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At least 109 records · Page 6
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DOE OSTI2024

Correlation function distributions for O ( N ) lattice field theories in the disordered phase

Numerical computations in strongly interacting quantum field theories are often performed using Monte Carlo sampling methods. A key task in these calculations is to estimate the value of a given physical quantity from the distribution of stochastic samples that are generated using the Monte Carlo method. Typically, the sample mean and sample variance are used to define the expectation values and uncertainties of computed quantities. However, the Monte Carlo sample distribution contains more information than these basic properties, and it is useful to investigate it more generally. In this work, the exact form of the probability distributions of two-point correlation functions at zero momentum in O ( N ) lattice field theories in the disordered phase and in infinite volume are determined. These distributions allow for a robust investigation of the efficacy of the Monte Carlo sampling procedure and are shown also to allow for improved estimators of the target physical quantity to be constructed. The theoretical expectations are shown to agree with numerical calculations in the O ( 2 ) model. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2023

Muon capture on the deuteron in chiral effective field theory

Here, we consider the capture of a muon on a deuteron. An uncertainty analysis of the dominant channels is important for a careful analysis of forthcoming experimental data. We quantify the theoretical uncertainties of chiral effective-field-theory predictions of the muon-deuteron capture rate from the relevant neutron-neutron partial wave channels in the final state. We study the dependence on the cutoff used to regularize the interactions, low-energy constants calibrated using different fitting data and strategies, and truncation of the effective-field-theory expansion of the currents. Combining these approaches gives as an estimate of $Γ^{1/2}_{μd}$ = 399.1 ± 7.6 ± 4.4 s –1 for capture from the atomic doublet state, and $Γ^{3/2}_{μd}$= 12.31 ± 0.47 ± 0.04 s –1 for capture from the quartet state and the first and second uncertainties given here are due to the effective field theory truncation error and the uncertainty in the axial radius, respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Solitons in lattice field theories via tight-binding supersymmetry

Reflectionless potentials play an important role in constructing exact solutions to classical dynamical systems (such as the Korteweg-de Vries equation), non-perturbative solutions of various large-N field theories (such as the Gross-Neveu model), and closely related solitonic solutions to the Bogoliubov-de Gennes equations in the theory of superconductivity. These solutions rely on the inverse scattering method, which reduces these seemingly unrelated problems to identifying reflectionless potentials of an auxiliary one-dimensional quantum scattering problem. There are several ways of constructing these potentials, one of which is quantum mechanical supersymmetry (SUSY). In this paper, motivated by recent experimental platforms, we generalize this framework to develop a theory of lattice solitons. We first briefly review the classical inverse scattering method in the continuum limit, focusing on the Korteweg-de Vries (KdV) equation and SU(N) Gross-Neveu model in the large N limit. We then generalize this methodology to lattice versions of interacting field theories. Our analysis hinges on the use of trace identities, which are relations connecting the potential of an equation of motion to the scattering data. For a discrete Schrödinger operator, such trace identities had been known as far back as Toda; however, we derive a new set of identities for the discrete Dirac operator. We then use these identities in a lattice Gross-Neveu and chiral Gross-Neveu (Nambu-Jona-Lasinio) model to show that lattice solitons correspond to reflectionless potentials associated with the discrete scattering problem. These models are of significance as they are equivalent to a mean-field theory of a lattice superconductor. To explicitly construct these solitons, we generalize supersymmetric quantum mechanics to tight-binding models. We show that a matrix transformation exists that maps a tight-binding model to an isospectral one which shares the same structure and scattering properties. The corresponding soliton solutions have both modulated hopping and onsite potential, the former of which has no analogue in the continuum limit. We explicitly compute both topological and non-topological soliton solutions as well as bound state spectra in the aforementioned models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

DMFTwDFT: An open-source code combining Dynamical Mean Field Theory with various density functional theory packages

We report Dynamical Mean Field Theory (DMFT) is a successful method to compute the electronic structure of strongly correlated materials, especially when it is combined with density functional theory (DFT). Here, we present an open-source computational package (and a library) combining DMFT with various DFT codes interfaced through the Wannier90 package. The correlated subspace is expanded as a linear combination of Wannier functions introduced in the DMFT approach as local orbitals. In particular, we provide a library mode for computing the DMFT density matrix. This library can be linked and then internally called from any DFT package, assuming that a set of localized orbitals can be generated in the correlated subspace. The existence of this library allows developers of other DFT codes to interface with our package and achieve the charge-self-consistency within DFT+DMFT loops. To test and check our implementation, we computed the density of states and the band structure of well-known solid-state correlated materials, namely LaNiO, SrVO, and NiO. The obtained results are compared to those obtained from other DFT+DMFT implementations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Interacting fractons in 2+1-dimensional quantum field theory

