Diagrammatic Technique Research Articles

Mapping the SMEFT to discoverable models

The matching of specific new physics scenarios onto the SMEFT framework is a well-understood procedure. The inverse problem, the matching of the SMEFT to UV scenarios, is more difficult and requires the development of new methods to perform a systematic exploration of models. In this paper we use a diagrammatic technique to construct in an automated way a complete set of possible UV models (given certain, well specified assumptions) that can produce specific groups of SMEFT operators, and illustrate its use by generating models with no tree-level contributions to four-fermion (4F) operators. Those scenarios, which only contribute to 4F at one-loop order, can contain relatively light particles that could be discovered at the LHC in direct searches. For this class of models, we find an interesting interplay between indirect SMEFT and direct searches. We discuss some examples on how this interplay would look like when combining low-energy observables with the SMEFT Higgs-fermion analyses and searches for resonance at the LHC.

Two loop ghost free quantisation of Wilson loops in [formula omitted] supersymmetric Yang-Mills

We report a perturbative calculation of the expectation value of the infinite straight line Maldacena-Wilson loop in N=4 supersymmetric Yang-Mills theory to order g6. Thus, we extend the previous perturbative result by one order. The vacuum expectation value is reformulated in terms of a non-linear and non-local transformation, the Nicolai map, mapping the full functional measure of the interacting theory to that of a free bosonic theory. The results are twofold. The perturbative cancellations of the different contributions to the Maldacena-Wilson loop are by no means trivial and seem to resemble those of the circular Maldacena-Wilson loop at order g4. Furthermore, we argue that our approach to computing quantum correlation functions is competitive with more standard diagrammatic techniques.

Relativistic quantum field theory of stochastic dynamics in the Hilbert space

We develop an action formulation of stochastic dynamics in the Hilbert space. By generalizing the Wiener process into 1+3-dimensional spacetime, we define a Lorentz-invariant random field. By coupling the random to quantum fields, we obtain a random-number action which has the statistical spacetime translation and Lorentz symmetries. The canonical quantization of the theory results in a Lorentz-invariant equation of motion for the state vector or density matrix. We derive the path integral formula of $S$-matrix and the diagrammatic rules for both the stochastic free field theory and stochastic $\phi^4$-theory. The Lorentz invariance of the random $S$-matrix is strictly proved. We then develop a diagrammatic technique for calculating the density matrix. Without interaction, we obtain the exact $S$-matrix and density matrix. With interaction, we prove a simple relation between the density matrices of stochastic and conventional $\phi^4$-theory. Our formalism leads to an ultraviolet divergence which has the similar origin as that in QFT. The divergence is canceled by renormalizing the coupling strength to random field. We prove that the stochastic QFT is renormalizable even in the presence of interaction. In the models with a linear coupling between random and quantum fields, the random field excites particles out of the vacuum, driving the universe towards an infinite-temperature state. The number of excited particles follows the Poisson distribution. The collision between particles is not affected by the random field. But the signals of colliding particles are gradually covered by the background excitations caused by random field.

Extending internalization theory: Integrating international business strategy with international management

AbstractResearch summaryInternational business strategy and international management are two distinct but related fields of study. This article explores the connections between them. It shows how internalization theory can act as a bridge between them. The key is to analyze not only core activities, such as production, marketing and R&D, but support services such as human resource management, information technology, and corporate finance. Internalization decisions and location decisions must be analyzed holistically, and diagrammatic techniques show how this can be done. These diagrams reveal the networks of communication and the hierarchical structures that emerge from such decisions.Managerial summaryThe organizational structure of a multinational enterprise is inherently complex, making it difficult to determine whether one organizational structure is more efficient than another. Delayering, decentralization, and agility are recommended, but what are their practical implications? Internalization theory addresses these problems in a simple and coherent way. It shows that it is not only core activities, namely production, marketing and R&D, that need to be coordinated, but support services too. Decisions on the location and out‐sourcing of support services must be aligned with similar decisions on core activities. A diagrammatic analysis is presented that facilitates the solution of these problems.

