Publications

2022

• Equation-of-motion and Lorentz-invariance relations for tensor-polarized parton distribution functions of spin-1 hadrons
  
  • Kumano S.
  • Song Qin-Tao
  Physics Letters B, Elsevier, 2022, 826, pp.136908. Structure functions of polarized spin-1 hadrons will be measured at various accelerator facilities in the near future. Recently, transverse-momentum-dependent and collinear parton distribution functions were theoretically proposed at twist 3 and twist 4 in addition to the twist-2 ones, so that full investigations became possible for structure functions of spin-1 hadrons in the same level with those of the spin-1/2 nucleons. Furthermore, twist-3 tensor-polarized multiparton distribution functions were also recently found for spin-1 hadrons. In this work, we show relations among the collinear parton- and multiparton-distribution functions for spin-1 hadrons by using equation of motion for quarks. These relations are valuable in constraining the distribution functions and learning about multiparton correlations in spin-1 hadrons. (10.1016/j.physletb.2022.136908)
  DOI : 10.1016/j.physletb.2022.136908
• Equipartition of entanglement in quantum Hall states
  
  • Oblak Blagoje
  • Regnault Nicolas
  • Estienne Benoit
  Physical Review B, American Physical Society, 2022, 105 (11), pp.115131. We study the full counting statistics (FCS) and symmetry-resolved entanglement entropies of integer and fractional quantum Hall states. For the filled lowest Landau level of spin-polarized electrons on an infinite cylinder, we compute exactly the charged moments associated with a cut orthogonal to the cylinder's axis. This yields the behavior of FCS and entropies in the limit of large perimeters: in a suitable range of fluctuations, FCS is Gaussian and entanglement spreads evenly among different charge sectors. Subleading charge-dependent corrections to equipartition are also derived. We then extend the analysis to Laughlin wave functions, where entanglement spectroscopy is carried out assuming the Li-Haldane conjecture. The results confirm equipartition up to small charge-dependent terms, and are then matched with numerical computations based on exact matrix product states. (10.1103/PhysRevB.105.115131)
  DOI : 10.1103/PhysRevB.105.115131
• Topological superconductivity on the honeycomb lattice: Effect of normal state topology
  
  • Wolf Sebastian
  • Gardener Tyler
  • Le Hur Karyn
  • Rachel Stephan
  Physical Review B, American Physical Society, 2022, 105 (10), pp.L100505. The search for topological superconductors is one of the most pressing and challenging questions in condensed-matter and material research. Despite some early suggestions that doping a topological insulator might be a successful recipe to find topological superconductors, to date there is no general understanding of the relationship of the topology of the superconductor and the topology of its underlying normal state system. One of the major obstacles is the strong effect of the Fermi surface and its subsequent pairing tendencies within the Hubbard model framework, which usually prevents a detailed comparison between different topological superconducting systems. Here we present an analysis of doped insulators—topological and trivial—where the dominant Fermi surface effects have been equalized. Our approach allows us to study and compare superconducting instabilities of different normal state systems and present rigorous results about the influence of the normal state system's topology. (10.1103/PhysRevB.105.L100505)
  DOI : 10.1103/PhysRevB.105.L100505
• HiRISE - High-Resolution Imaging and Spectroscopy Explorer - Ultrahigh resolution, interferometric and external occulting coronagraphic science
  