We analyze, in perturbation theory, a theory of weakly interacting fractons and non-relativistic fermions in a 2+1 dimensional Quantum Field Theory. In particular we compute the 1-loop corrections to the self energies and interaction vertex, and calculate the associated 1-loop Renormalization Group flows of the coupling constants. Surprisingly, we find that the fracton-fermion coupling does not flow due to an emergent coordinate-dependent symmetry of the effective Lagrangian, making this model a well-defined quantum field theory. We provide additional discussions on the regularization and renormalization of interacting fractonic theories, as well as both qualitative and quantitative remarks regarding the theory at finite temperature and finite chemical potential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Post-Minkowskian effective field theory for conservative binary dynamics

We develop an Effective Field Theory (EFT) formalism to solve for the conservative dynamics of binary systems in gravity via Post-Minkowskian (PM) scattering data. Our framework combines a systematic EFT approach to compute the deflection angle in the PM expansion, together with the ‘Boundary-to-Bound’ (B2B) dictionary introduced. Due to the nature of scattering processes, a remarkable reduction of complexity occurs both in the number of Feynman diagrams and type of integrals, compared to a direct EFT computation of the potential in a PM scheme. We provide two illustrative examples. Firstly, we compute all the conservative gravitational observables for bound orbits to 2PM, which follow from only one topology beyond leading order. The results agree with those, obtained through the ‘impetus formula’ applied to the classical limit of the one loop amplitude. For the sake of comparison we reconstruct the conservative Hamiltonian to 2PM order, which is equivalent to the one derived from a matching calculation. Secondly, we compute the scattering angle due to tidal effects from the electric- and magnetic-type Love numbers at leading PM order. Using the B2B dictionary we then obtain the tidal contribution to the periastron advance. We also construct a Hamiltonian including tidal effects at leading PM order. Although relying on (relativistic) Feynman diagrams, the EFT formalism developed here does not involve taking the classical limit of a quantum amplitude, neither integrals with internal massive fields, nor additional matching calculations, nor spurious (‘super-classical’) infrared singularities. By construction, the EFT approach can be automatized to all PM orders.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

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

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

Physics↗
DOE OSTI2021

Effective field theory approach to rotational bands in odd-mass nuclei

In this work, we extend an effective field theory developed to describe rotational bands in even-even nuclei to the odd-mass case. This organizes Bohr and Mottelson's treatment of a particle coupled to a rotor as a model-independent expansion in powers of the angular velocity of the overall system. We carry out this expansion up to fourth order in the angular velocity and present results for 99 Tc, 159 Dy, 167,169 Er, 167,169 Tm, 183 W, 235 U, and 239 Pu. In each case, the accuracy and breakdown scale of the effective field theory can be understood based on the single-particle and vibrational energy scales in that nucleus.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Topological symmetry in quantum field theory

We introduce a definition and framework for internal topological symmetries in quantum field theory, including “noninvertible symmetries” and “categorical symmetries”. We outline a calculus of topological defects which takes advantage of well-developed theorems and techniques in topological field theory. Our discussion focuses on finite symmetries, and we give indications for a generalization to other symmetries. We treat quotients and quotient defects (often called “gauging” and “condensation defects”), finite electromagnetic duality, and duality defects, among other topics. We include an appendix on finite homotopy theories, which are often used to encode finite symmetries and for which computations can be carried out using methods of algebraic topology. Throughout we emphasize exposition and examples over a detailed technical treatment.

Mathematics↗
DOE OSTI2020

Sterile neutrinos and neutrinoless double beta decay in effective field theory

We investigate neutrinoless double beta decay (0νββ) in the presence of sterile neutrinos with Majorana mass terms. These gauge-singlet fields are allowed to interact with Standard-Model (SM) fields via renormalizable Yukawa couplings as well as higher-dimensional gauge-invariant operators up to dimension seven in the Standard Model Effective Field Theory extended with sterile neutrinos. At the GeV scale, we use Chiral effective field theory involving sterile neutrinos to connect the operators at the level of quarks and gluons to hadronic interactions involving pions and nucleons. This allows us to derive an expression for 0νββ rates for various isotopes in terms of phase-space factors, hadronic low-energy constants, nuclear matrix elements, the neutrino masses, and the Wilson coefficients of higher-dimensional operators. The required hadronic low-energy constants and nuclear matrix elements depend on the neutrino masses, for which we obtain interpolation formulae grounded in QCD and chiral perturbation theory that improve existing formulae that are only valid in a small regime of neutrino masses. The resulting framework can be used directly to assess the impact of 0νββ experiments on scenarios with light sterile neutrinos and should prove useful in global analyses of sterile-neutrino searches. We per- form several phenomenological studies of 0νββ in the presence of sterile neutrinos with and without higher-dimensional operators. We find that non-standard interactions involving sterile neutrinos have a dramatic impact on 0νββ phenomenology, and next-generation experiments can probe such interactions up to scales of $\mathcal O$ (100) TeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Dynamics of fractionalized mean-field theories: Consequences for Kitaev materials

