Ground-state phase diagram of the three-band Hubbard model from density matrix embedding theory

We determine the ground-state phase diagram of the three-band Hubbard model across a range of model parameters using density matrix embedding theory. We study the atomic-scale nature of the antiferromagnetic (AFM) and superconducting (SC) orders, explicitly including the oxygen degrees of freedom. All parametrizations of the model display AFM and SC phases, but the decay of AFM order with doping is too slow compared to the experimental phase diagram, and further, coexistence of AFM and SC orders occurs in all parameter sets. The local magnetic moment localizes entirely at the copper sites. The magnetic phase diagram is particularly sensitive to Δ_(pd) and t_(pp), and existing estimates of the charge transfer gap Δ_(pd) appear too large in so-called minimal model parametrizations. The electron-doped side of the phase diagram is qualitatively distinct from the hole-doped side and we find an unusual two-peak structure in the SC in the full model parametrization. Examining the SC order at the atomic scale, within the larger scale d_(x²−y²)-wave SC pairing order between Cu-Cu and O-O, we also observe a local p_(x(y)) [or d_(xz(yz))] symmetry modulation of the pair density on the Cu-O bonds. Our work highlights some of the features that arise in a three-band versus one-band picture, the role of the oxygen degrees of freedom in new kinds of atomic-scale SC orders, and the necessity of re-evaluating current parametrizations of the three-band Hubbard model

PAC-Bayesian Spectrally-Normalized Bounds for Adversarially Robust Generalization

Deep neural networks (DNNs) are vulnerable to adversarial attacks. It is found empirically that adversarially robust generalization is crucial in establishing defense algorithms against adversarial attacks. Therefore, it is interesting to study the theoretical guarantee of robust generalization. This paper focuses on norm-based complexity, based on a PAC-Bayes approach (Neyshabur et al., 2017). The main challenge lies in extending the key ingredient, which is a weight perturbation bound in standard settings, to the robust settings. Existing attempts heavily rely on additional strong assumptions, leading to loose bounds. In this paper, we address this issue and provide a spectrally-normalized robust generalization bound for DNNs. Compared to existing bounds, our bound offers two significant advantages: Firstly, it does not depend on additional assumptions. Secondly, it is considerably tighter, aligning with the bounds of standard generalization. Therefore, our result provides a different perspective on understanding robust generalization: The mismatch terms between standard and robust generalization bounds shown in previous studies do not contribute to the poor robust generalization. Instead, these disparities solely due to mathematical issues. Finally, we extend the main result to adversarial robustness against general non-$\ell_p$ attacks and other neural network architectures.Comment: NeurIPS 202

The energy distribution of relativistic electrons in the kilo-parsec scale jet of M87 with Chandra

The X-ray emission from the jets in Active Galactic Nuclei (AGN) carries important information on the distributions of relativistic electrons and magnetic fields on large scales. We reanalyze archival Chandra observations on the jet of M87 from 2000 to 2016 with a total exposure of 1460 kiloseconds to explore the X-ray emission characteristics along the jet. We investigate the variability behaviours of the nucleus and the inner jet component HST-1, and confirm indications for day-scale X-ray variability in the nucleus contemporaneous to the 2010 high TeV gamma-ray state. HST-1 shows a general decline in X-ray flux over the last few years consistent with its synchrotron interpretation. We extract the X-ray spectra for the nucleus and all knots in the jet, showing that they are compatible with a single power-law within the X-ray band. There are indications of the resultant X-ray photon index to exhibit a trend, with slight but significant index variations ranging from $\simeq 2.2$ (e.g. in knot D) to $\simeq 2.4-2.6$ (in the outer knots F, A, and B). When viewed in a multi-wavelength context, a more complex situation is arising. Fitting the radio to X-ray spectral energy distributions (SEDs) assuming a synchrotron origin, we show that a broken power-law electron spectrum with break energy $E_b$ around $1~(300\mu G/B)^{1/2}$ TeV allows a satisfactorily description of the multi-band SEDs for most of the knots. However, in the case of knots B, C and D we find indications that an additional high energy component is needed to adequately reproduce the broadband SEDs. We discuss the implications and suggest that a stratified jet model may account for the differences.Comment: accepted for publication in A&

