoretical phase diagram versus carrier density and displacement field agrees qualitatively with experiment.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Applying Noether's theorem to matter in the Milky Way: evidence for external perturbations and non-steady-state effects from Gaia Data Release 2

We apply Noether's theorem to observations of main-sequence stars from the Gaia Data Release 2 archive to probe the matter distribution function of the Galaxy. That is, we examine the axial symmetry of stars at vertical heights $z$, $0.2 \le |z| \le 3$ kpc, to probe the quality of the angular momentum $L_z$ as an integral of motion. The failure of this symmetry test would speak to a Milky Way, in both its visible and dark matter, that is not isolated and/or not in steady state. The left-right symmetry-breaking pattern we have observed, north and south, reveals both effects, with a measured deviation from symmetry of typically 0.5%. We show that a prolate form of the gravitational distortion of the Milky Way by the Large Magellanic Cloud, determined from fits to the Orphan stream by Erkal et al., 2019, is compatible with the size and sign of the axial-symmetry-breaking effects we have discovered in our sample of up to 14.4 million main-sequence stars, speaking to a distortion of an emergent, rather than static, nature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Replica symmetry breaking in spin glasses in the replica-free Keldysh formalism

We show that the algebra of Parisi ultrametric matrices is recovered by the real-time, replica-free, Dyson-Keldysh equations of infinite-range quantum spin glasses in the late time glassy limit. This connects to earlier results on classical and quantum systems showing how ultrametricity emerges from the persistent slow aging dynamics of the glass phase. The stationary spin glass state thereby spontaneously breaks thermal symmetry, or the Kubo-Martin-Schwinger relation of a state in global thermal equilibrium. We describe the Keldysh path integral of the infinite-range Ising model in transverse and longitudinal fields, and in the context of the Landau expansion of the action functional, show how the long-time limit connects to the full replica symmetry breaking obtained in the equilibrium formalism. We also illustrate our formalism by applying it to the spherical quantum p p -spin model, which only exhibits one-step replica symmetry breaking.

Lang, Johannes (ORCID:0000000283533392)↗

DOE OSTI2023

Symmetry-resolved entanglement entropy, spectra & boundary conformal field theory

We perform a comprehensive analysis of the symmetry-resolved (SR) entanglement entropy (EE) for one single interval in the ground state of a 1 + 1D conformal field theory (CFT), that is invariant under an arbitrary finite or compact Lie group, G. We utilize the boundary CFT approach to study the total EE, which enables us to find the universal leading order behavior of the SREE and its first correction, which explicitly depends on the irreducible representation under consideration and breaks the equipartition of entanglement. We present two distinct schemes to carry out these computations. The first relies on the evaluation of the charged moments of the reduced density matrix. This involves studying the action of the defect-line, that generates the symmetry, on the boundary states of the theory. This perspective also paves the way for discussing the infeasibility of studying symmetry resolution when an anomalous symmetry is present. The second scheme draws a parallel between the SREE and the partition function of an orbifold CFT. This approach allows for the direct computation of the SREE without the need to use charged moments. From this standpoint, the infeasibility of defining the symmetry-resolved EE for an anomalous symmetry arises from the obstruction to gauging. Finally, we derive the symmetry-resolved entanglement spectra for a CFT invariant under a finite symmetry group. We revisit a similar problem for CFT with compact Lie group, explicitly deriving an improved formula for U(1) resolved entanglement spectra. Using the Tauberian formalism, we can estimate the aforementioned EE spectra rigorously by proving an optimal lower and upper bound on the same. In the abelian case, we perform numerical checks on the bound and find perfect agreement.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Quantum teleportation implies symmetry-protected topological order

We constrain a broad class of teleportation protocols using insights from locality. In the ``standard'' teleportation protocols we consider, all outcome-dependent unitaries are Pauli operators conditioned on linear functions of the measurement outcomes. We find that all such protocols involve preparing a ``resource state'' exhibiting symmetry-protected topological (SPT) order with Abelian protecting symmetry G k = ( Z 2 × Z 2 ) k . The k logical states are teleported between the edges of the chain by measuring the corresponding 2 k string order parameters in the bulk and applying outcome-dependent Paulis. Hence, this single class of nontrivial SPT states is both necessary and sufficient for the standard teleportation of k qubits. We illustrate this result with several examples, including the cluster state, variants thereof, and a nonstabilizer hypergraph state.