  • Erdélyi Robertus
  • Damé Luc
  • Fludra Andrzej
  • Mathioudakis Mihalis
  • Amari T.
  • Belucz B.
  • Berrilli F.
  • Bogachev S.
  • Bolsée D.
  • Bothmer V.
  • Brun S.
  • Dewitte S.
  • Dudok de Wit Thierry
  • Faurobert M.
  • Gizon L.
  • Gyenge N.
  • Korsós M.
  • Labrosse N.
  • Matthews S.
  • Meftah Mustapha
  • Morgan H.
  • Pallé P.
  • Rochus P.
  • Rozanov E.
  • Schmieder B.
  • Tsinganos K.
  • Verwichte E.
  • Zharkov S.
  • Zuccarello F.
  • Wimmer-Schweingruber R.
  Experimental Astronomy, Springer Link, 2022, 54, pp.227-256. Recent solar physics missions have shown the definite role of waves and magnetic fields deep in the inner corona, at the chromosphere-corona interface, where dramatic and physically dominant changes occur. HiRISE (High Resolution Imaging and Spectroscopy Explorer), the ambitious new generation ultra-high resolution, interferometric, and coronagraphic, solar physics mission, proposed in response to the ESA Voyage 2050 Call, would address these issues and provide the best-ever and most complete solar observatory, capable of ultra-high spatial, spectral, and temporal resolution observations of the solar atmosphere, from the photosphere to the corona, and of new insights of the solar interior from the core to the photosphere. HiRISE, at the L1 Lagrangian point, would provide meter class FUV imaging and spectroimaging, EUV and XUV imaging and spectroscopy, magnetic fields measurements, and ambitious and comprehensive coronagraphy by a remote external occulter (two satellites formation flying 375 m apart, with a coronagraph on a chaser satellite). This major and state-of-the-art payload would allow us to characterize temperatures, densities, and velocities in the solar upper chromosphere, transition zone, and inner corona with, in particular, 2D very high resolution multi-spectral imaging-spectroscopy, and, direct coronal magnetic field measurement, thus providing a unique set of tools to understand the structure and onset of coronal heating. HiRISE's objectives are natural complements to the Parker Solar Probe and Solar Orbiter-type missions. We present the science case for HiRISE which will address: i) the fine structure of the chromosphere-corona interface by 2D spectroscopy in FUV at very high resolution; ii) coronal heating roots in the inner corona by ambitious externally-occulted coronagraphy; iii) resolved and global helioseismology thanks to continuity and stability of observing at the L1 Lagrange point; and iv) solar variability and space climate with, in addition, a global comprehensive view of UV variability. (10.1007/s10686-022-09831-2)
  DOI : 10.1007/s10686-022-09831-2
• Unraveling correlated material properties with noisy quantum computers: Natural orbitalized variational quantum eigensolving of extended impurity models within a slave-boson approach
  
  • Besserve Pauline
  • Ayral Thomas
  Physical Review B, American Physical Society, 2022, 105 (11), pp.115108. We propose a method for computing space-resolved correlation properties of the two-dimensional Hubbard model within a quantum-classical embedding strategy that uses a noisy, intermediate scale quantum (NISQ) computer to solve the embedded model. While previous approaches were limited to purely local, one-impurity embedded models, requiring at most four qubits and relatively shallow circuits, we solve a two-impurity model requiring eight qubits with an advanced hybrid scheme on top of the variational quantum eigensolver algorithm. This iterative scheme, dubbed natural orbitalization (NOization), gradually transforms the single-particle basis to the approximate natural-orbital basis, in which the ground state can be minimally expressed, at the cost of measuring the one-particle reduced density matrix of the embedded problem. We show that this transformation tends to make the variational optimization of existing (but too deep) Ansatz circuits faster and more accurate, and we propose an Ansatz, the multireference excitation-preserving (MREP) Ansatz, that achieves great expressivity without requiring a prohibitive gate count, thus bridging the gap between hardware-efficient and physically motivated strategies in variational Ansatz design. The one-impurity version of the Ansatz has only one parameter, making the ground-state preparation a trivial step, which supports the optimal character of our approach. Within a rotationally invariant slave boson embedding scheme that requires a minimal number of bath sites and does not require computing the full Green's function, the NOization combined with the MREP Ansatz allow us to compute accurate, space-resolved quasiparticle weights and static self-energies for the Hubbard model even in the presence of noise levels representative of current NISQ processors. This paves the way to a controlled solution of the Hubbard model with larger and larger embedded problems solved by quantum computers. (10.1103/PhysRevB.105.115108)
  DOI : 10.1103/PhysRevB.105.115108
• Melonic Large $N$ Limit of $5$-Index Irreducible Random Tensors
  
  • Carrozza Sylvain
  • Harribey Sabine
  Communications in Mathematical Physics, Springer Verlag, 2022, 390 (3), pp.1219-1270. We demonstrate that random tensors transforming under rank-5 irreducible representations of $\mathrm {O}(N)$ can support melonic large N expansions. Our construction is based on models with sextic (5-simplex) interaction, which generalize previously studied rank-3 models with quartic (tetrahedral) interaction (Benedetti et al. in Commun Math Phys 371:55, 2019. arXiv:1712.00249; Carrozza in JHEP 06:039, 2018. arXiv:1803.02496). Beyond the irreducible character of the representations, our proof relies on recursive bounds derived from a detailed combinatorial analysis of the Feynman graphs. Our results provide further evidence that the melonic limit is a universal feature of irreducible tensor models in arbitrary rank. (10.1007/s00220-021-04299-1)
  DOI : 10.1007/s00220-021-04299-1
• Sextic tensor model in rank 3 at next-to-leading order
  