Tentative evidence of spatially extended GeV emission from SS433/W50

We analyze 10 years of Fermi-LAT data towards the SS433/W50 region. With the latest source catalog and diffuse background models, the gamma-ray excess from SS433/W50 is detected with a significance of 6{\sigma} in the photon energy range of 500 MeV - 10 GeV. Our analysis indicates that an extended flat disk morphology is preferred over a point-source description, suggesting that the GeV emission region is much larger than that of the TeV emission detected by HAWC. The size of the GeV emission is instead consistent with the extent of the radio nebula W50, a supernova remnant being distorted by the jets, so we suggest that the GeV emission may originate from this supernova remnant. The spectral result of the GeV emission is also consistent with an supernova remnant origin. We also derive the GeV flux upper limits on the TeV emission region, which put moderate constrains on the leptonic models to explain the multiwavelength data.Comment: 7 pages, 4 figures, accepted for publication in A&

Non-strange partner of strangeonium-like state Y(2175)

Inspired by the observed Y(2175) state, we predict its non-strange partner Y(1915), which has a resonance structure with mass around 1915 MeV and width about $317\sim 354$ MeV. Experimental search for Y(1915) is proposed by analyzing the $\omega f_0(980)$ or $\omega \pi\pi$ invariant mass spectrum of the $e^+e^-\to \omega f_0(980), \omega \pi\pi$ and $J/\psi\to \eta \omega f_0(980)$ processes, which are accessible at Belle, BaBar, BESIII and forthcoming BelleII. Considering similarity between two families, the comparison of the mass spectra of $\omega$ and $\phi$ families can provide important information on the 1D state of $\phi$ family, $\phi(1910)$, which has a very broad resonance structure with mass around 1910 MeV regarded as the strangeonium partner of $\omega(1650)$. This also answers the question why the 1D state $\phi(1910)$ is still missing in experiment. This is supported by our former study on the properties of Y(2175), which explains Y(2175) as the 2D strangeonium because our theoretical total width is comparable with the Belle data.Comment: 5 pages, 5 figures. More discussions and numerical results added. Typos correcte

Probing the XYZXYZ states through radiative decays

In this work, we have adopted the spin rearrangement scheme in the heavy quark limit and extensively investigated three classes of the radiative decays: $\mathfrak{M}\to (b\bar{b})+\gamma$, $(b\bar{b})\to \mathfrak{M}+\gamma$, $\mathfrak{M} \to \mathfrak{M}^\prime+\gamma$, corresponding to the electromagnetic transitions between one molecular state and bottomonium, one bottomonium and molecular state, and two molecular states respectively. We also extend the same formalism to study the radiative decays of the molecular states with hidden charm. We have derived some model independent ratios when the initial or final states belong to the same spin flavor multiplet. Future experimental measurement of these ratios will test the molecular picture and explore the underlying structures of the $XYZ$ states.Comment: 21 pages, 10 tables Accepted by Phys.Rev.

Adversarial Rademacher Complexity of Deep Neural Networks

Deep neural networks are vulnerable to adversarial attacks. Ideally, a robust model shall perform well on both the perturbed training data and the unseen perturbed test data. It is found empirically that fitting perturbed training data is not hard, but generalizing to perturbed test data is quite difficult. To better understand adversarial generalization, it is of great interest to study the adversarial Rademacher complexity (ARC) of deep neural networks. However, how to bound ARC in multi-layers cases is largely unclear due to the difficulty of analyzing adversarial loss in the definition of ARC. There have been two types of attempts of ARC. One is to provide the upper bound of ARC in linear and one-hidden layer cases. However, these approaches seem hard to extend to multi-layer cases. Another is to modify the adversarial loss and provide upper bounds of Rademacher complexity on such surrogate loss in multi-layer cases. However, such variants of Rademacher complexity are not guaranteed to be bounds for meaningful robust generalization gaps (RGG). In this paper, we provide a solution to this unsolved problem. Specifically, we provide the first bound of adversarial Rademacher complexity of deep neural networks. Our approach is based on covering numbers. We provide a method to handle the robustify function classes of DNNs such that we can calculate the covering numbers. Finally, we provide experiments to study the empirical implication of our bounds and provide an analysis of poor adversarial generalization