Impact of Vertex Functionalization on Flexibility of Porous Organic Cages
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37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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Fermi-liquid theory and divergences of the two-particle irreducible vertex in the periodic Anderson lattice
Here we analyze the divergences of the irreducible vertex function in dynamical mean field theory, which may indicate either a nonphysical breakdown of the perturbation theory or a response to some physical phenomenon. To investigate this question, we construct a quasiparticle vertex from the diverging irreducible vertex functions. This vertex describes the scattering between quasiparticles and quasiholes in a Fermi liquid. We show that the quasparticle vertex does not diverge in the charge channel, wherein the irreducible vertex does diverge; and we show that the quasiparticle vertex does diverge in the spin channel, wherein the irreducible vertex does not diverge. This divergence occurs at the Mott transition, wherein the Fermi-liquid theory breaks down. Both the half filled Hubbard and Anderson lattices are investigated. In general, our results support that the divergences of the irreducible vertex function do not indicate a nonphysical failure of the perturbation theory. Instead, the divergences are the mathematical consequence of inverting a matrix (the local charge susceptibility) which accumulates increasingly negative diagonal elements as the Hubbard interaction suppresses charge fluctuations. Indeed, we find that the first divergences of the irreducible vertex in both Hubbard and Anderson lattices occurs near the maximum magnitude of the (negative) vertex-connected part of the charge susceptibility.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Operator gauge transformations and gauge transformations of the third kind.
Gauge transformations of third kind and operator gauge transformations of first and second kinds, relating electron and photon propagators to quantum electrodynamical vertex function
QUANTUM ELECTRODYNAMICS↗
Using the Dimensionality Reduction (DR) Approach to Treat Singular and Near-Singular Source and Test Integrals on Triangles for Moment Methods
Recently, the authors presented preliminary results of an initial study of a dimensional reduction scheme for treating (near-)singular integrals (D. R. Wilton et al., “Dimensionality Reduction Approach for Treating Singular and Near-Singular Multidimensional Integrals of Electromagnetics,” 2022 URSI USNC National Radio Science Meeting, Boulder, CO, Jan. 2022). The approach reported there refined and extended several ideas appearing in a recent paper (R. R. Chang, Z. Wang, and Q. Xie, "Fast Convergent Quadrature Method for Evaluating the RWG- and SWG-Related Convolutional Integrals," IEEE Trans. Antennas Propagat., 69, Dec. 2021). That paper reported a curated collection of important, previously published results all leading to very efficient and accurate line integral methods for handling the most common (near-)singular integrals associated with triangles and tetrahedrons with RWG and SWG bases, respectively. Our contributions provided a simpler exposition as well as a more unified, systematic, and robust overall framework for deriving and applying the approach. This presentation further elucidates our extensions to the approach and broadens our initial study to examine the convergence behaviors of the various potential forms over a wider range of triangular source element shape and observation point parameters for various smoothing transformations; we also examine convergence, not just at the subtriangle level, but also overcomplete triangles. In addition, we investigate the application of the recently reported “vertex function” concept to develop faster converging test integrals (Rivero et al., “Acceleration of the Surface Test Integral Using Vertex Functions,” 2021 IEEE Int’l Symp. Ant. Propagat. and USNC-URSI Rad. Sci. Meeting,” Singapore, 4-10 Dec. 2021). Combining these separate schemes has the potential for yielding a near-optimal approach for accurately evaluating singular and near-singular integrals for moment methods.