There have been substantial recent efforts, both experimentally and theoretically, to find a material realization of the Kitaev spin liquid—the ground state of the exactly solvable Kitaev model on the honeycomb lattice. Candidate materials are now plentiful, but the presence of non-Kitaev terms makes comparison between theory and experiment challenging. Here, we rederive time-dependent Majorana mean-field theory and extend it to include quantum phase information, allowing the direct computation of the experimentally relevant dynamical spin-spin correlator, which reproduces exact results for the unperturbed model. In contrast to previous work, we find that small perturbations do not substantially alter the exact result, implying that α-RuCl 3 is perhaps farther from the Kitaev phase than originally thought. Our approach generalizes to any correlator and to any model where Majorana mean-field theory is a valid starting point.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Mean string field theory: Landau-Ginzburg theory for 1-form symmetries

By analogy with the Landau-Ginzburg theory of ordinary zero-form symmetries, we introduce and develop a Landau-Ginzburg theory of one-form global symmetries, which we call mean string field theory. The basic dynamical variable is a string field – defined on the space of closed loops – that can be used to describe the creation, annihilation, and condensation of effective strings. Like its zero-form cousin, the mean string field theory provides a useful picture of the phase diagram of broken and unbroken phases. We provide a transparent derivation of the area law for charged line operators in the unbroken phase and describe the dynamics of gapless Goldstone modes in the broken phase. The framework also provides a theory of topological defects of the broken phase and a description of the phase transition that should be valid above an upper critical dimension, which we discuss. We also discuss general consequences of emergent one-form symmetries at zero and finite temperature.

Iqbal, Nabil↗
DOE OSTI2020

Systematically localizable operators for quantum simulations of quantum field theories

Correlations and measures of entanglement in ground-state wave functions of relativistic quantum field theories are spatially localized over length scales set by the mass of the field. We utilize this localization to design digital quantum circuits for preparing the ground states of lattice scalar quantum field theories. Controlled rotations that are exponentially localized in their position-space extent are found to provide exponentially convergent wave function fidelity. These angles scale with the correlation between sites and the classical two-point correlation function, as opposed to the more localized mutual information or the hyperlocalized (1×1)-site negativity. We anticipate that further investigations will uncover quantum circuit designs with controlled rotations dictated by the measures of entanglement. This work is expected to impact quantum simulations of systems of importance to nuclear physics, high-energy physics, and basic energy sciences research.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

An effective field theory for non-maximal quantum chaos

In non-maximally quantum chaotic systems, the exponential behavior of out-of-time-ordered correlators (OTOCs) results from summing over exchanges of an infinite tower of higher “spin” operators. We construct an effective field theory (EFT) to capture these exchanges in (0 + 1) dimensions. The EFT generalizes the one for maximally chaotic systems, and reduces to it in the limit of maximal chaos. The theory predicts the general structure of OTOCs both at leading order in the 1/N expansion (N is the number of degrees of freedom), and after resuming over an infinite number of higher order 1/N corrections. These general results agree with those previously explicitly obtained in specific models. We also show that the general structure of the EFT can be extracted from the large q SYK model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Tabulated equations of state from models informed by chiral effective field theory

Abstract We construct four equation of state (EoS) tables, tabulated over a range of temperatures, densities, and charge fractions, relevant for neutron star applications such as simulations of neutron star mergers. The EoS are computed from a relativistic mean-field theory constrained by the pure neutron matter EoS from chiral effective field theory, inferred properties of isospin-symmetric nuclear matter, and astrophysical observations of neutron star structure. To model nuclear matter at low densities, we attach an EoS that models inhomogeneous nuclear matter at arbitrary temperatures and charge fractions. The four EoS tables we develop are available from the CompOSE EoS repository https://compose.obspm.fr/eos/297 and gitlab.com/ahaber/qmc-rmf-tables .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Quantum field theory of topological spin dynamics