  • Harribey Sabine
  Journal of High Energy Physics, Springer, 2022, 10, pp.037. We compute the four-loop beta functions of short and long-range multi-scalar models with general sextic interactions and complex fields. We then specialize the beta functions to a U(N)$^{3}$ symmetry and study the renormalization group at next-to-leading order in N and small ϵ. In the short-range case, ϵ is the deviation from the critical dimension while it is the deviation from the critical scaling of the free propagator in the long-range case. This allows us to find the 1/N corrections to the rank-3 sextic tensor model of [1]. In the short-range case, we still find a non-trivial real IR stable fixed point, with a diagonalizable stability matrix. All couplings, except for the so-called wheel coupling, have terms of order ϵ$^{0}$ at leading and next-to-leading order, which makes this fixed point different from the other melonic fixed points found in quartic models. In the long-range case, the corrections to the fixed point are instead not perturbative in ϵ and hence unreliable; we thus find no precursor of the large-N fixed point. (10.1007/JHEP10(2022)037)
  DOI : 10.1007/JHEP10(2022)037
• Bootstrapping line defects with $O(2)$ global symmetry
  
  • Gimenez-Grau Aleix
  • Lauria Edoardo
  • Liendo Pedro
  • van Vliet Philine
  Journal of High Energy Physics, Springer, 2022, 11, pp.018. We use the numerical bootstrap to study conformal line defects with $O(2)$ global symmetry. Our results are very general and capture in particular conformal line defects originating from bulk CFTs with a continuous global symmetry, which can either be preserved or partially broken by the presence of the defect. We begin with an agnostic approach and perform a systematic bootstrap study of correlation functions between two canonical operators on the defect: the displacement and the tilt. We then focus on two interesting theories: a monodromy line defect and a localized magnetic field line defect. To this end, we combine the numerical bootstrap with the $\varepsilon$-expansion, where we complement existing results in the literature with additional calculations. For the monodromy defect our numerical results are consistent with expectations, with known analytic solutions sitting inside our numerical bounds. For the localized magnetic field line defect our plots show a series of intriguing cusps which we explore. (10.1007/JHEP11(2022)018)
  DOI : 10.1007/JHEP11(2022)018
• Celestial holography on Kerr-Schild backgrounds
  
  • Gonzo Riccardo
  • Mcloughlin Tristan
  • Puhm Andrea
  Journal of High Energy Physics, Springer, 2022, 10, pp.073. We explore the celestial holography proposal for non-trivial asymptotically flat backgrounds including the Coulomb field of a static and spinning point charge, their gravitational counterparts described by the Schwarzschild and Kerr metrics, as well as the Aichelburg-Sexl shockwave and spinning shockwave geometries and their electromagnetic cousins. We compute celestial two-point amplitudes on these Kerr-Schild type backgrounds which have the desirable feature, due to the presence of an external source, that they are non-vanishing for general operator positions and are not constrained by the kinematic delta functions of flat space celestial CFT correlators. Of particular interest is the case of shockwave backgrounds where the two-point scattering amplitude of massless scalars can be interpreted as a standard CFT three-point correlator between two massless asymptotic states and a conformal primary shockwave operator. We furthermore show that the boundary on-shell action for general backgrounds becomes the generating functional for tree-level correlation functions in celestial CFT. Finally, we derive (conformal) Faddeev-Kulish dressings for particle-like backgrounds which remove all infrared divergent terms in the two-point functions to all orders in perturbation theory. (10.1007/JHEP10(2022)073)
  DOI : 10.1007/JHEP10(2022)073
• A novel background field approach to the confinement-deconfinement transition
  