Singular Integrals↗
Dynamical model of J/ψ photoproduction on the nucleon
Here, a dynamical model based on a phenomenological charm quark-nucleon (c – N) potential v cN and the Pomeronexchange mechanism is constructed to investigate the J/ψ photoproduction on the nucleon from threshold to invariant mass W = 300 GeV. The J/ψ – N potential, V J/ψN (r), is constructed by folding v cN into the wave function φ J/ψ ($c\bar{c}$) of J/ψ within a constituent quark model (CQM) of Segovia et al. [Int. J. Mod. Phys. E 22, 1330026 (2013)]. A photoproduction amplitude is also generated by v cN by a $c\bar{c}$–loop integration over the γ → $c\bar{c}$ vertex function and φ J/ψ ($c\bar{c}$). No commonly used vector meson dominance assumption is used to define this photoproduction amplitude which is needed to describe the data near the threshold. The c – N potential v cN (r) is parameterized in a form such that the predicted V J/ψN (r) at large distances has the same Yukawa potential form extracted from a lattice QCD (LQCD) calculation of Kawanai and Sasaki, [Phys. Rev. D 82, 091501(R) (2010)]. The parameters of vcN are determined by fitting the total cross-section data of Jefferson Laboratory (JLab) by performing calculations that include J/ψ – N final-state interactions (FSI). The resulting differential cross sections dσ /dt are found in good agreements with the data. It is shown that the FSI effects dominate the cross section in the very near-threshold region, allowing for sensitive testing of the predicted J/ψ – N scattering amplitudes. By imposing the constraints of J/ψ – N potential extracted from the LQCD calculation of Kawanai and Sasaki, [Phys. Rev. D 82, 091501(R) (2010)], we have obtained three J/ψ – N potentials which fit the JLab data equally well. The resulting J/ψ – N scattering lengths are in the range of a = [-0.05, -0.25] fm. With the determined v cN (r) and the wave functions generated from the same CQM, the constructed model is used to predict the cross sections of photoproduction of η c (1S) and ψ(2S) mesons for future experimental tests.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Effective description of sub-maximal chaos: stringy effects for SYK scrambling
It has been proposed that the exponential decay and subsequent power law saturation of out-of-time-order correlation functions can be universally described by collective ‘scramblon’ modes. We develop this idea from a path integral perspective in several examples, thereby establishing a general formalism. After reformulating previous work on the Schwarzian theory and identity conformal blocks in two-dimensional CFTs relevant for systems in the infinite coupling limit with maximal quantum Lyapunov exponent, we focus on theories with sub-maximal chaos: we study the large-q limit of the SYK quantum dot and chain, both of which are amenable to analytical treatment at finite coupling. In both cases we identify the relevant scramblon modes, derive their effective action, and find bilocal vertex functions, thus constructing an effective description of chaos. The final results can be matched in detail to stringy corrections to the gravitational eikonal S-matrix in holographic CFTs, including a stringy Regge trajectory, bulk to boundary propagators, and multi-string effects that are unexplored holographically.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Single-top-quark production in the t-channel at NNLO
We present a calculation of t-channel single-top-quark production and decay in the five-flavor scheme at NNLO. Our results resolve a disagreement between two previous calculations of this process that found a difference in the inclusive cross section at the level of the NNLO coefficient itself. We compare in detail with the previous calculations at the inclusive, differential and fiducial level including b-quark tagging at a fixed scale μ = m t . In addition, we advocate the use of double deep inelastic scattering (DDIS) scales ( μ 2 = Q 2 for the light-quark line and μ 2 = Q 2 + m t 2 for the heavy-quark line) that maximize perturbative stability and allow for robust scale uncertainties. All NNLO and NLOⓍNLO contributions for production and decay are included in the on-shell and vertex-function approximation. We present fiducial and differential results for a variety of observables used in Standard Model and Beyond Standard Model analyses, and find an important difference between the NLO and NNLO predictions of exclusive t + n-jet cross sections. Overall we find that NNLO corrections are crucial for a precise identification of the t-channel process.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Dynamical vertex approximation for many-electron systems with spontaneously broken SU(2) symmetry
We generalize the formalism of the dynamical vertex approximation (DΓA)—a diagrammatic extension of the dynamical mean-field theory (DMFT)—to treat magnetically ordered phases. To this aim, we start by concisely illustrating the many-electron formalism for performing ladder resummations of Feynman diagrams in systems with broken SU(2) symmetry associated to ferromagnetic (FM) or antiferromagnetic (AF) order. We then analyze the algorithmic simplifications introduced by taking the local approximation of the two-particle irreducible vertex functions in the Bethe-Salpeter equations, which defines the ladder implementation of DΓA for magnetic systems. The relation of this assumption with the DMFT limit of large coordination-number/high dimensions is explicitly discussed. As a last step, we derive the expression for the ladder DΓA self-energy in the FM- and AF-ordered phases of the Hubbard model. The physics emerging in the AF-ordered case is explicitly illustrated by means of approximated calculations based on a static mean-field input for DΓA equations. The results obtained capture fundamental aspects of both metallic and insulating ground states of two-dimensional antiferromagnets, providing a reliable compass for future, more extensive applications of our approach. Furthermore, possible routes to further develop diagrammatic-based treatments of magnetic phases in correlated electron systems are briefly outlined in the Conclusions.
2-dimensional systems↗
Spectral density sum rules, current algebra, and zero-mass extrapolations.
Partially conserved axial vector currents and current algebra to obtain vertex functions at point having zero mass by extrapolations
Dooher, J.↗
Evaluation of Near Singular Integrals for Computational Electromagnetics by Dimensionality Reduction
With the need for ever faster codes, a limiting factor that must be dealt with is the accurate yet efficient evaluation of interaction integrals between the more problematic near-field elements. Several recent works have together shown that all evaluations of source potential integrals and their derivatives for the most common bases and elements can be reduced to the evaluation of boundary line integrals; these can be evaluated by Gauss-Legendre quadrature, though integrand-smoothing transforms are often needed to accelerate their computation. In this paper, we modify the reported approach to eliminate cancellation errors in the line integral integrand, reinterpret the integral as a vertex function, and study the scalar potential integral form under the sinh transform and static subtraction acceleration methods.