Loop corrections to cosmological particle creation

We consider dynamics of the massive minimally coupled scalar field theory in an expanding Friedmann-Lema\^{\i}tre-Robertson-Walker universe. We consider the standard toy model of the conformally flat space-time where the conformal factor becomes constant at the distant past and the distant future. Employing the Schwinger-Keldysh diagrammatic technique, we compute infrared loop corrections to the occupation number and anomalous quantum average of the scalar field and show that these corrections are growing with time. Using these observations, we demonstrate that the regularized stress-energy tensor at the distant future acquires substantial quantum corrections which exceed the long known tree-level contributions to the particle flux.

Effect of disorder on density of states and conductivity in higher-order Van Hove singularities in two-dimensional bands

We study systems with energy bands in two dimensions, hosting higher order Van Hove singularities (HOVHS) in the presence of disorder, using standard diagrammatic techniques for impurity averaging. In the clean limit, such singularities cause power-law divergence in the density of states (DOS), and this is expected to strongly affect electronic correlation. In order to analyse the signatures of these singularities in disordered systems, we employ various Born approximations, culminating in the self-consistent (non) Born approximation. Although the divergence of the DOS is smeared, we find that the shape of the DOS, as characterized by the power law tail and the universal ratio of prefactors, is retained slightly away from the singularity. This could help us to understand current and future experiments on materials that can be tuned to host HOVHS. The impurity induced smearing is calculated and analysed for several test cases of singularities. We also study the effects of impurities on electrical conductivity and determine the regimes where the quantitative features of the power law DOS manifest in the conductivity.

Q -Laguerre spectral density and quantum chaos in the Wishart-Sachdev-Ye-Kitaev model

We study the Wishart-Sachdev-Ye-Kitaev (WSYK) model consisting of two $\hat{q}$-body Sachdev-Ye-Kitaev (SYK) models with general complex couplings, one the Hermitian conjugate of the other, living in off-diagonal blocks of a larger WSYK Hamiltonian. The spectrum is positive with a hard edge at zero energy. We employ diagrammatic and combinatorial techniques to compute analytically the low-order moments of the Hamiltonian. In the limit of large number $N$ of Majoranas, we have found striking similarities with the moments of the weight function of the Al-Salam-Chihara $Q$-Laguerre polynomials. For $\hat{q} = 3, 4$, the $Q$-Laguerre prediction, with $Q=Q(\hat{q},N)$ also computed analytically, agrees well with exact diagonalization results for $30 < N \leq 34$ while we observe some deviations for $\hat q = 2$. The most salient feature of the spectral density is that, for odd $\hat{q}$, low-energy excitations grow as a stretched exponential, with a functional form different from that of the supersymmetric SYK model. For $\hat q = 4$, a detailed analysis of level statistics reveals quantum chaotic dynamics even for time scales substantially shorter than the Heisenberg time. More specifically, the spacing ratios in the bulk of the spectrum and the microscopic spectral density and the number variance close to the hard edge are very well approximated by that of an ensemble of random matrices that, depending on $N$, belong to the chiral or superconducting universality classes. In particular, we report the first realization of level statistics belonging to the chGUE universality class, which completes the tenfold-way classification in the SYK model.

Page curve for entanglement negativity through geometric evaporation

We compute the entanglement negativity for various pure and mixed state configurations in a bath coupled to an evaporating two dimensional non-extremal Jackiw-Teitelboim (JT) black hole obtained through the partial dimensional reduction of a three dimensional BTZ black hole. Our results exactly reproduce the analogues of the Page curve for the entanglement negativity which were recently determined through diagrammatic technique developed in the context of random matrix theory.

Threshold resummation of new partonic channels at next-to-leading power

Collider observables involving heavy particles are subject to large logarithmic terms near threshold, which must be summed to all orders in perturbation theory to obtain sensible results. Relatively recently, this resummation has been extended to next-to-leading power in the threshold variable, using a variety of approaches. In this paper, we consider partonic channels that turn on only at next-to-leading power, and show that it is possible to resum leading logarithms using well-established diagrammatic techniques in Quantum Chromodynamics. We first consider deep inelastic scattering, where we reproduce the results of a recent study using an effective theory approach. Next, we consider the quark-gluon channel in both Drell-Yan and Higgs boson production, showing that an explicit all-order form for the leading logarithmic partonic cross section can be obtained. Our results agree with previous conjectures based on fixed-order results.