  • van Egmond Duifje Maria
  • Reinosa Urko
  • Serreau Julien
  • Tissier Matthieu
  SciPost Physics, SciPost Foundation, 2022, 12 (3), pp.087. We propose a novel approach to the confinement-deconfinement transition in Yang-Mills theories in the context of gauge-fixed calculations. The method is based on a background-field generalisation of the Landau gauge (to which it reduces at vanishing temperature) with a given, center-symmetric background. This is to be contrasted with most implementations of background field methods in gauge theories, where one uses a variable, self-consistent background. Our proposal is a bona fide gauge fixing that can easily be implemented on the lattice and in continuum approaches. The resulting gauge-fixed action explicitly exhibits the center symmetry of the nonzero temperature theory that controls the confinement-deconfinement transition. We show that, in that gauge, the electric susceptibility diverges at a second order transition [e.g., in the SU(2) theory], so that the gluon propagator is a clear probe of the transition. We implement our proposal in the perturbative Curci-Ferrari model, known for its successful description of various infrared aspects of Yang-Mills theories, including the confinement-deconfinement transition. Our one-loop calculation confirms our general expectation for the susceptibility while providing transition temperatures in excellent agreement with the SU(2) and SU(3) lattice values. Finally, the Polyakov loops above the transition show a more moderate rise, in contrast to previous implementations of the Curci-Ferrari model using a self-consistent background, and our SU(3) result agrees quite well with lattice results in the range $[0,2T_c]$. (10.21468/SciPostPhys.12.3.087)
  DOI : 10.21468/SciPostPhys.12.3.087
• Planckian metal at a doping-induced quantum critical point
  
  • Dumitrescu Philipp T.
  • Wentzell Nils
  • Georges Antoine
  • Parcollet Olivier
  Physical Review B, American Physical Society, 2022, 105 (18), pp.L180404. We numerically study a model of interacting spin-<math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math> electrons with random exchange coupling on a fully connected lattice. This model hosts a quantum critical point separating two distinct metallic phases as a function of doping: a Fermi-liquid phase with a large Fermi-surface volume and a low-doping phase with local moments ordering into a spin glass. We show that this quantum critical point has non-Fermi-liquid properties characterized by <math><mi>T</mi></math>-linear Planckian behavior, <math><mrow><mi>ω</mi><mo>/</mo><mi>T</mi></mrow></math> scaling, and slow spin dynamics of the Sachdev-Ye-Kitaev type. The <math><mrow><mi>ω</mi><mo>/</mo><mi>T</mi></mrow></math> scaling function associated with the electronic self-energy is found to have an intrinsic particle-hole asymmetry, a hallmark of a “skewed” non-Fermi liquid. (10.1103/PhysRevB.105.L180404)
  DOI : 10.1103/PhysRevB.105.L180404
• Precession Caused by Gravitational Waves
  
  • Seraj Ali
  • Oblak Blagoje
  Physical Review Letters, American Physical Society, 2022, 129 (6), pp.061101. We show that gravitational waves cause freely falling gyroscopes to precess relative to fixed distant stars, extending the stationary Lense-Thirring effect. The precession rate decays as the square of the inverse distance to the source and is proportional to a suitable Noether current for dual asymptotic symmetries at null infinity. Integrating the rate over time yields a net rotation—a “gyroscopic memory”—whose angle reproduces the known spin memory effect but also contains an extra contribution due to the generator of gravitational electric-magnetic duality. The angle’s order of magnitude for the first Laser Interferometer Gravitational Wave Observatory signal is estimated to be <math display="inline"><mrow><mi mathvariant="normal">Φ</mi><mo>∼</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>-</mo><mn>35</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>arc</mi><mtext> </mtext><mi>sec</mi></mrow></math> near Earth, but the effect may be substantially larger for supermassive black hole mergers. (10.1103/PhysRevLett.129.061101)
  DOI : 10.1103/PhysRevLett.129.061101
• Femtosecond laser-induced sub-wavelength plasma inside dielectrics. II. Second-harmonic generation
  
