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DOE OSTI2023

The connection between nonzero density and spontaneous symmetry breaking for interacting scalars

We consider U(1)-symmetric scalar quantum field theories at zero temperature. At nonzero charge densities, the ground state of these systems is usually assumed to be a superfluid phase, in which the global symmetry is spontaneously broken along with Lorentz boosts and time translations. We show that, in d > 2 spacetime dimensions, this expectation is always realized at one loop for arbitrary non-derivative interactions, confirming that the physically distinct phenomena of nonzero charge density and spontaneous symmetry breaking occur simultaneously in these systems. We quantify this result by deriving universal scaling relations for the symmetry breaking scale as a function of the charge density, at low and high density. Moreover, we show that the critical value of μ above which a nonzero density develops coincides with the pole mass in the unbroken, Poincaré invariant vacuum of the theory. The same conclusions hold non-perturbatively for an O(N) theory with quartic interactions in d = 3 and 4, at leading order in the 1/N expansion. We derive these results by computing analytically the zero-temperature, finite-μ one-loop effective potential, paying special attention to subtle points related to the iε terms. We check our results against the one-loop low-energy effective action for the superfluid phonons in λΦ 4 theory in d = 4 previously derived by Joyce and ourselves, which we further generalize to arbitrary potential interactions and arbitrary dimensions. As a byproduct, we find analytically the one-loop scaling dimension of the lightest charge-n operator for the λΦ 6 conformal superfluid in d = 3, at leading order in 1/n, reproducing a numerical result of Badel et al. For a λΦ 4 superfluid in d = 4, we also reproduce the Lee-Huang-Yang relation and compute relativistic corrections to it. Finally, we discuss possible extensions of our results beyond perturbation theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Differential equations for cosmological correlators

Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations satisfied by cosmological correlation functions. In this work, we provide a broader perspective on the origin and structure of these differential equations. As a concrete example, we study conformally coupled scalar fields in a power-law cosmology. The wavefunction coefficients in this model have integral representations, with the integrands being the product of the corresponding flat-space results and “twist factors” that depend on the cosmological evolution. Similar twisted integrals arise for loop amplitudes in dimensional regularization, and their recent study has led to the discovery of rich mathematical structures and powerful new tools for computing multi-loop Feynman integrals in quantum field theory. The integrals of interest in cosmology are also part of a finite-dimensional basis of master integrals, which satisfy a system of first-order differential equations. We develop a formalism to derive these differential equations for arbitrary tree graphs. The results can be represented in graphical form by associating the singularities of the differential equations with a set of graph tubings. Upon differentiation, these tubings grow in a local and predictive fashion. In fact, a few remarkably simple rules allow us to predict — by hand — the equations for all tree graphs. While the rules of this “kinematic flow” are defined purely in terms of data on the boundary of the spacetime, they reflect the physics of bulk time evolution. We also study the analogous structures in tr ϕ 3 theory, and see some glimpses of hidden structure in the sum over planar graphs. This suggests that there is an autonomous combinatorial or geometric construction from which cosmological correlations, and the associated spacetime, emerge.

Cosmological models↗
DOE OSTI2023

Extending the thermodynamic form factor bootstrap program: multiple particle-hole excitations, crossing symmetry, and reparameterization invariance

In this study, we further the thermodynamic bootstrap program which involves a set of recently developed ideas used to determine thermodynamic form factors of local operators in integrable quantum field theories. These form factors are essential building blocks for dynamic correlation functions at finite temperatures or non-equilibrium stationary states. In this work we extend this program in three ways. Firstly, we demonstrate that the conjectured annihilation pole axiom is valid in the low energy particle-hole excitations. Secondly, we introduce a crossing relation, which establishes a connection between form factors with different excitation content. Typically, the crossing relation is a consequence of Lorentz invariance, but due to the finite energy density of the considered states, Lorentz invariance is broken. Nonetheless a crossing relation involving excitations with both particles and holes can established using the finite volume representation of the thermodynamic form factors. Finally, we demonstrate that the thermodynamic form factors satisfy a reparameterization invariance, an invariance which encompasses crossing. Reparameterization invariance exploits the fact that the details of the representation of the thermodynamic state are unimportant. In the course of developing these results, we demonstrate the internal consistency of the thermodynamic form factor bootstrap program in a number of ways. Finally, we provide explicit computations of form factors of conserved charges and densities with crossed excitations and show our results can be used to infer information about thermodynamic form factors in the Lieb-Liniger model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Real-time chiral dynamics at finite temperature from quantum simulation