D R Wilton↗
Electronic Structure Correspondence of Singlet-Triplet Scale Separation in Strained Sr2RuO4
At a temperature of roughly 1 K, Sr 2 RuO 4 undergoes a transition from a normal Fermi liquid to a superconducting phase. Even while the former is relatively simple and well understood, the superconducting state has not even been understood after 25 years of study. More recently, it has been found that critical temperatures can be enhanced by the application of uniaxial strain, up to a critical strain, after which it falls off. In this work, we take an “instability” approach and seek divergences in susceptibilities. This provides an unbiased way to distinguish tendencies to competing ground states. We show that in the unstrained compound, the singlet and triplet instabilities of the normal Fermi liquid phase are closely spaced. Under uniaxial strain, electrons residing on all orbitals contributing to the Fermiology become more coherent, while the electrons of the Ru-dxy character become heavier, and the electrons of the Ru d x z , y z characters become lighter. In the process, Im χ(q,ω) increases rapidly around q = ( 0.3 , 0.3 , 0 ) 2 π / a and q = ( 0.5 , 0.25 , 0 ) 2 π / a , while it gets suppressed at all other commensurate vectors, in particular at q = 0, which is essential for spin-triplet superconductivity. We observe that the magnetic anisotropy under strain drops smoothly, which is concomitant with the increment in singlet instability. Thus, the triplet superconducting instability remains the lagging instability of the system, and the singlet instability enhances under strain, leading to a large energy-scale separation between these competing instabilities. However, since this happens even without spin-orbit coupling, we believe it is primarily the enhancement in the spin fluctuation glue around quasi-anti-ferromagnetic vectors that drives the Cooper pairing instead of the magnetic anisotropy. At large strain, an instability to a spin density wave overtakes the superconducting one. The analysis relies on a high-fidelity, ab initio description of the one-particle properties and two-particle susceptibilities, based on the quasiparticle self-consistent GW approximation augmented by dynamical mean field theory. This approach is described and its high fidelity confirmed by comparing to observed one- and two-particle properties.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Electronic Origin of T c in Bulk and Monolayer FeSe
FeSe is classed as a Hund’s metal, with a multiplicity of d bands near the Fermi level. Correlations in Hund’s metals mostly originate from the exchange parameter J, which can drive a strong orbital selectivity in the correlations. The Fe-chalcogens are the most strongly correlated of the Fe-based superconductors, with d xy the most correlated orbital. Yet little is understood whether and how such correlations directly affect the superconducting instability in Hund’s systems. By applying a recently developed ab initio theory, we show explicitly the connections between correlations in d xy and the superconducting critical temperature T c . Starting from the ab initio results as a reference, we consider various kinds of excursions in parameter space around the reference to determine what controls T c . We show small excursions in J can cause colossal changes in T c . Additionally we consider changes in hopping by varying the Fe-Se bond length in bulk, in the free standing monolayer M-FeSe, and M-FeSe on a SrTiO 3 substrate (M-FeSe/STO). The twin conditions of proximity of the dxy state to the Fermi energy, and the strength of J emerge as the primary criteria for incoherent spectral response and enhanced single- and two-particle scattering that in turn controls T c . Using c-RPA, we show further that FeSe in monolayer form (M-FeSe) provides a natural mechanism to enhance J. We explain why M-FeSe/STO has a high T c , whereas M-FeSe in isolation should not. Our study opens a paradigm for a unified understanding what controls Tc in bulk, layers, and interfaces of Hund’s metals by hole pocket and electron screening cloud engineering.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
QED corrections to the thermal neutrino interaction rate
Abstract Motivated by precision computations of neutrino decoupling at MeV temperatures, we show how QED corrections to the thermal neutrino interaction rate can be related to the electron-positron spectral function as well as an effective$$\overline{\nu }\nu \gamma $$vertex. The spectral function is needed both in a timelike and in a spacelike domain, and for both of its physical polarization states (transverse and longitudinal with respect to spatial momentum). Incorporating an NLO evaluation of this spectral function, an estimate of the$$\overline{\nu }\nu \gamma $$vertex, and HTL resummation of scatterings mediated by soft Bose-enhancedt-channel photons, we compute the interaction rate as a function of the neutrino momentum and flavour. Effects on the – (0. . .2)% level are found, noticeably smaller than a previous estimate of a related quantity.