  • Ardaneh Kazem
  • Hassan Mostafa
  • Morel Benoît
  • Meyer Rémi
  • Giust Remo
  • Couairon Arnaud
  • Bonnaud Guy
  • Courvoisier François
  Physics of Plasmas, American Institute of Physics, 2022, 29 (7), pp.072716. Second-harmonic emission at a frequency that is twice the laser frequency is an important diagnostic for nonlinear laser–plasma interaction. It is forbidden for centrosymmetric materials such as the bulk of sapphire. The symmetry, however, can be broken by dielectric discontinuities as a result of plasma generation inside a solid dielectric. In the present work, we explore the basic characteristics of experimentally observed second-harmonic emission during focusing a femtosecond Bessel beam inside sapphire. We employ three-dimensional particle-in-cell simulations and the Helmholtz wave equation for theoretical investigations. We analyze how the efficiency of second-harmonic generation and its polarization depend on the plasma parameters. We find that the second-harmonic is generated either due to the coalescence of two-surface electromagnetic waves or nonlinear interaction between the transverse electromagnetic wave and the longitudinal electron plasma wave driven by linear mode conversion. Experimental results agree with the theoretical predictions and confirm the existence of over-critical plasma inside the sapphire that is essential for the resonance of plasma waves or excitation of surface plasmons. (10.1063/5.0090270)
  DOI : 10.1063/5.0090270
• Anomalous mobility edges in one-dimensional quasiperiodic models
  
  • Liu Tong
  • Xia Xu
  • Longhi Stefano
  • Sanchez-Palencia Laurent
  SciPost Physics, SciPost Foundation, 2022, 12 (1), pp.027. Mobility edges, separating localized from extended states, are known to arise in the single-particle energy spectrum of disordered systems in dimension strictly higher than two and certain quasiperiodic models in one dimension. Here we unveil a different class of mobility edges, dubbed anomalous mobility edges, that separate energy intervals where all states are localized from energy intervals where all states are critical in diagonal and off-diagonal quasiperiodic models. We first introduce an exactly solvable quasi-periodic diagonal model and analytically demonstrate the existence of anomalous mobility edges. Moreover, numerical multifractal analysis of the corresponding wave functions confirms the emergence of a finite energy interval where all states are critical. We then extend the sudy to a quasiperiodic off-diagonal Su-Schrieffer-Heeger model and show numerical evidence of anomalous mobility edges. We finally discuss possible experimental realizations of quasi-periodic models hosting anomalous mobility edges. These results shed new light on the localization and critical properties of low-dimensional systems with aperiodic order. (10.21468/SciPostPhys.12.1.027)
  DOI : 10.21468/SciPostPhys.12.1.027
• Relativistic fluids, hydrodynamic frames and their Galilean versus Carrollian avatars
  
  • Petkou Anastasios C.
  • Petropoulos P. Marios
  • Betancour David Rivera
  • Siampos Konstantinos
  Journal of High Energy Physics, Springer, 2022, 09, pp.162. We comprehensively study Galilean and Carrollian hydrodynamics on arbitrary backgrounds, in the presence of a matter/charge conserved current. For this purpose, we follow two distinct and complementary paths. The first is based on local invariance, be it Galilean or Carrollian diffeomorphism invariance, possibly accompanied by Weyl invariance. The second consists in analyzing the relativistic fluid equations at large or small speed of light, after choosing an adapted gauge, Arnowitt-Deser-Misner-Zermelo for the former and Papapetrou-Randers for the latter. Unsurprisingly, the results agree, but the second approach is superior as it effortlessly captures more elaborate situations with multiple degrees of freedom. It furthermore allows to investigate the fate of hydrodynamic-frame invariance in the two limits at hand, and conclude that its breaking (in the Galilean) or its preservation (in the Carrollian) are fragile consequences of the behaviour of transport attributes at large or small c. Both methods do also agree on the doom of Nœtherian currents generated in the relativistic theory by isometries: conserved currents are not always guaranteed in Newton-Cartan or Carroll spacetimes as a consequence of Galilean or Carrollian isometries. Comparison of Galilean and Carrollian fluid equations exhibits a striking but often superficial resemblance, which we comment in relation to black-hole horizon dynamics, awkwardly akin to Navier-Stokes equations. This congruity is authentic in one instance though and turns out then to describe Aristotelian dynamics, which is the last item in our agenda. (10.1007/JHEP09(2022)162)
  DOI : 10.1007/JHEP09(2022)162
• Pion and nucleon relativistic charge four-current distributions
  