In this study, we explore the real-time dynamics of the chiral magnetic effect (CME) at a finite temperature in the (1+1)-dimensional QED, the massive Schwinger model. By introducing a chiral chemical potential μ 5 through a quench process, we drive the system out of equilibrium and analyze the induced vector currents and their evolution over time. The Hamiltonian is modified to include the time-dependent chiral chemical potential, thus allowing the investigation of the CME within a quantum computing framework. We employ the quantum imaginary time evolution (QITE) algorithm to study the thermal states, and utilize the Suzuki-Trotter decomposition for the real-time evolution. This study provides insights into the quantum simulation capabilities for modeling the CME and offers a pathway for studying chiral dynamics in low-dimensional quantum field theories.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Landau diagrams in AdS and S-matrices from conformal correlators

Quantum field theories in AdS generate conformal correlation functions on the boundary, and in the limit where AdS is nearly flat one should be able to extract an S-matrix from such correlators. We discuss a particularly simple position-space procedure to do so. It features a direct map from boundary positions to (on-shell) momenta and thereby relates cross ratios to Mandelstam invariants. This recipe succeeds in several examples, includes the momentum-conserving delta functions, and can be shown to imply the two proposals in based on Mellin space and on the OPE data. Interestingly the procedure does not always work: the Landau singularities of a Feynman diagram are shown to be part of larger regions, to be called ‘bad regions’, where the flat-space limit of the Witten diagram diverges. To capture these divergences we introduce the notion of Landau diagrams in AdS. As in flat space, these describe on-shell particles propagating over large distances in a complexified space, with a form of momentum conservation holding at each bulk vertex. As an application we recover the anomalous threshold of the four-point triangle diagram at the boundary of a bad region.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Modification to the Hawking temperature of a dynamical black hole by a flow-induced supertranslation

One interesting proposal to solve the black hole information loss paradox without modifying either general relativity or quantum field theory, is the soft hair, a diffeomorphism charge that records the anisotropic radiation in the asymptotic region. This proposal, however, has been challenged, given that away from the source the soft hair behaves as a coordinate transformation that forms an Abelian group, thus unable to store any information. To maintain the spirit of the soft hair but circumvent these obstacles, we consider Hawking radiation as a probe sensitive to the entire history of the black hole evaporation, where the soft hairs on the horizon are induced by the absorption of a null anisotropic flow, generalizing the shock wave considered in [1, 2]. To do so we introduce two different time-dependent extensions of the diffeomorphism associated with the soft hair, where one is the backreaction of the anisotropic null flow, and the other is a coordinate transformation that produces the Unruh effect and a Doppler shift to the Hawking spectrum. Together, they form an exact BMS charge generator on the entire manifold that allows the nonperturbative analysis of the black hole horizon, whose surface gravity, i.e. the Hawking temperature, is found to be modified. The modification depends on an exponential average of the anisotropy of the null flow with a decay rate of 4M, suggesting the emergence of a new 2-D degree of freedom on the horizon, which could be a way out of the information loss paradox.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Sharpening the Distance Conjecture in diverse dimensions

The Distance Conjecture holds that any infinite-distance limit in the scalar field moduli space of a consistent theory of quantum gravity must be accompanied by a tower of light particles whose masses scale exponentially with proper field distance ||$\phi$|| as m ~ exp(–λ||$\phi$||), where λ is order-one in Planck units. While the evidence for this conjecture is formidable, there is at present no consensus on which values of λ are allowed. In this paper, we propose a sharp lower bound for the lightest tower in a given infinite-distance limit in d dimensions: λ ≥ $1/\sqrt{d-2}$. In support of this proposal, we show that (1) it is exactly preserved under dimensional reduction, (2) it is saturated in many examples of string/M-theory compactifications, including maximal supergravity in d = 4 – 10 dimensions, and (3) it is saturated in many examples of minimal supergravity in d = 4 – 10 dimensions, assuming appropriate versions of the Weak Gravity Conjecture. We argue that towers with λ < $1/\sqrt{d-2}$ discussed previously in the literature are always accompanied by even lighter towers with λ ≥ $1/\sqrt{d-2}$, thereby satisfying our proposed bound. We discuss connections with and implications for the Emergent String Conjecture, the Scalar Weak Gravity Conjecture, the Repulsive Force Conjecture, large-field inflation, and scalar field potentials in quantum gravity. In particular, we argue that if our proposed bound applies beyond massless moduli spaces to scalar fields with potentials, then accelerated cosmological expansion cannot occur in asymptotic regimes of scalar field space in quantum gravity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Real-time spin systems from lattice field theory