Here, we develop a field theory of quantum magnets and magnetic (semi)metals, which is suitable for the analysis of their universal and topological properties. The systems of interest include collinear, coplanar, and general noncoplanar magnets. At the basic level, we describe the dynamics of magnetic moments using smooth vector fields in the continuum limit. Dzyaloshinskii-Moriya interaction is captured by a non-Abelian vector gauge field, and chiral spin couplings related to topological defects appear as higher-rank antisymmetric tensor gauge fields. We distinguish type-I and type-II magnets by their equilibrium response to the non-Abelian gauge flux, and characterize the resulting lattices of skyrmions and hedgehogs, the spectra of spin waves, and the chiral response to external perturbations. The general spin-orbit coupling of electrons is similarly described by non-Abelian gauge fields, including higher-rank tensors related to the electronic Berry flux. Itinerant electrons and local moments exchange their gauge fluxes through Kondo and Hund interactions. Hence, by utilizing gauge fields, this theory provides a unifying physical picture of “intrinsic” and “topological” anomalous Hall effects, spin-Hall effects, and other correlations between the topological properties of electrons and moments. We predict “topological” magnetoelectric effect in materials prone to hosting hedgehogs. Links to experiments and model calculations are provided by deriving the couplings and gauge fields from generic microscopic models, including the Hubbard model with spin-orbit interactions. Much of the formal analysis is generalized to d spatial dimensions in order to access the $π_{d–1}(S^{d–1})$ homotopy classification of the magnetic hedgehog topological defects, and establish the possibility of novel quantum spin liquids that exhibit a fractional magnetoelectric effect. However, we emphasize the form of all results in the physically relevant $\textit{d}$ = 3 dimensions, and discuss a few applications to topological magnetic conductors like Mn 3 Sn and Pr 2 Ir 2 O 7 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Effective field theory of Stückelberg vector bosons

We explore the effective field theory of a vector field $X^μ$ that has a Stückelberg mass. The absence of a gauge symmetry for $X^μ$ implies Lorentz-invariant operators are constructed directly from Xμ. Beyond the kinetic and mass terms, allowed interactions at the renormalizable level include $X_μX^μH^†H, (X_μX^μ)^2$, and $X_μj^μ$, where $j^μ$ is a global current of the SM or of a hidden sector. We show that all of these interactions lead to scattering amplitudes that grow with powers of $\sqrt{s}/m_X$, except for the case of $X_μj^μ$ where $j^μ$ is a nonanomalous global current. The latter is well-known when $\textit{X}$ is identified as a dark photon coupled to the electromagnetic current, often written equivalently as kinetic mixing between $\textit{X}$ and the photon. The power counting for the energy growth of the scattering amplitudes is facilitated by isolating the longitudinal enhancement. We examine in detail the interaction with an anomalous global vector current $X_μj^μ_{\text{anom}}$, carefully isolating the finite contribution to the fermion triangle diagram. We calculate the longitudinally-enhanced observables $Z → X_γ$ (when $m_X < m_Z), f\bar{f} → X_γ$, and $Z_γ → Z_γ$ when $\textit{X}$ couples to the baryon number current. Introducing a "fake" gauge-invariance by writing $X^μ = A^μ – ∂^μπ/m_X$, the would-be gauge anomaly associated with $A_μj^μ_{\text{anom}}$ is canceled by $j^μ_{\text{anom}}∂_μπ/m_X$; this is the four-dimensional Green-Schwarz anomaly-cancellation mechanism at work. Our analysis demonstrates there is a much larger set of possible interactions that an EFT with a Stückelberg vector field can have, revealing scattering amplitudes that grow with energy. The growth of these amplitudes can be tamed by a dark Higgs sector, but this requires dark Higgs boson interactions (and reintroduces fine-tuning in the dark Higgs sector) that can be separated from X interactions only in the limit $g \ll 1$ .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Topological field theory with Haagerup symmetry

Here, we construct a (1 + 1)d topological field theory (TFT) whose topological defect lines (TDLs) realize the transparent Haagerup $\mathscr{H}$ 3 fusion category. This TFT has six vacua, and each of the three non-invertible simple TDLs hosts three defect operators, giving rise to a total of 15 point-like operators. The TFT data, including the three-point coefficients and lasso diagrams, are determined by solving all the sphere four-point crossing equations and torus one-point modular invariance equations. We further verify that the Cardy states furnish a non-negative integer matrix representation under TDL fusion. While many of the constraints we derive are not limited to this particular TFT with six vacua, we leave open the construction of TFTs with two or four vacua. Finally, TFTs realizing the Haagerup $\mathscr{H}$ 1 and $\mathscr{H}$ 2 fusion categories can be obtained by gauging algebra objects. This article makes a modest offering in our pursuit of exotica and the quest for their eventual conformity.

97 MATHEMATICS AND COMPUTING↗