  • Chen Yi
  • Lorcé Cédric
  Physical Review D, American Physical Society, 2022, 106 (11), pp.116024. The quantum phase-space approach allows one to define relativistic spatial distributions inside a target with arbitrary spin and arbitrary average momentum. We apply this quasiprobabilistic formalism to the whole charge four-current operator in the case of spin-$0$ and spin-$\frac{1}{2}$ targets, study in detail the frame dependence of the corresponding spatial distributions, and compare our results with those from the light-front formalism. While former works focused on the charge distributions, we extend here the investigations to the current distributions. We clarify the role played by the Wigner rotation and argue that electromagnetic properties are most naturally understood in terms of Sachs form factors, contrary to what the light-front formalism previously suggested. Finally, we illustrate our results using the pion and nucleon electromagnetic form factors extracted from experimental data. (10.1103/PhysRevD.106.116024)
  DOI : 10.1103/PhysRevD.106.116024
• Fermionic wave functions from neural-network constrained hidden states
  
  • Moreno Javier Robledo
  • Carleo Giuseppe
  • Georges Antoine
  • Stokes James
  Proc.Nat.Acad.Sci., 2022, 119 (32), pp.1-21. We introduce a systematically improvable family of variational wave functions for the simulation of strongly correlated fermionic systems. This family consists of Slater determinants in an augmented Hilbert space involving “hidden” additional fermionic degrees of freedom. These determinants are projected onto the physical Hilbert space through a constraint that is optimized, together with the single-particle orbitals, using a neural network parameterization. This construction draws inspiration from the success of hidden-particle representations but overcomes the limitations associated with the mean-field treatment of the constraint often used in this context. Our construction provides an extremely expressive family of wave functions, which is proved to be universal. We apply this construction to the ground-state properties of the Hubbard model on the square lattice, achieving levels of accuracy that are competitive with those of state-of-the-art variational methods. (10.1073/pnas.2122059119)
  DOI : 10.1073/pnas.2122059119
• Femtosecond laser-induced sub-wavelength plasma inside dielectrics: I. Field enhancement
  
  • Ardaneh Kazem
  • Meyer Rémi
  • Hassan Mostafa
  • Giust Remo
  • Morel Benoît
  • Couairon Arnaud
  • Bonnaud Guy
  • Courvoisier François
  Physics of Plasmas, American Institute of Physics, 2022, 29 (7), pp.072715. The creation of high energy density ($\geq$ 10$^6$ joules per cm$^3$) over-critical plasmas in a large volume has essential applications in the study of warm dense matter, being present in the hot cores of stars and planets. It was recently shown that femtosecond Bessel beams enable creating over-critical plasmas inside sapphire with subwavelength radius and several tens of micrometers in length. Here, the dependence of field structure and absorption mechanism on the plasma density transverse profile are investigated by performing self-consistent Particle-In-Cell (PIC) simulations. Two limiting cases are considered: one is a homogeneous step-like profile, that can sustain plasmon formation, the second is an inhomogeneous Gaussian profile, where resonance absorption occurs. Comparing experimental absorption measures to analytical predictions allows determining the plasma parameters used in PIC simulations. The PIC simulation results are in good agreement with experimental diagnostics of total absorption, near-field fluence distribution, and far-field radiation pattern. We show that in each case an ambipolar field forms at the plasma surface due to the expansion of the hot electrons and that electron sound waves propagate into the over-critical region. (10.1063/5.0086708)
  DOI : 10.1063/5.0086708
• Algorithmically Solving the Tadpole Problem
  
  • Bena Iosif
  • Blåbäck Johan
  • Graña Mariana
  • Lüst Severin
  Advances in Applied Clifford Algebras, Springer Verlag, 2022, 32 (1), pp.7. The extensive computer-aided search applied in Bena et al. (The tadpole problem, 2020) to find the minimal charge sourced by the fluxes that stabilize all the (flux-stabilizable) moduli of a smooth K3 $\times $ K3 compactification uses differential evolutionary algorithms supplemented by local searches. We present these algorithms in detail and show that they can also solve our minimization problem for other lattices. Our results support the Tadpole Conjecture: The minimal charge grows linearly with the dimension of the lattice and, for K3 $\times $ K3, this charge is larger than allowed by tadpole cancellation. Even if we are faced with an NP-hard lattice-reduction problem at every step in the minimization process, we find that differential evolution is a good technique for identifying the regions of the landscape where the fluxes with the lowest tadpole can be found. We then design a “Spider Algorithm,” which is very efficient at exploring these regions and producing large numbers of minimal-tadpole configurations. (10.1007/s00006-021-01189-6)
  DOI : 10.1007/s00006-021-01189-6