We construct a lattice field theory method for computing the real-time dynamics of spin systems in a thermal bath. This is done by building on previous work of Takano with Schwinger-Keldysh and functional differentiation techniques. We derive a Schwinger-Keldysh path integral for generic spin Hamiltonians, then demonstrate the method on a simple system. Our path integral has a sign problem, which generally requires exponential run time in the system size, but requires only linear storage. The latter may place this method at an advantage over exact diagonalization, which is exponential in both. Our path integral is amenable to contour deformations, a technique for reducing sign problems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Variational approach to relative entropies with an application to QFT

Abstract We define a new divergence of von Neumann algebras using a variational expression similar in nature to Kosaki’s formula for Umegaki’s relative entropy. Our divergence satisfies several of the usual desirable properties, upper bounds the sandwiched Renyi entropy and reduces to the fidelity in a limit. As an illustration, we use the formula in quantum field theory to compute our divergence between the vacuum in a bipartite system and an “orbifolded”—in the sense of a conditional expectation—system in terms of the Jones index. We take the opportunity to point out an entropic certainty relation associated with an inclusion of von Neumann factors related to the relative entropy. This certainty relation has an equivalent formulation in terms of error correcting codes.

Hollands, Stefan↗
DOE OSTI2022

First principles thermal transport modeling in GaN and related materials

Gallium nitride is a wide bandgap material utilized in a variety of technologies, including high-power electronics and light-emitting diodes, partly due to its favorable thermal properties. This chapter describes modern first-principles-based modeling of phonons and lattice thermal conductivity (k) of GaN, III-nitrides and related materials. In particular, we describe the theoretical underpinnings of calculating phonon dispersions, intrinsic phonon interactions, and other lattice dynamical properties from quantum perturbation theory and density functional theory (DFT) methods. Description of how these methods are then coupled with the Peierls-Boltzmann transport (PBT) equation to determine phonon distributions and lifetimes relevant for thermal transport is given. These theoretical and numerical methods have demonstrated quantitative accuracy and predictive power for calculating pristine k and defect-limited k from first principles for a variety of materials. We present a review of the literature utilizing DFT-PBT methods to understand novel k behaviors in III-nitrides and related materials.

Lindsay, Lucas↗
DOE OSTI2021

Caravel: A C++ framework for the computation of multi-loop amplitudes with numerical unitarity

We present the first public version of Caravel, a C++17 framework for the computation of multi-loop scattering amplitudes in quantum field theory, based on the numerical unitarity method. Caravel is composed of modules for the D-dimensional decomposition of integrands of scattering amplitudes into master and surface terms, the computation of tree-level amplitudes in floating point or finite-field arithmetic, the numerical computation of one- and two-loop amplitudes in QCD and Einstein gravity, and functional reconstruction tools. Here, we provide programs that showcase Caravel's main functionalities and allow to compute selected one- and two-loop amplitudes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

tapir: A tool for topologies, amplitudes, partial fraction decomposition and input for reductions

The demand for precision predictions in the field of high energy physics has dramatically increased over recent years. Experiments conducted at the LHC, as well as precision measurements at the intensity frontier such as Belle II require equally precise theoretical predictions to make full use of the acquired data. To match the experimental precision, second-, third- and, for certain quantities, even higher-order calculations in perturbative quantum field theory are required. To facilitate such calculations, computer software automating as many steps as possible is required. Yet, each calculation poses different challenges and thus, a high level of configurability is required. In this context we present tapir: a tool for identification, manipulation and minimization of Feynman integral families. It is designed to integrate in toolchains based on the computer algebra system FORM, the use of which is common practice in the field. tapir can be used to reduce the complexity of multi-loop problems with cut-filters, topology mapping, partial fraction decomposition and alike. Program Title:tapir CPC Library link to program files:https://doi.org/10.17632/ptc9t46xyn.1 Developer's repository link:https://gitlab.com/tapir-devs/tapir Licensing provisions: GPLv3 Programming language:python 3, C++ Nature of problem: Multi-loop computations require the automatization of a large number of different tasks related to Feynman integral topologies. Among them are the identification and minimization of integral topologies, partial fraction decomposition of topologies in the case of linearly dependent propagators as well as mapping scalar products of loop momenta to scalar functions. Solution method: The minimization of topologies is performed by comparison of their respective Nickel indices [1], even further minimization utilizes Pak's algorithm [2]. To efficiently map scalar products of loop momenta to scalar functions FORM [3] code is generated. Additional comments including restrictions and unusual features: Minimization based on Pak's algorithm slows down for many lines and scales. A coarser minimization using the Nickel indices, however, is still possible. [1]B. Nickel, D. Meiron, G.A.J. Baker, Compilation of 2-pt and 4-pt graphs for continuous spin model, Report, University of Guelph, 1977.[2]A. Pak, J. Phys. Conf. Ser. 368 (2012) 012049, https://doi.org/10.1088/1742-6596/368/1/012049, arXiv:1111.0868.[3]B. Ruijl, T. Ueda, J. Vermaseren, FORM version 4.2, arXiv:1707.06453, 7 2017.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

