Holographic Butterfly Effect at Quantum Critical Points

When the Lyapunov exponent $\lambda_L$ in a quantum chaotic system saturates the bound $\lambda_L\leqslant 2\pi k_BT$, it is proposed that this system has a holographic dual described by a gravity theory. In particular, the butterfly effect as a prominent phenomenon of chaos can ubiquitously exist in a black hole system characterized by a shockwave solution near the horizon. In this paper we propose that the butterfly velocity can be used to diagnose quantum phase transition (QPT) in holographic theories. We provide evidences for this proposal with an anisotropic holographic model exhibiting metal-insulator transitions (MIT), in which the derivatives of the butterfly velocity with respect to system parameters characterizes quantum critical points (QCP) with local extremes in zero temperature limit. We also point out that this proposal can be tested by experiments in the light of recent progress on the measurement of out-of-time-order correlation function (OTOC).Comment: 7 figures, 15 page

Holographic Metal-Insulator Transition in Higher Derivative Gravity

We introduce a Weyl term into the Einstein-Maxwell-Axion theory in four dimensional spacetime. Up to the first order of the Weyl coupling parameter $\gamma$, we construct charged black brane solutions without translational invariance in a perturbative manner. Among all the holographic frameworks involving higher derivative gravity, we are the first to obtain metal-insulator transitions (MIT) when varying the system parameters at zero temperature. Furthermore, we study the holographic entanglement entropy (HEE) of strip geometry in this model and find that the second order derivative of HEE with respect to the axion parameter exhibits maximization behavior near quantum critical points (QCPs) of MIT. It testifies the conjecture in 1502.03661 and 1604.04857 that HEE itself or its derivatives can be used to diagnose quantum phase transition (QPT).Comment: 20 pages, 4 figures; typo corrected, added 3 references; minor revisio

When Causal Intervention Meets Adversarial Examples and Image Masking for Deep Neural Networks

Discovering and exploiting the causality in deep neural networks (DNNs) are crucial challenges for understanding and reasoning causal effects (CE) on an explainable visual model. "Intervention" has been widely used for recognizing a causal relation ontologically. In this paper, we propose a causal inference framework for visual reasoning via do-calculus. To study the intervention effects on pixel-level features for causal reasoning, we introduce pixel-wise masking and adversarial perturbation. In our framework, CE is calculated using features in a latent space and perturbed prediction from a DNN-based model. We further provide the first look into the characteristics of discovered CE of adversarially perturbed images generated by gradient-based methods \footnote{~~https://github.com/jjaacckkyy63/Causal-Intervention-AE-wAdvImg}. Experimental results show that CE is a competitive and robust index for understanding DNNs when compared with conventional methods such as class-activation mappings (CAMs) on the Chest X-Ray-14 dataset for human-interpretable feature(s) (e.g., symptom) reasoning. Moreover, CE holds promises for detecting adversarial examples as it possesses distinct characteristics in the presence of adversarial perturbations.Comment: Noted our camera-ready version has changed the title. "When Causal Intervention Meets Adversarial Examples and Image Masking for Deep Neural Networks" as the v3 official paper title in IEEE Proceeding. Please use it in your formal reference. Accepted at IEEE ICIP 2019. Pytorch code has released on https://github.com/jjaacckkyy63/Causal-Intervention-AE-wAdvIm

Holographic Superconductor on Q-lattice

We construct the simplest gravitational dual model of a superconductor on Q-lattices. We analyze the condition for the existence of a critical temperature at which the charged scalar field will condense. In contrast to the holographic superconductor on ionic lattices, the presence of Q-lattices will suppress the condensate of the scalar field and lower the critical temperature. In particular, when the Q-lattice background is dual to a deep insulating phase, the condensation would never occur for some small charges. Furthermore, we numerically compute the optical conductivity in the superconducting regime. It turns out that the presence of Q-lattice does not remove the pole in the imaginary part of the conductivity, ensuring the appearance of a delta function in the real part. We also evaluate the gap which in general depends on the charge of the scalar field as well as the Q-lattice parameters. Nevertheless, when the charge of the scalar field is relatively large and approaches the probe limit, the gap becomes universal with $\omega_g \simeq 9T_c$ which is consistent with the result for conventional holographic superconductors.Comment: 20 pages, version to appear in JHE