A Qualitative Validation of Two Diagrammatic Measures of Attachment Network Structure

Abstract. In two qualitative evaluation studies, we explored the construct validity of two diagrammatic measures of attachment network structure, including the Bull’s Eye diagrammatic technique and a significantly modified version, the Web-based Hierarchical Mapping Technique (WHMT). In the first study, 20 young adults completed a Bull’s Eye diagram followed by a semi-structured interview in which participants explained their placement of support figures in their diagrams. Interview transcripts were analyzed using theory-driven thematic analysis to determine the presence of attachment-related themes, including safe haven, secure base effect, and proximity maintenance. Findings indicated mixed support for the Bull’s Eye as a measure of attachment networks. Although attachment themes were dominant among participants who identified a parent as their primary attachment figure, this was not the case among participants who identified a peer as a primary attachment figure. Participant justifications for peer attachments relied on non-attachment themes, including identity exploration and companionship. In the second study, we applied the same qualitative method to investigate the WHMT. Saturation was reached sooner, and attachment themes were dominant for both parent and peered primary attachment. Findings support the construct validity of the WHMT as a new measure of attachment network composition and strength.

Interplay of dark states and superconducting correlations in charge transport through quantum dot trimers

Electronic transport through a hybrid triple quantum dot system is theoretically studied by means of the real-time diagrammatic technique in the lowest order of perturbation theory. The central part of the system is arranged in a triangular geometry, with two quantum dots weakly coupled to metallic electrodes, while the third dot is proximitized by an s-wave superconductor. The focus is put on the transport regimes, where one- and two-electron dark states are formed due to the destructive interference of the electronic wavefunctions. This effect greatly influences the properties of the system, leading to the coherent population trapping and consequently to current blockade, negative differential conductance and enhanced shot-noise. It is shown that the presence of the superconducting pairing correlations in the system can lift the dark state blockade and reduce the shot-noise. Moreover, the current oscillations due to the magnetic flux enclosed by the triangular structure and the effect of superconducting correlations are considered. When the dark state has eigenenergy near the chemical potential of superconducting electrode, the amplitude of oscillations is strongly reduced while the current blockade is lifted. However, when the eigenenergy of the dark state is shifted away from the chemical potential of superconducting lead, the current oscillations remain unaffected.

Time-resolved photoemission spectroscopy on correlated electrons: Insights from dynamical mean-field theory

Time- and angular-resolved photoemission spectroscopy (trARPES) can directly probe the electronic structure of quantum materials out of equilibrium. This can shed light on the interaction of the electrons with spin, lattice, and orbital degrees of freedom, and help to unravel pathways towards novel out-of-equilibrium phases. Dynamical mean-field theory (DMFT) and its extensions provide a versatile toolbox to interpret such experiments through a theoretical simulation of the underlying microscopic processes. The approach can be applied both to Mott insulators and correlated metals, and it is formulated in terms of non-equilibrium Green's functions, which directly relate to the photoemission spectrum. This article reviews the theoretical description of trARPES within DMFT and related diagrammatic non-equilibrium Green's function techniques. Several applications are discussed, including the photo-induced melting of excitonic order, femtosecond relaxation processes in Mott insulators, and the manipulation of the electronic structure of Mott and charge transfer insulators using photo-doping and strong THz fields.

Diagrammatics of tunable interactions in anisotropic colloids in rotating electric or magnetic fields: New kind of dipole-like interactions.

Anisotropic particles are widely presented in nature, from colloidal to bacterial systems, and control over their interactions is of crucial importance for many applications, from self-assembly of novel materials to microfluidics. Placed in rapidly rotating external electric fields, colloidal particles attain a tunable long-range and many-body part in their interactions. For spherical colloids, this approach has been shown to offer rich capabilities to construct the tunable interactions via designing the internal structure of particles and spatial hodographs of external rotating fields, but in the case of anisotropic particles, the interactions remain poorly understood. Here, we show that tunable interactions between anisotropic rod-like and spheroidal colloidal particles in rotating electric or magnetic fields can be calculated and analyzed with the diagrammatic technique we developed in the present work. With this technique, we considered an in-plane rotating electric field, obtained the long-range asymptotics of the anisotropic interactions, calculated the tunable interactions between particles rotating synchronously, and found conditions for rotator repulsion. We compared the mechanisms providing tunable interactions to those for orientational (Keesom), induction (Debye), and dispersion (London) interactions in molecular systems and found that the tunable interactions between anisotropic particles represent a novel kind of dipole-like interaction. The method can be directly generalized for magnetically induced interactions, 3D systems, and fields with spatial hodographs. The results provide significant advance in theoretical methods for tunable interactions in colloids and, therefore, are of broad interest in condensed matter, chemical physics, physical chemistry, materials science, and soft matter.