Physics↗
Many-body theory of phonon-induced spin relaxation and decoherence
First-principles calculations enable accurate predictions of electronic interactions and dynamics. However, computing the electron spin dynamics remains challenging. The spin-orbit interaction causes various dynamical phenomena that couple with phonons, such as spin precession and spin-flip e-ph scattering, which are difficult to describe with current first-principles calculations. Here, in this work, we show a rigorous framework to study phonon-induced spin relaxation and decoherence, by computing the spin-spin correlation function and its vertex corrections due to e-ph interactions. We apply this approach to a model system and develop corresponding first-principles calculations of spin relaxation in GaAs. Our vertex-correction formalism is shown to capture the Elliott-Yafet, Dyakonov-Perel, and strong-precession mechanisms—three independent spin decoherence regimes with distinct physical origins—thereby unifying their theoretical treatment and calculation. Our method is general and enables quantitative studies of spin relaxation, decoherence, and transport in a wide range of materials and devices.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Decomposition Algorithms for Scalable Quantum Annealing
The presented python code provides wrapper functions for two decomposition algorithms: One algorithm to decompose Maximum Clique problems and one to decompose Minimum Vertex Cover problems. The functions take as input a networkx graph object, and decompose either problem on the input graph recursively into subproblems such that the optimal solution can be constructed from the optimal solutions of both subproblems. The recursion ends as soon as the subproblems reach a pre-specified size limit by the user, and they can be solved using any method provided in advance by the user as external function. This includes exact solvers or an adiabatic quantum annealer.
Pelofske, Elijah↗
Boundary Layer Effect on the Surface Pressure of an Infinite Cone in Supersonic Flow
The theory of Taylor and Maccoll (Ref,1) gives the surface pressure on an infinite cone in supersonic flow as a function of the cone vertex angle and the free stream Mach number and static pressure for a gas of vanishing viscosity. When a slender conical probe is used together with an impact pressure probe to determine the static pressure and Mach number in a low density gas stream, it is desirable to have some theoretical estimate of the effect of viscous boundary layer on the probe readings. Theoretical and experimental results with respect to impact probes have been presented in Refs. 5 and 6. A simple approximation for a conical probe based on linearized supersonic flow and compressible boundary layer theory is presented here.
Lin, T. C.↗
Experimental realization of classical Z 2 spin liquids in a programmable quantum device
We build and probe a Z 2 spin liquid in a programmable quantum device, the D-Wave DW-2000Q. Specifically, we observe the classical eight-vertex and six-vertex (spin ice) states and transitions between them. To realize this state of matter, we design a Hamiltonian with combinatorial gauge symmetry using only pairwise-qubit interactions and a transverse field, i.e., interactions which are accessible in this quantum device. The combinatorial gauge symmetry remains exact along the full quantum annealing path, landing the system onto the classical eight-vertex model at the endpoint of the path. The output configurations from the device allow us to directly observe the loop structure of the classical model. Moreover, we deform the Hamiltonian so as to vary the weights of the eight vertices and show that we can selectively attain the classical six-vertex (ice) model, or drive the system into a ferromagnetic state. Additionally, we present studies of the classical phase diagram of the system as a function of the eight-vertex deformations and effective temperature, which we control by varying the relative strengths of the programmable couplings, and we show that the experimental results are consistent with theoretical analysis. Finally, we identify additional capabilities that, if added to these devices, would allow us to realize Z 2 quantum spin liquids on which to build topological qubits.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Trigonometric continuous-variable gates and hybrid quantum simulations of the sine-Gordon model
Hybrid qubit-qumode quantum computing platforms provide a natural setting for simulating interacting bosonic quantum field theories. However, existing continuous-variable gate constructions rely predominantly on polynomial functions of canonical quadratures. In this work, we introduce a complementary universality paradigm based on trigonometric continuous-variable gates, which enable a Fourier-like representation of bosonic operators and are particularly well suited for periodic and non-perturbative interactions. We present an ancilla-based framework for implementing trigonometric gates with arguments given by arbitrary Hermitian functions of qumode quadratures. The protocol yields unitary gates deterministically, and non-unitary gates through probabilistic post-selection. As a concrete application, we develop a hybrid qubit-qumode quantum simulation of the lattice sine-Gordon model. Using these gates, we prepare ground states via quantum imaginary-time evolution, simulate real-time dynamics, compute time-dependent vertex two-point correlation functions, and extract quantum kink profiles under topological boundary conditions. Our results demonstrate that trigonometric continuous-variable gates provide a physically natural framework for simulating interacting field theories on near-term hybrid quantum hardware, while establishing a parallel route to universality beyond polynomial gate constructions. We expect that the trigonometric gates introduced here to find broader applications, including quantum simulations of condensed matter systems, quantum chemistry, and biological models.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