Hong, Yifan↗

DOE OSTI2022

Full-potential KKR within the removed-sphere method: A practical and accurate solution to the Poisson equation

Here an efficient and accurate generalization of the removed-sphere method (RSM) to solve the Poisson equation for total charge density in a solid with space-filling convex Voronoi polyhedra (VPs) and any symmetry is presented. The generalized RSM avoids the use of multipoles and VP shape functions for cellular integrals, which have associated ill-convergent large, double-internal L sums in spherical-harmonic expansions, so that fast convergence in single-L sums is reached. Our RSM adopts full Ewald formulation to work for all configurations or when symmetry breaking occurs, such as for atomic displacements or elastic constant calculations. The structure-dependent coefficients A L that define RSM can be calculated once for a fixed structure and speed up the whole self-consistent-field procedure. The accuracy and rapid convergence properties are confirmed using two analytic models, including the Coulomb potential and energy. We then implement the full-potential RSM using the Green's function Korringa-Kohn-Rostoker (KKR) method for real applications and compare the results with other first-principle methods and experimental data, showing that they are equally as accurate.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Impact of Chiral Symmetry Breaking on Spin-Texture and Lone Pair Expression in Chiral Crystals of Hybrid Antimony and Bismuth Halides

Chiral organic building blocks can be incorporated into hybrid organic-inorganic metal-halide crystalline semiconductors so as to control and impact the interconversion between light, charge, and spin. Here, we report a series of hybrid antimony and bismuth halide materials of the general formula MBA 4 B 2 X 10 (B = Sb 3+ , Bi 3+ ; X = Br - , I - ) and study how chiral symmetry breaking imposed by the templating organic chiral methylbenzylammonium (MBA) cations induces symmetry breaking within the inorganic sublattice and leads to a unique spin-texture. The chiral MBA cations introduce two structural modifications to the metal-halide sublattice that consists of isolated edge-sharing dimers of B 2 X 10 octahedra: (1) the dimers have a chiral spatial arrangement with respect to one another and (2) there is an asymmetric distortion of the two subunits within the individual dimers with a higher distortion caused by strong stereochemical activity of the Sb 5s 2 lone pair electrons. The structural distortions and chiral arrangement result in circular dichroism (CD) at the band edge of the inorganic framework with dissymmetry factors in the range of 10 -4 . Chiral spin-splitting of the inorganic states, caused by breaking of the inversion symmetry and large spin-orbit coupling, is studied via density functional theory (DFT), and a multiband effective mass theory was developed that links the DFT-derived spin-splitting of helical character (i.e., spin expectation value not perpendicular to the crystal momentum) to the observed CD. Furthermore, we also find broad red photoluminescence from the MBA 4 Sb 2 Br 10 compounds, which we attribute to self-trapped excitonic emission driven by the large distortion due to the lone pair expression.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Monte Carlo Global QCD Analyses of the Pion Parton Distribution Functions

As the lightest hadron, the pion presents itself as a dichotomy. While being the pseudo Goldstone boson associated with chiral symmetry breaking, it is simultaneously regarded as the lightest pseudoscalar meson typically composed of constituent quark and antiquark. As the chiral symmetry shares the same global symmetry as QCD, studying the pion and its internal structure is key in understanding one of the four fundamental forces of nature, namely the quantum chromodynamic strong interaction. We study the pion's parton distribution functions (PDFs), which are universal quantities that describe the structure of the pion in terms of its constituent quarks, antiquarks, and gluons. Our goal is to discover what the available data reveal for these universal quantities, namely the PDFs. Through the use of factorization theorems and perturbative QCD, we use Monte Carlo (MC) methods to extract the PDFs from the available Drell-Yan (DY) and leading neutron (LN) data. While the DY process involves two hadrons colliding, the LN electroproduction involves an electron beam incident on a target nucleon. We can constrain well the pion PDFs at large momentum fraction using DY data, and at low momentum fraction using LN data. We also use threshold resummation in the DY process to gather predictable higher order terms associated with the soft gluon radiation because their contributions to the cross section are nontrivial. In this dissertation, we parametrize the pion PDFs and fit those parameters to the available data. We make use of Bayesian inference and use MC techniques to sample the parameter space. Three sets of results are presented. We first extract the pion PDFs by fitting the DY and LN data. Then, we include transverse momentum dependent DY data in conjunction with the DY and LN data to extract the pion PDFs. Finally, we apply various methods of threshold resummation to the DY cross section and extract pion PDFs. The pion PDFs presented here are the first global QCD analyses performed as well as the first MC extracted pion PDFs, which are at the forefront of the pion PDF community.

Barry, Patrick↗

DOE OSTI2021

Probing atomic-scale symmetry breaking by rotationally invariant machine learning of multidimensional electron scattering

Abstract The 4D scanning transmission electron microscopy (STEM) method maps the structure and functionality of solids on the atomic scale, yielding information-rich data sets describing the interatomic electric and magnetic fields, structural and electronic order parameters, and other symmetry breaking distortions. A critical bottleneck is the dearth of analytical tools that can reduce complex 4D-STEM data to physically relevant descriptors. We propose an approach for the systematic exploration of 4D-STEM data using rotationally invariant variational autoencoders (rrVAE), which disentangle the general rotation of the object from other latent representations. The implementation of purely rotational rrVAE is discussed as are applications to simulated data for graphene and zincblende structures. The rrVAE analysis of experimental 4D-STEM data of defects in graphene is illustrated and compared to the classical center-of-mass analysis. This approach is universal for probing symmetry-breaking phenomena in complex systems and can be implemented for a broad range of diffraction methods.

36 MATERIALS SCIENCE↗