Phonon transport in disordered alloys: A Multiple-scattering approach

I present a formalism to calculate the configuration-averaged lattice thermal conductivity for substitutional random alloys. The method is based on multiple-scattering approach which can capture the effect of disorder-induced configuration fluctuations on single-particle and two-particle phonon Green functions in random alloys. The randomness of the system is dealt within the augmented space theorem. This is combined with a generalized Feynman diagrammatic technique to extract various useful results in the form of mathematical expressions. I show the structure of all possible scattering diagrams up to the fourth order and subsequently illustrate how to obtain Dyson's equation from a resummation of the diagrammatic series. I also study how disorder scattering affects two-particle Green functions associated with thermal response. It was shown explicitly how the disorder scattering renormalizes both the phonon propagators as well as the heat currents. I derive the relation between these renormalized heat currents and the self-energy of the propagators. I have also studied a different class of scattering diagrams which are not related to the self-energy but rather to the vertex corrections. The configuration-averaging scheme is straightforward to apply to other relevant quantities such as joint density of states, thermal diffusivity, etc., for random alloys. The developed formalism is applied to a realistic ${\mathrm{Au}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}$ binary alloy. The effect of disorder-induced corrections (as compared to the simple virtual crystal approximation) turns out to be appreciable in this alloy. The configuration-averaged lattice thermal conductivity for ${\mathrm{Au}}_{50}{\mathrm{Fe}}_{50}$ shows a quadratic behavior in low-temperature regime ($T\ensuremath{\le}30$ K), which increases smoothly to a $T$-independent saturated value at high $T$. Simulated thermal diffusivity $D(\ensuremath{\nu})$ helps to numerically estimate the mobility $\mathrm{edge}\phantom{\rule{0.28em}{0ex}}({\ensuremath{\nu}}_{c})$ which in turn evaluates the fraction of localized states. $D(\ensuremath{\nu})$ is found to decrease smoothly (almost linearly) in the high-$\ensuremath{\nu}$ range, which when fitted to ${({\ensuremath{\nu}}_{c}\ensuremath{-}\ensuremath{\nu})}^{\ensuremath{\alpha}}$ gives the critical $\mathrm{exponent}\phantom{\rule{0.28em}{0ex}}(\ensuremath{\alpha})$ to be 1.018 for ${\mathrm{Au}}_{50}{\mathrm{Fe}}_{50}$ alloy. This agrees fairly well with the scaling and other theories of Andersen localization.

Quantum phase transition of many interacting spins coupled to a bosonic bath: Static and dynamical properties

By using worldline and diagrammatic quantum Monte Carlo techniques, matrix product state, and a variational approach \`a la Feynman, we investigate the equilibrium properties and relaxation features of a quantum system of $N$ spins antiferromagnetically interacting with each other, with strength $J$, and coupled to a common bath of bosonic oscillators, with strength $\ensuremath{\alpha}$. We show that, in the Ohmic regime, a Beretzinski-Thouless-Kosterlitz quantum phase transition occurs. While for $J=0$ the critical value of $\ensuremath{\alpha}$ decreases asymptotically with $1/N$ by increasing $N$, for nonvanishing $J$ it turns out to be practically independent on $N$, allowing to identify a finite range of values of $\ensuremath{\alpha}$ where spin phase coherence is preserved also for large $N$. Then, by using matrix product state simulations, and the Mori formalism and the variational approach \`a la Feynman jointly, we unveil the features of the relaxation, that, in particular, exhibits a nonmonotonic dependence on the temperature reminiscent of the Kondo effect. For the observed quantum phase transition we also establish a criterion analogous to that of the metal-insulator transition in solids.