2p x-ray absorption spectroscopy of 3d transition metal systems

This review provides an overview of the different methods and computer codes that are used to interpret 2p x-ray absorption spectra of 3d transition metal ions. We first introduce the basic parameters and give an overview of the methods used. We start with the semi-empirical multiplet codes and compare the different codes that are available. A special chapter is devoted to the user friendly interfaces that have been written on the basis of these codes. Next we discuss the first principle codes based on band structure, including a chapter on Density Functional theory based approaches. We also give an overview of the first-principle multiplet codes that start from a cluster calculation and we discuss the wavefunction based methods, including multi-reference methods. We end the review with a discussion of the link between theory and experiment and discuss the open issues in the spectral analysis.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Anomalous neutron nuclear-magnetic interference spectroscopy

The electron–phonon interaction plays a critical role in materials’ electrical, thermal, optical, and superconducting properties. However, measuring the phonon mode-resolved electron–phonon interaction has been challenging. Here we propose neutron-scattering-based Anomalous Neutron nUclear-Magnetic Interference Spectroscopy (ANUBIS), where the co-existence of neutron nuclear scattering and magnetic scattering leads to anomalous dynamical structure factor under the presence of the electron–phonon interaction. Such anomalous structure factor is linear in electron–phonon coupling constant at the phonon wavevector, and is directly proportional to the momentum and energy-resolved dielectric function. The experimental configuration can be achieved using existing polarized inelastic neutron scattering setup, and an order-of-magnitude estimate shows the viability to observe the anomalous scattering signal is around to 10 –4 to 10 –3 relative to phonon scattering, which is examined through the preliminary experiments and achievable at emerging neutron facilities. As a result, our proposal offers an alternative neutron-based metrology to probe the crucial electronic properties.

Electron-phonon interactions↗
DOE OSTI2022

Universal corner symmetry and the orbit method for gravity

A universal symmetry algebra organizing the gravitational phase space has been recently found. It corresponds to the subset of diffeomorphisms that become physical at corners – codimension-2 surfaces supporting Noether charges. It applies to both finite distance and asymptotic corners. In this paper, we study this algebra and its representations, via the coadjoint orbit method. We show that generic orbits of the universal algebra split into sub-orbits spanned by finite distance and asymptotic corner symmetries, such that the full universal symmetry algebra gives rise to a unified treatment of corners in a manifold. We then identify the geometric structure that captures these algebraic properties on corners, which is the Atiyah Lie algebroid associated to a principal GL(2,R) $\ltimes$ R 2 -bundle. This structure is suggestive of the existence of a novel quantum gravitational theory which would unitarily glue such geometric structures, with spacetime geometries appearing as semi-classical configurations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Physical resurgent extrapolation

Expansions of physical functions are controlled by their singularities, which have special structure because they themselves are physical, corresponding to instantons, caustics or saddle configurations. Resurgent asymptotics formalizes this idea mathematically, and leads to significantly more powerful extrapolation methods to extract physical information from a finite number of terms of an expansion, including precise decoding of non-perturbative effects. We quantify the gain of precision for various extrapolation procedures, showing that significant improvements can be achieved using exactly the same input data, and we illustrate the general method with examples from quantum mechanics and quantum field theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

The Fermi function and the neutron's lifetime

The traditional Fermi function ansatz for nuclear beta decay describes enhanced perturbative effects in the limit of large nuclear charge Z and/or small electron velocity β. We define and compute the quantum field theory object that replaces this ansatz for neutron beta decay, where neither of these limits hold. We present a new factorization formula that applies in the limit of small electron mass, analyze the components of this formula through two loop order, and resum perturbative corrections that are enhanced by large logarithms. We apply our results to the neutron lifetime, supplying the first two-loop input to the long-distance corrections. Our result can be summarized as τ n x |V ud | 2 [1 + 3λ 2 ] [1 + Δ R ] = $\frac{5263.284(17) s}{1 + 27.04(7) x 10^{-3}}$ with |V ud | the up-down quark mixing parameter, τ n the neutron's lifetime, λ the ratio of axial to vector charge, and Δ R the short-distance matching correction. We find a shift in the long-distance radiative corrections compared to previous work, and discuss implications for extractions of |V ud | and tests of the Standard Model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