Diagrammatic approach to scattering of multiphoton states in waveguide QED

We give an exposure to diagrammatic techniques in waveguide QED systems. A particular emphasis is placed on the systems with delayed coherent quantum feedback. Specifically, we show that the $N$-photon scattering matrices in single-qubit waveguide QED systems, within the rotating wave approximation, admit for a parametrization in terms of $N-1$-photon effective vertex functions and provide a detailed derivation of a closed hierarchy of generalized Bethe-Salpeter equations satisfied by these vertex functions. The advantage of this method is that the above mentioned integral equations hold independently of the number of radiation channels, their bandwidth, the dispersion of the modes they are supporting, and the structure of the radiation-qubit coupling interaction, thus enabling one to study multi-photon scattering problems beyond the Born-Markov approximation. Further, we generalize the diagrammatic techniques to the systems containing more than a single emitter by presenting an exact set of equations governing the generic two and three-photon scattering operators. The above described theoretical machinery is then showcased on the example of a three-photon scattering on a giant acoustic atom, recently studied experimentally [Nat. Phys. 15, 1123 (2019)].

Quantum theory of the nonlinear Hall effect

The nonlinear Hall effect is an unconventional response, in which a voltage can be driven by two perpendicular currents in the Hall-bar measurement. Unprecedented in the family of the Hall effects, it can survive time-reversal symmetry but is sensitive to the breaking of discrete and crystal symmetries. It is a quantum transport phenomenon that has deep connection with the Berry curvature. However, a full quantum description is still absent. Here we construct a quantum theory of the nonlinear Hall effect by using the diagrammatic technique. Quite different from nonlinear optics, nearly all the diagrams account for the disorder effects, which play decisive role in the electronic transport. After including the disorder contributions in terms of the Feynman diagrams, the total nonlinear Hall conductivity is enhanced but its sign remains unchanged for the 2D tilted Dirac model, compared to the one with only the Berry curvature contribution. We discuss the symmetry of the nonlinear conductivity tensor and predict a pure disorder-induced nonlinear Hall effect for point groups C3, C3h, C3v, D3h, D3 in 2D, and T, Td, C3h, D3h in 3D. This work will be helpful for explorations of the topological physics beyond the linear regime.

Evolution of Non-Gaussian Hydrodynamic Fluctuations.

In the context of the search for the QCD critical point using non-Gaussian fluctuations, we obtain the evolution equations for non-Gaussian cumulants to the leading order of the systematic expansion in the magnitude of thermal fluctuations. We develop a diagrammatic technique in which the leading order contributions are given by tree diagrams. We introduce a Wigner transform for multipoint correlators and derive the evolution equations for three- and four-point Wigner functions for the problem of nonlinear stochastic diffusion with multiplicative noise.

Particle creation in nonstationary large N quantum mechanics

We consider an analog of particle production in a quartic $O(N)$ quantum oscillator with time-dependent frequency, which is a toy model of particle production in the dynamical Casimir effect and de Sitter space. We calculate exact quantum averages, Keldysh propagator, and particle number using two different methods. First, we employ a kind of rotating wave approximation to estimate these quantities for small deviations from stationarity. Second, we extend these results to arbitrarily large deviations using the Schwinger-Keldysh diagrammatic technique. We show that in strongly nonstationary situations, including resonant oscillations, loop corrections to the tree-level expressions effectively result in an additional degree of freedom, $N \to N + \frac{3}{2}$, which modifies the average number and energy of created particles.

Multi-particle production in proton\u2013nucleus collisions in the color glass condensate

We compute multi-gluon production in the Color Glass Condensate approach in dilute-dense collisions, hbox {p}A, extending previous calculations up to four gluons. We include the contributions that are leading in the overlap area of the collision but keep all orders in the expansion in the number of colors. We develop a diagrammatic technique to write the numerous color contractions and exploit the symmetries to group the diagrams and simplify the expressions. To proceed further, we use the McLerran–Venugopalan and Golec–Biernat–Wüsthoff models for the projectile and target averages, respectively. We use a form of the Lipatov vertices that leads to the Wigner function approach for the projectile previously employed, that we generalise to take into account quantum correlations in the projectile wave function. We provide analytic expressions for integrated and differential two gluon cumulants and show a smooth dependence on the parameters defining the projectile and target Wigner function and dipole, respectively. For four gluon correlations we find that the second order four particle cumulant is negative, so a sensible second Fourier azimuthal coefficient can be defined. The effect of correlations in the projectile on this result results qualitatively and quantitatively large.